IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-06-16T09:08:47ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2011-07-27T09:16:35Z2014-07-17T12:22:57Zhttp://eprints.imtlucca.it/id/eprint/482This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4822011-07-27T09:16:35ZOn-line optimization via off-line parametric optimization toolsIn this paper, on-line optimization problems with a quadratic performance criteria and linear constraints are formulated as multi-parametric quadratic programs, where the input and state variables, corresponding to a plant, are treated as optimization variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-line optimization problem is solved off-line via parametric programming techniques, hence, at each time interval (i) no optimization solver is called on-line, (ii) simple function evaluations are required for obtaining the optimal inputs to the plant for the current state of the plant.Efstratios N. PistikopoulosVivek DuaNikolaos A. BozinisAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:16:33Z2014-07-17T12:21:08Zhttp://eprints.imtlucca.it/id/eprint/569This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5692011-07-27T09:16:33ZThe explicit solution of model predictive control via multiparametric quadratic programming The control based on online optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for constrained systems. The main limitation of MPC is, however, its online computational complexity. For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law associated with MPC, and show that it is piecewise linear and continuous. The controller inherits all the stability and performance properties of MPC, but the online computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling applications which cannot be covered satisfactorily with anti-windup schemesAlberto Bemporadalberto.bemporad@imtlucca.itManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:11:24Z2014-07-17T12:17:57Zhttp://eprints.imtlucca.it/id/eprint/612This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6122011-07-27T09:11:24ZModel predictive control: a multi-parametric programming approachIn this paper, linear model predictive control problems are formulated as multi-parametric quadratic programs, where the control variables are treated as optimization variables and the state variables as parameters. It is shown that the control variables are affine functions of the state variables and each of these affine functions is valid in a certain polyhedral region in the space of state variables. An approach for deriving the explicit expressions of all the affine functions and their corresponding polyhedral regions is presented. The key advantage of this approach is that the control actions are computed off-line: the on-line computation simply reduces to a function evaluation problem.Alberto Bemporadalberto.bemporad@imtlucca.itNikolaos A. BozinisVivek DuaManfred MorariEfstratios N. Pistikopoulos2011-07-27T09:05:54Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/444This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4442011-07-27T09:05:54ZThe Explicit Linear Quadratic Regulator for Constrained SystemsFor discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamiltonâ€“Jacobiâ€“Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.Alberto BemporadManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:05:50Z2011-08-08T08:07:22Zhttp://eprints.imtlucca.it/id/eprint/486This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4862011-07-27T09:05:50ZOn-line optimization via off-line parametric optimization toolsIn this paper, model predictive control (MPC) based previous termoptimizationnext term problems with a quadratic performance criterion and linear constraints are formulated as multi-previous termparametricnext term quadratic programs (mp-QP), where the input and state variables, corresponding to a plant model, are treated as previous termoptimizationnext term variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-previous termline optimizationnext term problem is solved previous termoff-line via parametricnext term programming techniques. Hence (i) no previous termoptimizationnext term solver is called on-previous termline,next term and (ii) only simple function evaluations are required, to obtain the optimal inputs to the plant for the current state of the plant.Efstratios N. PistikopoulosVivek DuaNikolaos A. BozinisAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:02:41Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/483This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4832011-07-27T09:02:41ZCorrigendum to: "The explicit linear quadratic regulator for constrained systems" [Automatica 38(1) (2002) 3-20]We apologize that Example 7.1 as publishedin Bemporad,
Morari, Dua, andPistikopoulos (2002) is incorrect due to a
miscalculation of the weight matrix P on the terminal stateAlberto Bemporadalberto.bemporad@imtlucca.itManfred MorariVivek DuaEfstratios N. Pistikopoulos