IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-22T19:29:00ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2014-07-08T13:40:37Z2014-07-08T13:40:37Zhttp://eprints.imtlucca.it/id/eprint/2251This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22512014-07-08T13:40:37ZAn algorithm for PWL approximations of nonlinear functionsIn this report we provide some technical details for some of the results appeared in [Alessio et al.(2005)]. In the first section we provide the proof of continuity of the PPWA function computed with the ”squaring the circle” algorithm stated in ACC 06. Then, we analyze the complexity of the previous algorithm, in terms of the desired level of accuracy in the approximation of the PPWA function.Alessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itB. AddisAlessandro Pasini2012-04-26T10:50:14Z2012-07-06T12:20:13Zhttp://eprints.imtlucca.it/id/eprint/1264This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12642012-04-26T10:50:14ZAssessment of non-centralised model predictive control techniques for electrical power networks Model predictive control (MPC) is one of the few advanced control methodologies that have proven to be very successful in real-life applications. An attractive feature of MPC is its capability of explicitly taking state and input constraints into account. Recently, there has been an increasing interest in the usage of MPC schemes to control electrical power networks. The major obstacle for implementation lies in the large scale of these systems, which is prohibitive for a centralised approach. In this article, we therefore assess and compare the suitability of several non-centralised predictive control schemes for power balancing, to provide valuable insights that can contribute to the successful implementation of non-centralised MPC in the real-life electrical power system. Ralph M. HermansAndrej JokicMircea LazarAlessandro AlessioPaul Van den boschIan HiskensAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T12:51:25Z2011-08-05T11:12:37Zhttp://eprints.imtlucca.it/id/eprint/725This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7252011-07-27T12:51:25ZDecentralized model predictive control of dynamically coupled linear systemsThis paper proposes a decentralized model predictive control (DMPC) scheme for large-scale dynamical processes subject to input constraints. The global model of the process is approximated as the decomposition of several (possibly overlapping) smaller models used for local predictions. The degree of decoupling among submodels represents a tuning knob of the approach: the less coupled are the submodels, the lighter the computational burden and the load for transmission of shared information; but the smaller is the degree of cooperativeness of the decentralized controllers and the overall performance of the control system. Sufficient criteria for analyzing asymptotic closed-loop stability are provided for input constrained open-loop asymptotically stable systems and for unconstrained open-loop unstable systems, under possible intermittent lack of communication of measurement data between controllers. The DMPC approach is also extended to asymptotic tracking of output set-points and rejection of constant measured disturbances. The effectiveness of the approach is shown on a relatively large-scale simulation example on decentralized temperature control based on wireless sensor feedback.Alessandro AlessioDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:43:43Z2011-08-05T13:38:38Zhttp://eprints.imtlucca.it/id/eprint/538This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5382011-07-27T08:43:43ZSquaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal onesThis paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear systems, possibly affected by disturbances. Given a beta-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets betaE and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costsMircea LazarAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. Heemels2011-07-27T08:43:40Z2011-08-05T13:37:53Zhttp://eprints.imtlucca.it/id/eprint/543This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5432011-07-27T08:43:40ZConvex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an explicit form of the MPC controller, the approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V(x) les gamma of the MPC value function (implicitly defined by the quadratic programming problem associated with MPC or explicitly computed via multiparametric quadratic programming), while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program (implicitly or explicitly defined). The level gamma acts as a tuning parameter for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (gamma = 0) to the maximum invariant set around the origin where the solution to the unconstrained MPC problem remains feasible, up to the whole domain of definition of the controller (possibly the whole state space Ropfn) (gamma = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loopsAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsMircea Lazar2011-07-27T08:41:35Z2011-08-05T13:35:14Zhttp://eprints.imtlucca.it/id/eprint/540This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5402011-07-27T08:41:35ZFeasible mode enumeration and cost comparison for explicit quadratic model predictive control of hybrid systemsFor hybrid systems in piecewise affine (PWA) form, this paper presents a new methodology for computing the solution, defined over a set of (possibly overlapping) polyhedra, of the finite-time constrained optimal control problem based on quadratic costs. First, feasible mode sequences are determined via backward reachability analysis, and multiparametric quadratic programming is employed to determine candidate polyhedral regions of the solution and the corresponding value functions and optimal control gains. Then, the value functions associated with overlapping regions are compared in order to discard those regions whose associated control law is never optimal. The comparison problem is, in general, nonconvex and is tackled here as a DC (Difference of Convex functions) programming problem.Alessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:36:50Z2011-08-05T13:03:30Zhttp://eprints.imtlucca.it/id/eprint/479This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4792011-07-27T08:36:50ZSquaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal onesThis paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a β-contractive ellipsoidal set View the MathML source, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets View the MathML source and View the MathML source. A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired polyhedral set. The problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.
Alessandro AlessioMircea LazarAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. Heemels2011-07-27T08:36:41Z2014-01-20T15:22:08Zhttp://eprints.imtlucca.it/id/eprint/507This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5072011-07-27T08:36:41ZDecentralized model predictive control of constrained linear systemsAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:36:19Z2012-04-26T10:50:02Zhttp://eprints.imtlucca.it/id/eprint/616This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6162011-07-27T08:36:19ZAssessment of decentralized model predictive control techniques for power networksModel predictive control (MPC) is one of the few advanced control methodologies that have proven to be very successful in real-life control applications. MPC has the capability to guarantee optimality with respect to a de- sired performance cost function, while explicitly taking con- straints into account. Recently, there has been an increas- ing interest in the usage of MPC schemes to control power networks. The major obstacle for implementation lies in the large scale of power networks, which is prohibitive for a centralized approach. In this paper we critically assess and compare the suitability of three model predictive control schemes for controlling power networks. These techniques are analyzed with respect to the following relevant characteristics: the performance of the closed-loop system, which is evaluated and compared to the performance achieved with the classical automatic generation control (AGC) structure; the decentralized implementation, which is investigated in terms of size of the models used for prediction, required measurements and data communication, type of cost function and the computational time required by each algorithm to obtain the control action. Based on the investigated properties mentioned above, the study presented in this paper provides valuable insights that can contribute to the successful decentralized implementation of MPC in real-life electrical power networks.Armand DamoiseauxAndrej JokicMircea LazarAlessandro AlessioPaul Van den boschIan HiskensAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:34:45Z2014-07-08T12:41:47Zhttp://eprints.imtlucca.it/id/eprint/618This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6182011-07-27T08:34:45ZStability conditions for decentralized model predictive control under packet drop communicationWe propose a decentralized model predictive control (MPC) design approach for possibly large-scale processes whose structure may not be dynamically decoupled. The decoupling assumption only appears in the prediction models used by the different MPC control agents. In [1] we presented a sufficient criterion for analyzing a posteriori the asymptotic stability of the process model in closed-loop with the set of decentralized MPC controllers. The communication model among neighboring MPC controllers was supposed faultless, so that each MPC could successfully receive the information about the states of its corresponding submodel. Here we present a sufficient condition for ensuring closed-loop stability of the overall closed-loop system when a certain number of packets containing state measurements may be lost.Alessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:31:50Z2011-08-05T12:33:40Zhttp://eprints.imtlucca.it/id/eprint/511This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5112011-07-27T08:31:50ZA survey on explicit model predictive controlExplicit model predictive control (MPC) addresses the problem of removing one of the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action. This computation prevents the application of MPC in several contexts, either because the computer technology needed to solve the optimization problem within the sampling time is too expensive or simply infeasible, or because the computer code implementing the numerical solver causes software certification concerns,especially in safety critical applications.
Explicit MPC allows one to solve the optimization problem off-line for a given range of operating conditions of interest. By exploiting multiparametric programming techniques, explicit MPC computes the optimal control action off line as an “explicit” function of the state and reference vectors, so that on-line operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller maps into a lookup table of linear gains.
In this paper we survey the main contributions on explicit MPC appeared in the scientific literature. After recalling the basic concepts and problem formulations of MPC, we review the main approaches to solve explicit MPC problems, including a novel and simple suboptimal practical approach to reduce the complexity of the explicit form. The paper concludes with some comments on future research directions.
Alessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it