IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-06-16T09:36:58ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2016-10-04T08:56:19Z2016-10-04T08:56:19Zhttp://eprints.imtlucca.it/id/eprint/3545This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/35452016-10-04T08:56:19ZPiecewise affine regression via recursive multiple least squares and multicategory discriminationIn nonlinear regression choosing an adequate model structure is often a challenging problem. While simple models (such as linear functions) may not be able to capture the underlying relationship among the variables, over-parametrized models described by a large set of nonlinear basis functions tend to overfit the training data, leading to poor generalization on unseen data. Piecewise-affine (PWA) models can describe nonlinear and possible discontinuous relationships while maintaining simple local affine regressor-to-output mappings, with extreme flexibility when the polyhedral partitioning of the regressor space is learned from data rather than fixed a priori. In this paper, we propose a novel and numerically very efficient two-stage approach for {PWA} regression based on a combined use of (i) recursive multi-model least-squares techniques for clustering and fitting linear functions to data, and (ii) linear multi-category discrimination, either offline (batch) via a Newton-like algorithm for computing a solution of unconstrained optimization problems with objective functions having a piecewise smooth gradient, or online (recursive) via averaged stochastic gradient descent.Valentina BreschiDario Pigadario.piga@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2016-04-27T07:56:32Z2016-04-27T07:56:32Zhttp://eprints.imtlucca.it/id/eprint/3474This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/34742016-04-27T07:56:32ZA probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic boundingSet-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures PP as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zeroth order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P.Alessio BenavoliDario Pigadario.piga@imtlucca.it2016-04-27T07:52:54Z2016-04-27T07:52:54Zhttp://eprints.imtlucca.it/id/eprint/3472This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/34722016-04-27T07:52:54ZSparse optimization for automated energy end use disaggregationRetrieving the household electricity consumption at individual appliance level is an essential requirement to assess the contribution of different end uses to the total household consumption, and thus to design energy saving policies and user-tailored feedback for reducing household electricity usage. This has led to the development of nonintrusive appliance load monitoring (NIALM), or energy disaggregation, algorithms, which aim to decompose the aggregate energy consumption data collected from a single measurement point into device-level consumption estimations. Existing NIALM algorithms are able to provide accurate estimate of the fraction of energy consumed by each appliance. Yet, in the authors' experience, they provide poor performance in reconstructing the power consumption trajectories overtime. In this brief, a new NIALM algorithm is presented, which, besides providing very accurate estimates of the aggregated consumption by appliance, also accurately characterizes the appliance power consumption profiles overtime. The proposed algorithm is based on the assumption that the unknown appliance power consumption profiles are piecewise constant overtime (as it is typical for power use patterns of household appliances) and it exploits the information on the time-of-day probability in which a specific appliance might be used. The disaggregation problem is formulated as a least-square error minimization problem, with an additional (convex) penalty term aiming at enforcing the disaggregate signals to be piecewise constant overtime. Testing on household electricity data available in the literature is reported.Dario Pigadario.piga@imtlucca.itAndrea CominolaMatteo GiulianiAndrea CastellettiAndrea Emilio Rizzoli2016-02-29T08:59:31Z2016-02-29T08:59:31Zhttp://eprints.imtlucca.it/id/eprint/3151This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/31512016-02-29T08:59:31ZDirect learning ofLPVcontrollers from dataIn many control applications, it is attractive to describe nonlinear (NL) and time-varying (TV) plants by linear parametervarying (LPV) models and design controllers based on such representations to regulate the behaviour of the system. The LPV system class offers the representation of NL and TV phenomena as a linear dynamic relationship between input and output signals, which relationship is dependent on some measurable signals, e.g., operating conditions, often called as scheduling variables. For such models, powerful control synthesis tools are available, but the way how to systematically convert available first principles models to LPV descriptions of the plant, to efficiently identify LPV models for control from data and to understand how modeling errors affect the control performance are still subject of undergoing research. Therefore, it is attractive to synthesize the controller directly from data without the need of modeling the plant and addressing the underlying difficulties. Hence, in this paper, a novel data-driven synthesis scheme is proposed in a stochastic framework to provide a practically applicable solution for synthesizing LPV controllers directly from data. Both the cases of fixed order controller tuning and controller structure learning are discussed and two different design approaches are provided. The effectiveness of the proposed methods is also illustrated by means of an academic example and a real application based simulation case study.Simone FormentinDario Pigadario.piga@imtlucca.itRoland TóthSergio M. Savaresi2016-02-29T08:58:00Z2016-02-29T08:58:00Zhttp://eprints.imtlucca.it/id/eprint/3150This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/31502016-02-29T08:58:00ZComputation of the Structured Singular Value via Moment LMI RelaxationsThe Structured Singular Value (SSV) provides a powerful tool to test robust stability and performance of feedback systems subject to structured uncertainties. Unfortunately, computing the SSV is an NP-hard problem, and the polynomial-time algorithms available in the literature are only able to provide, except for some special cases, upper and lower bounds on the exact value of the SSV. In this work, we present a new algorithm to compute an upper bound on the SSV in case of mixed real/complex uncertainties. The underlying idea of the developed approach is to formulate the SSV computation as a (nonconvex) polynomial optimization problem, which is relaxed into a sequence of convex optimization problems through moment-based relaxation techniques. Two heuristics to compute a lower bound on the SSV are also discussed. The analyzed numerical examples show that the developed approach provides tighter bounds than the ones computed by the algorithms implemented in the Robust Control Toolbox in Matlab, and it provides, in most of the cases, coincident lower and upper bounds on the structured singular value.Dario Pigadario.piga@imtlucca.it2015-10-26T12:20:25Z2015-10-29T14:19:05Zhttp://eprints.imtlucca.it/id/eprint/2782This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27822015-10-26T12:20:25ZBenefits and challenges of using smart meters for advancing residential water demand modeling and management: a reviewOver the last two decades, water smart metering programs have been launched in a number of medium to large cities worldwide to nearly continuously monitor water consumption at the single household level. The availability of data at such very high spatial and temporal resolution advanced the ability in characterizing, modeling, and, ultimately, designing user-oriented residential water demand management strategies. Research to date has been focusing on one or more of these aspects but with limited integration between the specialized methodologies developed so far. This manuscript is the first comprehensive review of the literature in this quickly evolving water research domain. The paper contributes a general framework for the classification of residential water demand modeling studies, which allows revising consolidated approaches, describing emerging trends, and identifying potential future developments. In particular, the future challenges posed by growing population demands, constrained sources of water supply and climate change impacts are expected to require more and more integrated procedures for effectively supporting residential water demand modeling and management in several countries across the world.Andrea CominolaMatteo GiulianiDario Pigadario.piga@imtlucca.itAndrea CastellettiAndrea Emilio Rizzoli2015-03-26T11:47:08Z2016-06-30T12:29:59Zhttp://eprints.imtlucca.it/id/eprint/2637This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26372015-03-26T11:47:08ZAn Instrumental Least Squares Support Vector Machine for Nonlinear System IdentificationLeast-Squares Support Vector Machines (LS-SVMs), originating from Statistical Learning and Reproducing Kernel Hilbert Space (RKHS) theories, represent a promising approach to identify nonlinear systems via nonparametric estimation of the involved nonlinearities in a computationally and stochastically attractive way. However, application of LS-SVMs and other RKHS variants in the identification context is formulated as a regularized linear regression aiming at the minimization of the l2-loss of the prediction error. This formulation corresponds to the assumption of an auto-regressive noise structure, which is often found to be too restrictive in practical applications. In this paper, Instrumental Variable (IV) based estimation is integrated into the LS-SVM approach, providing, under minor conditions, consistent identification of nonlinear systems regarding the noise modeling error. It is shown how the cost function of the LS-SVM is modified to achieve an IV-based solution. Although, a practically well applicable choice of the instrumental variable is proposed for the derived approach, optimal choice of this instrument in terms of the estimates associated variance still remains to be an open problem. The effectiveness of the proposed IV based LS-SVM scheme is also demonstrated by a Monte Carlo study based simulation example.Vincent LaurainRoland TóthDario Pigadario.piga@imtlucca.itWei Xing Zheng2015-03-26T11:45:05Z2015-03-26T11:45:05Zhttp://eprints.imtlucca.it/id/eprint/2447This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24472015-03-26T11:45:05ZRobust pole placement for plants with semialgebraic parametric uncertaintyIn this paper we address the problem of robust pole placement for linear-time-invariant systems whose uncertain parameters are assumed to belong to a semialgebraic region. A dynamic controller is designed in order to constrain the coefficients of the closed-loop characteristic polynomial within prescribed intervals. Two main topics arising from the problem of robust pole placement are tackled by means of polynomial optimization. First, necessary conditions on the plant parameters for the existence of a robust controller are given. Then, the set of all admissible robust controllers is sought. Convex relaxation techniques based on sum-of-square decomposition of positive polynomials are used to efficiently solve the formulated optimization problems through semidefinite programming techniques.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-03-26T11:36:44Z2015-03-26T11:36:44Zhttp://eprints.imtlucca.it/id/eprint/2439This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24392015-03-26T11:36:44ZSet-membership EIV identification through LMI relaxation techniquesIn this paper the Set-membership Error-In-Variables (EIV) identification problem is considered, that is the identification of linear dynamic systems when both the output and the input measurements are corrupted by bounded noise. A new approach for the computation of the Parameters Uncertainty Intervals (PUIs) is discussed. First the problem is formulated in terms of non-convex semi-algebraic optimization. Then, a Linear-Matrix-Inequalities relaxation technique is presented to compute parameters bounds by means of convex optimization. Finally, convergence properties and computational complexity of the given algorithms are discussed. Advantages of the proposed technique with respect to previously published ones are discussed both theoretically and by means of a simulated example.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-02-09T08:41:42Z2015-02-09T08:41:42Zhttp://eprints.imtlucca.it/id/eprint/2571This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25712015-02-09T08:41:42ZLPV system identification under noise corrupted scheduling and
output signal observationsMost of the approaches available in the literature for the identification of Linear Parameter-Varying (LPV) systems rely on the assumption that only the measurements of the output signal are corrupted by the noise, while the observations of the scheduling variable are considered to be noise free. However, in practice, this turns out to be an unrealistic assumption in most of the cases, as the scheduling variable is often related to a measured signal and, thus, it is inherently affected by a measurement noise. In this paper, it is shown that neglecting the noise on the scheduling signal, which corresponds to an error-invariables
problem, can lead to a significant bias on the estimated parameters. Consequently, in order to overcome this corruptive phenomenon affecting practical use of data-driven LPV modeling, we present an identification scheme to compute a consistent estimate of LPV Input/Output (IO) models from noisy output and scheduling signal observations. A simulation example is provided to prove the effectiveness
of the proposed methodology.Dario Pigadario.piga@imtlucca.itPepijn Coxp.b.cox@tue.nlRoland Tóthr.toth@tue.nlVincent Laurainvincent.laurain@univ-lorraine.fr2015-01-13T14:42:02Z2015-01-13T14:42:02Zhttp://eprints.imtlucca.it/id/eprint/2478This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24782015-01-13T14:42:02ZA unified framework for solving a general class of conditional and robust set-membership estimation problemsIn this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Vito CeroneJean-Bernard LasserreDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T14:34:09Z2015-11-02T09:57:27Zhttp://eprints.imtlucca.it/id/eprint/2477This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24772015-01-13T14:34:09ZCharacteristic polynomial assignment for plants with semialgebraic uncertainty: a robust diophantine equation approachIn this paper, we address the problem of robust characteristic polynomial assignment for LTI systems whose parameters are assumed to belong to a semialgebraic uncertainty region. The objective is to design a dynamic fixed-order controller in order to constrain the coefficients of the closed-loop characteristic polynomial within prescribed intervals. First, necessary conditions on the plant parameters for the existence of a robust controller are reviewed, and it is shown that such conditions are satisfied if and only if a suitable Sylvester matrix is nonsingular for all possible values of the uncertain plant parameters. The problem of checking such a robust nonsingularity condition is formulated in terms of a nonconvex optimization problem. Then, the set of all feasible robust controllers is sought through the solution to a suitable robust diophantine equation. Convex relaxation techniques based on sum-of-square decomposition of positive polynomials are used to efficiently solve the formulated optimization problems by means of semidefinite programming. The presented approach provides a generalization of the results previously proposed in the literature on the problem of assigning the characteristic polynomial in the presence of plant parametric uncertainty.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T14:24:45Z2015-01-13T14:24:45Zhttp://eprints.imtlucca.it/id/eprint/2476This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24762015-01-13T14:24:45ZA bias-corrected estimator for nonlinear systems with output-error type model structures Abstract Parametric identification of linear time-invariant (LTI) systems with output-error (OE) type of noise model structures has a well-established theoretical framework. Different algorithms, like instrumental-variables based approaches or prediction error methods (PEMs), have been proposed in the literature to compute a consistent parameter estimate for linear {OE} systems. Although the prediction error method provides a consistent parameter estimate also for nonlinear output-error (NOE) systems, it requires to compute the solution of a nonconvex optimization problem. Therefore, an accurate initialization of the numerical optimization algorithms is required, otherwise they may get stuck in a local minimum and, as a consequence, the computed estimate of the system might not be accurate. In this paper, we propose an approach to obtain, in a computationally efficient fashion, a consistent parameter estimate for output-error systems with polynomial nonlinearities. The performance of the method is demonstrated through a simulation example. Dario Pigadario.piga@imtlucca.itRoland Tóth2015-01-13T14:22:23Z2015-01-13T14:22:23Zhttp://eprints.imtlucca.it/id/eprint/2475This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24752015-01-13T14:22:23ZApproximation of model predictive control laws for polynomial systemsA fast implementation of a given predictive controller for polynomial systems is introduced by approximating the optimal control law with a piecewise constant function defined over a hyper-cube partition of the system state space. Such a state-space partition is computed in order to guarantee stability, an a priori fixed trajectory error as well as input and state constraints fulfilment. The presented approximation procedure is achieved by solving a set of nonconvex polynomial optimization problems, whose approximate solutions are computed by means of semidefinite relaxation techniques for semialgebraic problems.Massimo CanaleVito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T14:18:27Z2015-01-13T14:18:27Zhttp://eprints.imtlucca.it/id/eprint/2474This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24742015-01-13T14:18:27ZAn SDP approach for l0-minimization: application to ARX model segmentation Abstract Minimizing the ℓ 0 -seminorm of a vector under convex constraints is a combinatorial (NP-hard) problem. Replacement of the ℓ 0 -seminorm with the ℓ 1 -norm is a commonly used approach to compute an approximate solution of the original ℓ 0 -minimization problem by means of convex programming. In the theory of compressive sensing, the condition that the sensing matrix satisfies the Restricted Isometry Property (RIP) is a sufficient condition to guarantee that the solution of the ℓ 1 -approximated problem is equal to the solution of the original ℓ 0 -minimization problem. However, the evaluation of the conservativeness of the ℓ 1 -relaxation approaches is recognized to be a difficult task in case the {RIP} is not satisfied. In this paper, we present an alternative approach to minimize the ℓ 0 -norm of a vector under given constraints. In particular, we show that an ℓ 0 -minimization problem can be relaxed into a sequence of semidefinite programming problems, whose solutions are guaranteed to converge to the optimizer (if unique) of the original combinatorial problem also in case the {RIP} is not satisfied. Segmentation of {ARX} models is then discussed in order to show, through a relevant problem in system identification, that the proposed approach outperforms the ℓ 1 -based relaxation in detecting piece-wise constant parameter changes in the estimated model. Dario Pigadario.piga@imtlucca.itRoland Tóth2015-01-13T14:12:42Z2015-01-13T14:12:42Zhttp://eprints.imtlucca.it/id/eprint/2473This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24732015-01-13T14:12:42ZA convex relaxation approach to set-membership identification of LPV systems Abstract Identification of linear parameter varying models is considered in this paper, under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, the problem of computing parameter uncertainty intervals is formulated in terms of nonconvex optimization. Then, on the basis of the analysis of the regressor structure, we present an ad hoc convex relaxation scheme for computing parameter bounds by means of semidefinite optimization. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T14:08:50Z2015-01-13T14:08:50Zhttp://eprints.imtlucca.it/id/eprint/2472This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24722015-01-13T14:08:50ZFixed-order FIR approximation of linear systems from quantized input and output data Abstract The problem of identifying a fixed-order {FIR} approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order {FIR} model providing the best approximation of the input–output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T14:01:48Z2015-01-13T14:01:48Zhttp://eprints.imtlucca.it/id/eprint/2471This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24712015-01-13T14:01:48ZComputational load reduction in bounded error identification of Hammerstein systemsIn this technical note we present a procedure for the identification of Hammerstein systems from measurements affected by bounded noise. First, we show that computation of tight parameter bounds requires the solution to nonconvex optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, in order to reduce the computational burden of the identification problem, we propose a procedure to relax the formulated problem into a collection of polynomial optimization problems where the number of variables does not depend on the number of measurements. Advantages of the presented approach with respect to previously published results are discussed and highlighted by means of a simulation example.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T13:57:44Z2015-01-13T14:35:23Zhttp://eprints.imtlucca.it/id/eprint/2470This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24702015-01-13T13:57:44ZBounding the parameters of block-structured nonlinear feedback systemsIn this paper, a procedure for set-membership identification of block-structured nonlinear feedback systems is presented. Nonlinear block parameter bounds are first computed by exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner signal are computed. Finally, linear block parameter bounds are evaluated on the basis of output measurements and computed inner-signal bounds. The computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. The problem of linear block parameter evaluation is formulated in terms of a bounded errors-in-variables identification problem. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T13:52:43Z2015-01-13T14:35:42Zhttp://eprints.imtlucca.it/id/eprint/2469This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24692015-01-13T13:52:43ZOptimization of airborne wind energy generatorsThis paper presents novel results related to an innovative airborne wind energy technology, named Kitenergy, for the conversion of high-altitude wind energy into electricity. The research activities carried out in the last five years, including theoretical analyses, numerical simulations, and experimental tests, indicate that Kitenergy could bring forth a revolution in wind energy generation, providing renewable energy in large quantities at a lower cost than fossil energy. This work investigates three important theoretical aspects: the evaluation of the performance achieved by the employed control law, the optimization of the generator operating cycle, and the possibility to generate continuously a constant and maximal power output. These issues are tackled through the combined use of modeling, control, and optimization methods that result to be key technologies for a significant breakthrough in renewable energy generation.Lorenzo FagianoMario MilaneseDario Pigadario.piga@imtlucca.it2015-01-13T13:40:47Z2015-01-13T13:40:47Zhttp://eprints.imtlucca.it/id/eprint/2468This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24682015-01-13T13:40:47ZBounded error identification of Hammerstein systems through sparse polynomial optimization In this paper we present a procedure for the evaluation of bounds on the parameters of Hammerstein systems, from output measurements affected by bounded errors. The identification problem is formulated in terms of polynomial optimization, and relaxation techniques, based on linear matrix inequalities, are proposed to evaluate parameter bounds by means of convex optimization. The structured sparsity of the formulated identification problem is exploited to reduce the computational complexity of the convex relaxed problem. Analysis of convergence properties and computational complexity is reported. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-13T13:28:37Z2015-01-13T13:28:37Zhttp://eprints.imtlucca.it/id/eprint/2467This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24672015-01-13T13:28:37ZSet-Membership Error-in-variables identification through convex relaxation techniques In this technical note, the set membership error-in-variables identification problem is considered, that is the identification of linear dynamic systems when both output and input measurements are corrupted by bounded noise. A new approach for the computation of parameter uncertainty intervals is presented. First, the identification problem is formulated in terms of nonconvex optimization. Then, relaxation techniques based on linear matrix inequalities are employed to evaluate parameter bounds by means of convex optimization. The inherent structured sparsity of the original identification problems is exploited to reduce the computational complexity of the relaxed problems. Finally, convergence properties and complexity of the proposed procedure are discussed. Advantages of the presented technique with respect to previously published results are discussed and shown by means of two simulated examples.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T14:46:07Z2015-01-12T14:46:07Zhttp://eprints.imtlucca.it/id/eprint/2466This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24662015-01-12T14:46:07ZEnforcing stability constraints in set-membership identification of linear dynamic systems In this paper, we consider the identification of linear systems, a priori known to be stable, from input–output data corrupted by bounded noise. By taking explicitly into account a priori information on system stability, a formal definition of the feasible parameter set for a stable linear system is provided. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameter uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T14:39:42Z2015-01-13T14:49:53Zhttp://eprints.imtlucca.it/id/eprint/2465This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24652015-01-12T14:39:42ZSet-membership LPV model identification of vehicle lateral dynamics Set-membership identification of a Linear Parameter Varying (LPV) model describing the vehicle lateral dynamics is addressed in the paper. The model structure, chosen as much as possible on the ground of physical insights into the vehicle lateral behavior, consists of two single-input single-output {LPV} models relating the steering angle to the yaw rate and to the sideslip angle. A set of experimental data obtained by performing a large number of maneuvers is used to identify the vehicle lateral dynamics model. Prior information on the error bounds on the output and the time-varying parameter measurements are taken into account. Comparison with other vehicle lateral dynamics models is discussed. Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T14:32:40Z2015-01-12T14:32:40Zhttp://eprints.imtlucca.it/id/eprint/2464This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24642015-01-12T14:32:40ZImproved parameter bounds for set-membership EIV problemsIn this paper, we consider the set-membership error-in-variables identification problem, that is the identification of linear dynamic systems when output and input measurements are corrupted by bounded noise. A new approach for the computation of parameters uncertainty intervals is presented. First, the problem is formulated in terms of nonconvex optimization. Then, a relaxation procedure is proposed to compute parameter bounds by means of semidefinite programming techniques. Finally, accuracy of the estimate and computational complexity of the proposed algorithm are discussed. Advantages of the proposed technique with respect to previously published ones are discussed both theoretically and by means of a simulated exampleVito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T14:29:10Z2015-01-12T14:29:10Zhttp://eprints.imtlucca.it/id/eprint/2463This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24632015-01-12T14:29:10ZHigh-Altitude wind power generationThe paper presents the innovative technology of high-altitude wind power generation, indicated as Kitenergy, which exploits the automatic flight of tethered airfoils (e.g., power kites) to extract energy from wind blowing between 200 and 800 m above the ground. The key points of this technology are described and the design of large scale plants is investigated, in order to show that it has the potential to overcome the limits of the actual wind turbines and to provide large quantities of renewable energy, with competitive cost with respect to fossil sources. Such claims are supported by the results obtained so far in the Kitenergy project, undergoing at Politecnico di Torino, Italy, including numerical simulations, prototype experiments, and wind data analyses.Lorenzo FagianoMario MilaneseDario Pigadario.piga@imtlucca.it2015-01-12T13:20:30Z2015-01-12T13:20:30Zhttp://eprints.imtlucca.it/id/eprint/2461This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24612015-01-12T13:20:30ZShrinking complexity of scheduling dependencies in LS-SVM based LPV system identification(I) In the past years, Linear Parameter-Varying (LPV) identification has rapidly evolved from parametric identification methods to nonparametric methods allowing the relaxation of restrictive assumptions. For example, Least-Square Support Vector Machines (LS-SVMs) offer an attractive way of estimating LPV models directly from data without requiring from the user to specify the functional dependencies of the model coefficients on the scheduling variable. These methods have also been recently extended in order to automatically determine the model order directly from data by the help of regularization. Nonetheless, despite all these recent improvements, LPV identification methods still require some strong a priori such as i) the dependencies are static or dynamic, ii) it is known which variables are considered to be the scheduling or iii) all coefficient functions of the underlaying system depend on all scheduling variables. This prevents the complexity of the scheduling dependency of the model to be shrunk gradually and independently until an optimal bias-variance trade off is found. In this paper, a novel reformulation of the LPV LS-SVM approach is proposed which, besides of the non-parametric estimation of the coefficient functions, achieves data-driven coefficient complexity selection via convex optimization. The properties of the introduced approach are illustrated by a simulation study.René DuijkersRoland TóthDario Pigadario.piga@imtlucca.itVincent Laurain2015-01-12T12:49:00Z2015-01-12T12:49:00Zhttp://eprints.imtlucca.it/id/eprint/2460This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24602015-01-12T12:49:00ZLPV model order selection in an LS-SVM settingIn parametric identification of Linear Parameter-Varying (LPV) systems, the scheduling dependencies of the model coefficients are commonly parameterized in terms of linear combinations of a-priori selected basis functions. Such functions need to be adequately chosen, e.g., on the basis of some first-principles or expert's knowledge of the system, in order to capture the unknown dependencies of the model coefficient functions on the scheduling variable and, at the same time, to achieve a low-variance of the model estimate by limiting the number of parameters to be identified. This problem together with the well-known model order selection problem (in terms of number of input lags, output lags and input delay of the model structure) in system identification can be interpreted as a trade-off between bias and variance of the resulting model estimate. The problem of basis function selection can be avoided by using a non-parametric estimator of the coefficient functions in terms of a recently proposed Least-Square Support-Vector-Machine (LS-SVM) approach. However, the selection of the model order still appears to be an open problem in the identification of LPV systems via the LS-SVM method. In this paper, we propose a novel reformulation of the LPV LS-SVM approach, which, besides of the non-parametric estimation of the coefficient functions, achieves data-driven model order selection via convex optimization. The properties of the introduced approach are illustrated via a simulation example.Dario Pigadario.piga@imtlucca.itRoland Tóth2015-01-12T12:41:33Z2015-01-12T12:42:48Zhttp://eprints.imtlucca.it/id/eprint/2459This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24592015-01-12T12:41:33ZDirect data-driven control of linear parameter-varying systemsIn many control applications, nonlinear plants can be modeled as linear parameter-varying (LPV) systems, by which the dynamic behavior is assumed to be linear, but also dependent on some measurable signals, e.g., operating conditions. When a measured data set is available, LPV model identification can provide low complexity linear models that can embed the underlying nonlinear dynamic behavior of the plant. For such models, powerful control synthesis tools are available, but the way the modeling error and the conservativeness of the embedding affect the control performance is still largely unknown. Therefore, it appears to be attractive to directly synthesize the controller from data without modeling the plant. In this paper, a novel data-driven synthesis scheme is proposed to lay the basic foundations of future research on this challenging problem. The effectiveness of the proposed approach is illustrated by a numerical example.Simone FormentinDario Pigadario.piga@imtlucca.itRoland TóthSergio M. Savaresi2015-01-12T12:06:11Z2015-01-12T12:06:11Zhttp://eprints.imtlucca.it/id/eprint/2458This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24582015-01-12T12:06:11ZSM identification of input-output LPV models with uncertain time-varying parametersIn this chapter, we consider the identification of single-input single-output linear-parameter-varying models when both the output and the time-varying parameter measurements are affected by bounded noise. First, the problem of computing exact parameter uncertainty intervals is formulated in terms of semialgebraic optimization. Then, a suitable relaxation tecnique is presented to compute parameter bounds by means of convex optimization. Advantages of the presented approach with respect to previously published results are discussed.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T11:47:05Z2015-01-12T11:47:05Zhttp://eprints.imtlucca.it/id/eprint/2457This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24572015-01-12T11:47:05ZBounded error identification of Hammerstein Systems with backlashActuators and sensors commonly used in control systems may exhibit a variety of nonlinear behaviours that may be responsible for undesirable phenomena such as delays and oscillations, which may severely limit both the static and the dynamic performance of the system under control (see, e.g., [22]). In particular, one of the most relevant nonlinearities affecting the performance of industrial machines is the backlash (see Figure 22.1), which commonly occurs in mechanical, hydraulic and magnetic components like bearings, gears and impact dampers (see, e.g., [17]). This nonlinearity, which can be classified as dynamic (i.e., with memory) and hard (i.e. non-differentiable), may arise from unavoidable manufacturing tolerances or sometimes may be deliberately incorporated into the system in order to describe lubrication and thermal expansion effects [3]. The interested reader is referred to [22] for real-life examples of systems with either input or output backlash nonlinearities.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-12T11:36:39Z2015-01-12T11:36:39Zhttp://eprints.imtlucca.it/id/eprint/2456This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24562015-01-12T11:36:39ZFrequency-Domain Least-Squares Support Vector Machines to deal with correlated errors when identifying linear time-varying systemsA Least-Squares Support Vector Machine (LS-SVM) estimator, formulated in the frequency domain is proposed to identify linear time-varying dynamic systems. The LS-SVM aims at learning the structure of the time variation in a data driven way. The frequency domain is chosen for its superior robustness w.r.t. correlated errors for the calibration of the hyper parameters of the model. The time-domain and the frequency-domain implementations are compared on a simulation example to show the effectiveness of the proposed approach. It is demonstrated that the time-domain formulation is mislead during the calibration due to the fact that the noise on the estimation and calibration data sets are correlated. This is not the case for the frequency-domain implementation.John LataireDario Pigadario.piga@imtlucca.itRoland Tóth2015-01-09T13:37:33Z2015-01-09T13:37:33Zhttp://eprints.imtlucca.it/id/eprint/2453This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24532015-01-09T13:37:33ZPolytopic outer approximations of semialgebraic setsThis paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ⊆ Rn. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties of the presented algorithm and its possible applications in the analysis, identification and control of uncertain systems are discussed.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T13:32:04Z2015-01-09T13:32:04Zhttp://eprints.imtlucca.it/id/eprint/2452This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24522015-01-09T13:32:04ZFixed order LPV controller design for LPV models in input-output formIn this work, a new synthesis approach is proposed to design fixed-order H∞ controllers for linear parameter-varying (LPV) systems described by input-output (I/O) models with polynomial dependence on the scheduling variables. First, by exploiting a suitable technique for polytopic outer approximation of semi-algebraic sets, the closed loop system is equivalently rewritten as an LPV I/O model depending affinely on an augmented scheduling parameter vector constrained inside a polytope. Then, the problem is reformulated in terms of bilinear matrix inequalities (BMI) and solved by means of a suitable semidefinite relaxation technique.Vito CeroneDario Pigadario.piga@imtlucca.itDiego RegrutoRoland Tóth2015-01-09T12:49:50Z2015-01-09T12:49:50Zhttp://eprints.imtlucca.it/id/eprint/2451This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24512015-01-09T12:49:50ZBounded-error identification of linear systems with input and output backlashIn this paper we present a single-stage procedure for computing bounds on the parameters of linear systems with input and output backlash from output data corrupted by bounded measurement noise. By properly selecting a sequence of input/output measurements, the problem of evaluating parameter bounds is formulated as a collection of sparse nonconvex optimization problems. Convex-relation techniques are exploited to efficiently compute guaranteed bounds on system parameters by means of semidefinite programming.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T12:25:17Z2015-01-09T12:25:17Zhttp://eprints.imtlucca.it/id/eprint/2450This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24502015-01-09T12:25:17ZFIR approximation of linear systems from quantized recordsIn this paper we consider the problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization. In particular, a FIR model of given order which provides the best approximation of the input-output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. First we show that the considered problem can be formulated in terms of robust optimization. Then, we present two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques. The effectiveness of the proposed approach is illustrated by means of a simulation example.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T12:12:01Z2015-01-09T12:12:01Zhttp://eprints.imtlucca.it/id/eprint/2449This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24492015-01-09T12:12:01ZLPV identification of the glucose-insulin dynamics in Type I DiabetesIn this paper we address the problem of identifying a linear parameter varying (LPV) model of the glucose-insulin dynamics in Type I diabetic patients. First, the identification problem is formulated in the framework of bounded-error identification, then an algorithm for parameter bounds computation, based on semidefinite programming, is presented. The effectiveness of the proposed approach is tested in simulation by means of the widely adopted nonlinear Sorensen patient model.Vito CeroneDario Pigadario.piga@imtlucca.itDiego RegrutoSintayehu Berehanu2015-01-09T11:59:20Z2015-01-09T11:59:20Zhttp://eprints.imtlucca.it/id/eprint/2448This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24482015-01-09T11:59:20ZInput-Output LPV Model identification with guaranteed quadratic stabilityThe problem of identifying linear parameter-varying (LPV) systems, a-priori known to be quadratically stable, is considered in the paper using an input-output model structure. To solve this problem, a novel constrained optimization-based algorithm is proposed which guarantees quadratic stability of the identified model. It is shown that this estimation objective corresponds to a nonconvex optimization problem, defined by a set of polynomial matrix inequalities (PMI), whose optimal solution can be approximated by means of suitable convex semidefinite relaxations. Applicability of such relaxation-based estimation approach in the presence of either stochastic or deterministic bounded noise is discussed. A simulation example is also given to demonstrate the effectiveness of the resulting identification method.Vito CeroneDario Pigadario.piga@imtlucca.itDiego RegrutoRoland Tóth2015-01-09T11:36:20Z2015-01-09T11:52:42Zhttp://eprints.imtlucca.it/id/eprint/2446This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24462015-01-09T11:36:20ZMinimal LPV state-space realization driven set-membership identificationSet-membership identification algorithms have been recently proposed to derive linear parameter-varying (LPV) models in input-output form, under the assumption that both measurements of the output and the scheduling signals are affected by bounded noise. In order to use the identified models for controller synthesis, linear time-invariant (LTI) realization theory is usually applied to derive a statespace model whose matrices depend statically on the scheduling signals, as required by most of the LPV control synthesis techniques. Unfortunately, application of the LTI realization theory leads to an approximate state-space description of the original LPV input-output model. In order to limit the effect of the realization error, a new set-membership algorithm for identification of input/output LPV models is proposed in the paper. A suitable nonconvex optimization problem is formulated to select the model in the feasible set which minimizes a suitable measure of the state-space realization error. The solution of the identification problem is then derived by means of convex relaxation techniques.Vito CeroneDario Pigadario.piga@imtlucca.itDiego RegrutoRoland Tóth2015-01-09T11:31:37Z2015-01-09T11:31:37Zhttp://eprints.imtlucca.it/id/eprint/2445This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24452015-01-09T11:31:37ZSet-membership identification of Hammerstein-Wiener systemsSet-membership identification of Hammerstein-Wiener models is addressed in the paper. First, it is shown that computation of tight parameter bounds requires the solutions to a number of nonconvex constrained polynomial optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, a suitable convex relaxation procedure is presented to significantly reduce the computational burden of the identification problem. A detailed discussion of the identification algorithm properties is reported. Finally, a simulated example is used to show the effectiveness and the computational tractability of the proposed approach.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T11:26:33Z2015-01-09T11:26:33Zhttp://eprints.imtlucca.it/id/eprint/2444This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24442015-01-09T11:26:33ZFast implementation of model predictive control with guaranteed performanceA fast implementation of a given predictive controller for nonlinear systems is introduced through a piecewise constant approximate function defined over an hyper-cube partition of the system state space. Such a state partition is obtained by maximizing the hyper-cube volumes in order to guarantee, besides stability, an a priori fixed trajectory error as well as input and state constraints satisfaction. The presented approximation procedure is achieved by solving a set of nonconvex polynomial optimization problems, whose approximate solutions are computed by means of semidefinite relaxation techniques for semialgebraic problems.Massimo CanaleVito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T11:12:20Z2015-01-09T11:12:20Zhttp://eprints.imtlucca.it/id/eprint/2443This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24432015-01-09T11:12:20ZComputational burden reduction in set-membership Hammerstein system identificationHammerstein system identification from measurements affected by bounded noise is considered in the paper. First, we show that computation of tight parameter bounds requires the solution to nonconvex optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, in order to reduce the computational burden of the identification problem, we propose a procedure to relax the previously formulated problem to a set of polynomial optimization problems where the number of variables does not depend on the size of the measurements sequence. Advantages of the presented approach with respect to previously published results are discussed.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T10:28:51Z2015-01-09T10:28:51Zhttp://eprints.imtlucca.it/id/eprint/2442This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24422015-01-09T10:28:51ZConvex relaxation techniques for set-membership identification of LPV systemsSet-membership identification of single-input single-output linear parameter varying models is considered in the paper under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, we show that the problem of computing the parameter uncertainty intervals requires the solutions to a number of nonconvex optimization problems. Then, on the basis of the analysis of the regressor structure, we present some ad hoc convex relaxation schemes to compute parameter bounds by means of semidefinite optimization. Advantages of the new techniques with respect to previously published results are discussed both theoretically and by means of simulations.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T10:25:09Z2015-01-09T10:25:09Zhttp://eprints.imtlucca.it/id/eprint/2441This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24412015-01-09T10:25:09ZHammerstein systems parameters bounding through sparse polynomial optimizationA single-stage procedure for the evaluation of tight bounds on the parameters of Hammerstein systems from output measurements affected by bounded errors is presented. The identification problem is formulated in terms of polynomial optimization, and relaxation techniques based on linear matrix inequalities are proposed to evaluate parameters bounds by means of convex optimization. The structured sparsity of the identification problem is exploited to reduce the computational complexity of the convex relaxed problem. Convergence proper ties, complexity analysis and advantages of the proposed technique with respect to previously published ones are discussed.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-09T10:00:06Z2015-01-09T10:00:06Zhttp://eprints.imtlucca.it/id/eprint/2440This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24402015-01-09T10:00:06ZBounding the parameters of linear systems with stability constraintsIdentification of linear systems, a priori known to be stable, from input output measurements corrupted by bounded noise is considered in the paper. A formal definition of the feasible parameter set is provided, taking explicitly into account prior information on system stability. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameters uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-08T14:09:38Z2015-01-08T14:09:38Zhttp://eprints.imtlucca.it/id/eprint/2438This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24382015-01-08T14:09:38ZControl as a key technology for a radical innovation in wind energy generationThis paper is concerned with an innovative technology, denoted as Kitenergy, for the conversion of high-altitude wind energy into electricity. The research activities carried out in the last five years, including theoretical analyses, numerical simulations and experimental tests, indicate that Kitenergy could bring forth a revolution in wind energy generation, providing renewable energy in large quantities at lower cost than fossil energy. After an overview of the main features of the technology, this work investigates three important aspects: the evaluation of the performance achieved by the employed control law, the optimization of the generator operating cycle and the possibility to generate continuously a constant and maximal power output. These issues are tackled through the combined use of advanced modeling, control and optimization methods, which results to be key technologies for a significant breakthrough in renewable energy generation.Mario MilaneseLorenzo FagianoDario Pigadario.piga@imtlucca.it2015-01-08T13:49:05Z2015-01-08T13:49:05Zhttp://eprints.imtlucca.it/id/eprint/2437This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24372015-01-08T13:49:05ZKitenergy: a radical innovation in wind energy generationThis paper presents an innovative technology of high-altitude wind power generation, indicated as Kitenergy, which exploits the automatic flight of tethered airfoils (e.g. power kites) to extract energy from wind blowing between 200 and 800 meters above the ground. The key points of such a technology are described and the design of large scale plants is investigated here, in order to show that Kitenergy technology has the potential to provide large quantities of renewable energy with competitive cost with respect to fossil sources. Such claims are supported by the results obtained so far in the research activities undergoing at Politecnico di Torino, Italy, including numerical simulations, prototype experiments and wind data analyses.Lorenzo FagianoMario MilaneseDario Pigadario.piga@imtlucca.it2015-01-08T13:24:07Z2015-01-08T13:24:07Zhttp://eprints.imtlucca.it/id/eprint/2436This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24362015-01-08T13:24:07ZSet-membership identification of block-structured nonlinear feedback systemsIn this paper a three-stage procedure for set-membership identification of block-structured nonlinear feedback systems is proposed. Nonlinear block parameters bounds are computed in the first stage exploiting steady-state measurements. Then, given the uncertain description of the nonlinear block, bounds on the unmeasurable inner-signal are computed in the second stage. Finally, linear block parameters bounds are computed in the third stage on the basis of output measurements and computed inner signal bounds. Computation of both the nonlinear block parameters and the inner-signal bounds is formulated in terms of semialgebraic optimization and solved by means of suitable convex LMI relaxation techniques. Linear block parameters are bounded solving a number of linear programming problems.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-08T11:51:23Z2015-01-08T11:51:23Zhttp://eprints.imtlucca.it/id/eprint/2434This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24342015-01-08T11:51:23ZParameter bounds evaluation for linear systems with output backlashIn this paper a procedure is presented for deriving parameters bounds of linear systems with output backlash when the output measurement errors are bounded. First, using steady-state input/output data, parameters of the backlash are bounded. Then, given the estimated uncertain backlash and the output measurements collected exciting the system with a PRBS, bounds on the unmeasurable inner signal are computed. Finally, such bounds, together with the input sequence, are used for bounding the parameters of the linear block.Vito CeroneDario Pigadario.piga@imtlucca.itDiego Regruto2015-01-08T11:08:23Z2015-01-12T13:16:19Zhttp://eprints.imtlucca.it/id/eprint/2433This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24332015-01-08T11:08:23ZAn instrumental Least Squares Support Vector Machine for system identificationRoland TóthVincent LaurainDario Pigadario.piga@imtlucca.it2015-01-08T11:00:48Z2015-01-08T11:00:48Zhttp://eprints.imtlucca.it/id/eprint/2432This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24322015-01-08T11:00:48ZSegmentation of ARX systems through SDP-relaxation techniquesSegmentation of ARX models can be formulated as a combinato-
rial minimization problem in terms of the ℓ0-norm of the param-
eter variations and the ℓ2-loss of the prediction error. A typical
approach to compute an approximate solution to such a prob-
lem is based on ℓ1-relaxation. Unfortunately, evaluation of the
level of accuracy of the ℓ1-relaxation in approximating the opti-
mal solution of the original combinatorial problem is not easy to
accomplish. In this poster, an alternative approach is proposed
which provides an attractive solution for the ℓ0-norm minimiza-
tion problem associated with segmentation of ARX models.Dario Pigadario.piga@imtlucca.itRoland Tóth2015-01-08T10:57:52Z2015-01-08T11:01:10Zhttp://eprints.imtlucca.it/id/eprint/2431This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24312015-01-08T10:57:52ZDealing with correlated errors in Least-Squares Support Vector Machine EstimatorsJohn LataireDario Pigadario.piga@imtlucca.itRoland Tóth2015-01-08T10:35:27Z2015-01-08T10:55:43Zhttp://eprints.imtlucca.it/id/eprint/2430This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24302015-01-08T10:35:27ZData-driven LPV modeling of continuous pulp digestersIn this technical report, the LPV-IO identification techniques described in Kauven et al. [2013]
(Chapter 5) are applied in order to estimate an LPV model of a continuous pulp digester. The pulp
digester simulator (described in Modén [2011]) has been provided by ABB for benchmark studies
as part of its participation in the EU project AutoprofitDario Pigadario.piga@imtlucca.itRoland Tóth2015-01-08T10:31:58Z2015-01-12T13:16:01Zhttp://eprints.imtlucca.it/id/eprint/2429This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24292015-01-08T10:31:58ZAn instrumental Least Squares Support Vector Machine for nonlinear system identification: enforcing zero-centering constraintsLeast-Squares Support Vector Machines (LS-SVM's), originating from Stochastic Learning
theory, represent a promising approach to identify nonlinear systems via nonparametric es-
timation of nonlinearities in a computationally and stochastically attractive way. However,
application of LS-SVM's in the identification context is formulated as a linear regression aim-
ing at the minimization of the ℓ2 loss in terms of the prediction error. This formulation
corresponds to a prejudice of an auto-regressive noise structure, which, especially in the non-
linear context, is often found to be too restrictive in practical applications. In [1], a novel
Instrumental Variable (IV) based estimation is integrated into the LS-SVM approach provid-
ing, under minor conditions, a consistent identification of nonlinear systems in case of a noise
modeling error. It is shown how the cost function of the LS-SVM is modified to achieve an IV-based solution.
In this technical report, a detailed derivation of the results presented in Section 5.2 of [1]
is given as a supplement material for interested readers.Vincent LaurainRoland TóthDario Pigadario.piga@imtlucca.it2015-01-08T10:09:00Z2015-01-08T13:05:30Zhttp://eprints.imtlucca.it/id/eprint/2428This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24282015-01-08T10:09:00ZA convex relaxation approach to set-membership identificationSet-membership identification of dynamical systems is dealt with in this thesis. Differently from the stochastic framework, in the set-membership context the statistical description of the measurement noise is not available and the only information on such an error is that its amplitude or energy is bounded. In the framework of Set-membership identification, the result of the estimation process is the set of all system parameter values consistent with measured data, assumed model structure and a-priori assumptions on the measurement error. The problem of evaluating bounds on system parameters belonging to the feasible parameter set can be formulated in terms of polynomial optimization problems, where the number of decision variables increases with the length of the experimental data sequence. Such problems are generally nonconvex and NP-hard. Therefore, standard nonlinear optimization tools can not be used to compute parameter bounds, since they can trap in local minima and, as a consequence, the computed bounds are not guaranteed to contain the true values of parameters, which is a key requirement in set-membership identification. In order to overcome such a problem, convex relaxation procedures based on the theory of moments are proposed to efficiently compute relaxed bounds which are guaranteed to contain the true values of system parameters. Unfortunately, a direct application of the theory of moments in relaxing set-membership identification problems leads to semidefinite programming problems with high computational burden, thus limiting, in practice, the use of such relaxation procedures to solve identification problems with a small number of measurements. The aim of the thesis is to derive a number of convex-relaxation based algorithms that, exploiting the peculiar properties of the considered identification problems, make it possible to perform bound computation also when the number of measurements is large. In particular, errors-in-variables (EIV) identification of linear models, concerning identification of linear-time-invariant (LTI) systems based on noise-corrupted measurements of both input and output signals, is tackled through two different relaxation approaches. The first method, which is referred to as dynamic-EIV approach, exploits the sparse structure of EIV problems in order to reduce the computational complexity of the semidefinite programming problems arising from theory-of-moment relaxations. The second technique, referred to as semi-static-EIV approach, is based on a suitable handling of the constraints defining the feasible parameter set, and leads to polynomial optimization problems where the number of decision variables does not depend on the size of the measurement sequence. Thanks to that problem reformulation, theory-of-moment relaxations can be efficiently applied to compute bounds on system parameters also from large data set. Identification of block-oriented nonlinear systems is also addressed. The considered model structures are: Hammerstein-Wiener systems; Hammerstein-like and Wiener-like structures with backlash nonlinearity and block-structured nonlinear feedback systems. The semi-static-EIV approach is extended with suitable modifications to estimate the parameters of Hammerstein-Wiener models with static blocks described by polynomial functions. Then, a unified approach for set-membership identification of Hammerstein and Wiener models with backlash is discussed. By properly selecting a sequence of input/output measurements, the evaluation of parameter bounds is formulated in terms of polynomial optimization problems and the structured sparsity of the formulated problems is exploited to reduce the computational complexity of theory-of-moment based relaxations. Finally, a two-stage method for identification of block-structured nonlinear feedback systems is presented. Nonlinear block parameter bounds are first computed by using input/output data collected from the response of the system to square wave inputs. Then, by stimulating the system with a persistently exciting input signal, bounds on the unmeasurable inner-signal are evaluated, which are used, together with noise-corrupted measurements of the output signal, to formulate the identification of linear block parameters in terms of EIV problems that can be solved either through the dynamic or the semi-static-EIV approach. Then, an "ad hoc" convex relaxation scheme is presented to compute guaranteed bounds on the parameters of linear-parameter-varying (LPV) models in input/output (I/O) form, under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. The developed set-membership identification algorithms are used to derive an LPV model describing vehicle lateral dynamics based on a set of experimental data, and an LPV model to describe glucose-insulin dynamics for patients affected by Type I diabetes. Finally, the problem of identifying systems a-priori known to be stable is discussed. In particular, suitable relaxation-based algorithms are proposed to enforce BIBO stability and quadratic stability constraints for the cases of LTI and LPV systems, respectively. Applicability of the proposed techniques both in the stochastic and in the set-membership framework is discussed.Dario Pigadario.piga@imtlucca.it