IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-27T21:48:00ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2011-07-27T08:47:42Z2011-08-05T13:54:34Zhttp://eprints.imtlucca.it/id/eprint/564This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5642011-07-27T08:47:42ZA dynamic programming approach for determining the explicit solution of MPC controllersRecently multi-parametric methods have been applied with success to model predictive control (MPC) schemes. In this paper we propose a novel method for linear systems to obtain the explicit description of the control law that is based on dynamic programming and exploits the structure of the MPC formulation.David Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:47:28Z2011-08-05T13:53:02Zhttp://eprints.imtlucca.it/id/eprint/533This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5332011-07-27T08:47:28ZA decomposition algorithm for feedback min-max model predictive controlAn algorithm for solving feedback min-max model predictive control for discrete time uncertain linear systems with constraints is presented in the paper. The algorithm solves the corresponding multi-stage min-max linear optimization problem. It is based on applying recursively a decomposition technique to solve the min-max problem via a sequence of low complexity linear programs. It is proved that the algorithm converges to the optimal solution in finite time. Simulation results are provided to compare the proposed algorithm with other approaches. David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itTeodoro Alamo2011-07-27T08:47:26Z2011-08-05T13:52:41Zhttp://eprints.imtlucca.it/id/eprint/534This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5342011-07-27T08:47:26ZStochastic programming applied to model predictive controlMany robust model predictive control (MPC) schemes are based on min-max optimization, that is, the future control input trajectory is chosen as the one which minimizes the performance due to the worst disturbance realization. In this paper we take a different route to solve MPC problems under uncertainty. Disturbances are modelled as random variables and the expected value of the performance index is minimized. The MPC scheme that can be solved using Stochastic Programming (SP), for which several efficient solution techniques are available. We show that this formulation guarantees robust constraint fulfillment and that the expected value of the optimum cost function of the closed loop system decreases at each time step. David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itTeodoro Alamo2011-07-27T08:44:00Z2011-08-05T13:44:03Zhttp://eprints.imtlucca.it/id/eprint/537This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5372011-07-27T08:44:00ZFeedback min-max model predictive control based on a quadratic cost functionFeedback min-max model predictive control based on a quadratic cost function is addressed in this paper. The main contribution is an algorithm for solving the min-max quadratic MPC problem with an arbitrary degree of approximation. The paper also introduces the "recourse horizon", which allows one to obtain a trade-off between computational complexity and performance of the control law. The results are illustrated by means of a simulation of a quadruple-tank processDavid Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:40:35Z2011-08-05T13:20:08Zhttp://eprints.imtlucca.it/id/eprint/490This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4902011-07-27T08:40:35ZA decomposition algorithm for feedback min-max model predictive controlAn algorithm for solving feedback min-max model predictive control for discrete-time uncertain linear systems with constraints is presented in this note. The algorithm is based on applying recursively a decomposition technique to solve the min-max problem via a sequence of low complexity linear programs. It is proved that the algorithm converges to the optimal solution in finite time. Simulation results are provided to compare the proposed algorithm with other approachesDavid Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho