Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

Abstract
This work presents a new algorithm for solving the explicit/multi- parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step. © 2011 Elsevier Ltd. All rights reserved.

Citation
Kouramas KI, Faísca NP, Panos C, Pistikopoulos EN (2011) Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming. Automatica 47: 1638–1645. Available: http://dx.doi.org/10.1016/j.automatica.2011.05.001.

Acknowledgements
The financial support of EPSRC (Projects GR/T02560, EP/047017/1). European Commission (PRISM ToK project, Contract No: MTKI-CT-2004-512233 and DIAMANTE ToK project, Contract No: MTKI-CT-2005-IAP-029544), European Research Council (MOBILE, ERC Advanced Grant No: 226462) and KAUST is gratefully acknowledged. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Berc Rustem.

Publisher
Elsevier BV

Journal
Automatica

DOI
10.1016/j.automatica.2011.05.001

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