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

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 pr...

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Published in:	Automatica (Oxford) Vol. 47; no. 8; pp. 1638 - 1645
Main Authors:	Kouramas, K.I., Faísca, N.P., Panos, C., Pistikopoulos, E.N.
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier Ltd 01.08.2011 Elsevier
Subjects:	Algorithms Applied sciences Computer science; control theory; systems Control theory. Systems Dynamic programming Dynamical systems Dynamics Exact sciences and technology Explicit Model Predictive Control Mathematical models Model Predictive Control Multi-parametric control Multi-parametric programming Optimal control Optimization Predictive control Programming Explicit Model Predictive Control Multi-parametric control Multi-parametric programming Dynamic programming Model Predictive Control Multimodel control Parametric programming Global optimum Dynamical system Convex programming Current control Model predictive control Control constraint Linear time invariant system Discrete time Potential method State constraint
ISSN:	0005-1098, 1873-2836
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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.
AbstractList	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.
Author	Kouramas, K.I. Faísca, N.P. Panos, C. Pistikopoulos, E.N.
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References	Pistikopoulos, Georgiadis, Dua (br000105) 2007; Vol. 2 Johansen, A. (2002). On multi-parametric nonlinear programming and explicit nonlinear model predictive control. In Kojima, Morari (br000065) 2004; 40 Pistikopoulos, E. N., Bozinis, N. A., & Dua, V. (2000). A MATLAB (© The Math Works, Inc.) implementation of multi-parametric mixed-integer linear programming algorithm. Centre for Process Systems Engineering, Imperial College. April. Rawlings, Mayne (br000115) 2009 (pp. 3167–3172). Bemporad, Morari, Dua, Pisitkopoulos (br000035) 2002; 38 Sakizlis, Kakalis, Dua, Perkins, Perkins (br000125) 2004; 40 Pistikopoulos, E. N., Faísca, N. P., Kouramas, K., & Panos, C. (2009). Explicit robust model predictive control. In Bertsekas (br000040) 2005 Pistikopoulos, Georgiadis, Dua (br000110) 2007; Vol. 1 Bemporad, A., Borrelli, F., & Morari, M. (2000). Piecewise linear optimal controllers for hybrid systems. In Pistikopoulos (br000085) 2009; 55 Sakizlis, V., Dua, V., Kakalis, N., Perkins, J. D., & Pistikopoulos, E. N. (2001). The explicit control law for hybrid systems via parametric programming. In (pp. 128–133). Dominguez, Pistikopoulos (br000050) 2010; 34 Bemporad, A. (2003). Multiparametric nonlinear integer programming and explicit quantized optimal control. In Mayne, Rakovíc, Vinter, Kerrigan (br000070) 2006; 42 Tondel, Johansen, Bemporad (br000140) 2003; 39 (pp. 939–944). Muñoz de la Peña, D., Alamo, T., Bemporad, A., & Camacho, E. F. (2004). A dynamic programming approach for determining the explicit solution of linear MPC controllers. In Bank, Guddat, Klatte, Kummer, Tammer (br000005) 1982 Bellman (br000010) 2003 Pistikopoulos, E. N. (2000). On-line optimization via off-line optimization!—A guided tour to parametric programming. In Pistikopoulos, Dua, Bozinis, Bemporad, Morari (br000095) 2002; 26 Borrelli, Baotić, Bemporad, Morari (br000045) 2005; 41 . Bemporad, Borrelli, Morari (br000030) 2003; 48 Faísca, Kouramas, Saraiva, Rüstem, Pistikopoulos (br000055) 2008; 2 Sakizlis, Perkins, Pistikopoulos (br000130) 2005; 152 Schrijver (br000135) 1986 (pp. 2479–2484). Bemporad, A., Borrelli, F., & Morari, M. (2001). Robust Model predictive control: piecewise linear explicit solution. In Bellman (10.1016/j.automatica.2011.05.001_br000010) 2003 Bertsekas (10.1016/j.automatica.2011.05.001_br000040) 2005 Pistikopoulos (10.1016/j.automatica.2011.05.001_br000095) 2002; 26 Pistikopoulos (10.1016/j.automatica.2011.05.001_br000085) 2009; 55 10.1016/j.automatica.2011.05.001_br000100 Schrijver (10.1016/j.automatica.2011.05.001_br000135) 1986 10.1016/j.automatica.2011.05.001_br000025 Rawlings (10.1016/j.automatica.2011.05.001_br000115) 2009 Sakizlis (10.1016/j.automatica.2011.05.001_br000130) 2005; 152 10.1016/j.automatica.2011.05.001_br000020 10.1016/j.automatica.2011.05.001_br000120 10.1016/j.automatica.2011.05.001_br000060 10.1016/j.automatica.2011.05.001_br000080 Pistikopoulos (10.1016/j.automatica.2011.05.001_br000110) 2007; Vol. 1 Faísca (10.1016/j.automatica.2011.05.001_br000055) 2008; 2 Bemporad (10.1016/j.automatica.2011.05.001_br000035) 2002; 38 Tondel (10.1016/j.automatica.2011.05.001_br000140) 2003; 39 Sakizlis (10.1016/j.automatica.2011.05.001_br000125) 2004; 40 Mayne (10.1016/j.automatica.2011.05.001_br000070) 2006; 42 Bemporad (10.1016/j.automatica.2011.05.001_br000030) 2003; 48 10.1016/j.automatica.2011.05.001_br000015 Borrelli (10.1016/j.automatica.2011.05.001_br000045) 2005; 41 Dominguez (10.1016/j.automatica.2011.05.001_br000050) 2010; 34 10.1016/j.automatica.2011.05.001_br000075 Kojima (10.1016/j.automatica.2011.05.001_br000065) 2004; 40 10.1016/j.automatica.2011.05.001_br000090 Bank (10.1016/j.automatica.2011.05.001_br000005) 1982 Pistikopoulos (10.1016/j.automatica.2011.05.001_br000105) 2007; Vol. 2
References_xml	– volume: 40 start-page: 1143 year: 2004 end-page: 1155 ident: br000065 article-title: Lq control for constrained continuous-time systems publication-title: Automatica – reference: Johansen, A. (2002). On multi-parametric nonlinear programming and explicit nonlinear model predictive control. In – volume: 48 start-page: 1600 year: 2003 end-page: 1606 ident: br000030 article-title: Min–max control of constrained uncertain discrete-time linear systems publication-title: IEEE Transactions on Automatic Control – volume: Vol. 1 year: 2007 ident: br000110 publication-title: Multi-parametric programming: theory, algorithms and applications – reference: Pistikopoulos, E. N., Bozinis, N. A., & Dua, V. (2000). A MATLAB (© The Math Works, Inc.) implementation of multi-parametric mixed-integer linear programming algorithm. Centre for Process Systems Engineering, Imperial College. April. – volume: 152 start-page: 443 year: 2005 end-page: 452 ident: br000130 article-title: Explicit solutions to optimal control problems for constrained continuous-time linear systems publication-title: IEE Proceedings: Control Theory and Applications – year: 1982 ident: br000005 article-title: Non-linear parametric optimization – volume: 39 start-page: 489 year: 2003 end-page: 497 ident: br000140 article-title: An algorithm for multi-parametric quadratic programming and explicit MPC solutions publication-title: Automatica – volume: 42 start-page: 371 year: 2006 end-page: 382 ident: br000070 article-title: Characterization of the solution to a constrained publication-title: Automatica – volume: 40 start-page: 189 year: 2004 end-page: 201 ident: br000125 article-title: Design of robust model-based controllers via parametric programming publication-title: Automatica – year: 2005 ident: br000040 article-title: Dynamic programming and optimal control – volume: Vol. 2 year: 2007 ident: br000105 publication-title: Multi-parametric model-based control: theory and applications – reference: Muñoz de la Peña, D., Alamo, T., Bemporad, A., & Camacho, E. F. (2004). A dynamic programming approach for determining the explicit solution of linear MPC controllers. In – reference: Sakizlis, V., Dua, V., Kakalis, N., Perkins, J. D., & Pistikopoulos, E. N. (2001). The explicit control law for hybrid systems via parametric programming. In – reference: (pp. 939–944). – reference: Bemporad, A. (2003). Multiparametric nonlinear integer programming and explicit quantized optimal control. In – volume: 26 start-page: 175 year: 2002 end-page: 185 ident: br000095 article-title: On-line optimization via off-line parametric optimization tools publication-title: Computers & Chemical Engineering – reference: Pistikopoulos, E. N., Faísca, N. P., Kouramas, K., & Panos, C. (2009). Explicit robust model predictive control. In – reference: Bemporad, A., Borrelli, F., & Morari, M. (2000). Piecewise linear optimal controllers for hybrid systems. In – reference: Bemporad, A., Borrelli, F., & Morari, M. (2001). Robust Model predictive control: piecewise linear explicit solution. In – year: 1986 ident: br000135 article-title: Theory of linear and integer programming – year: 2003 ident: br000010 article-title: Dynamic programming – reference: Pistikopoulos, E. N. (2000). On-line optimization via off-line optimization!—A guided tour to parametric programming. In – volume: 38 start-page: 3 year: 2002 end-page: 20 ident: br000035 article-title: The explicit linear quadratic regulator for constrained systems publication-title: Automatica – volume: 34 start-page: 2097 year: 2010 end-page: 2106 ident: br000050 article-title: Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems publication-title: Computers & Chemical Engineering – year: 2009 ident: br000115 article-title: Model predictive control: theory and design – reference: (pp. 2479–2484). – reference: (pp. 3167–3172). – volume: 2 start-page: 267 year: 2008 end-page: 280 ident: br000055 article-title: A multi-parametric programming approach for constrained dynamic programming problems publication-title: Optimization Letters – reference: (pp. 128–133). – reference: . – volume: 41 start-page: 1709 year: 2005 end-page: 1721 ident: br000045 article-title: Dynamic programming for constrained optimal control of discrete-time linear hybrid systems publication-title: Automatica – volume: 55 start-page: 1918 year: 2009 end-page: 1925 ident: br000085 article-title: Perspectives in multiparametric programming and explicit model predictive control publication-title: AIChE Journal – volume: 55 start-page: 1918 year: 2009 ident: 10.1016/j.automatica.2011.05.001_br000085 article-title: Perspectives in multiparametric programming and explicit model predictive control publication-title: AIChE Journal doi: 10.1002/aic.11965 – ident: 10.1016/j.automatica.2011.05.001_br000080 – volume: 40 start-page: 1143 year: 2004 ident: 10.1016/j.automatica.2011.05.001_br000065 article-title: Lq control for constrained continuous-time systems publication-title: Automatica doi: 10.1016/j.automatica.2004.02.007 – volume: 2 start-page: 267 year: 2008 ident: 10.1016/j.automatica.2011.05.001_br000055 article-title: A multi-parametric programming approach for constrained dynamic programming problems publication-title: Optimization Letters doi: 10.1007/s11590-007-0056-3 – year: 2003 ident: 10.1016/j.automatica.2011.05.001_br000010 – year: 1982 ident: 10.1016/j.automatica.2011.05.001_br000005 – volume: 48 start-page: 1600 year: 2003 ident: 10.1016/j.automatica.2011.05.001_br000030 article-title: Min–max control of constrained uncertain discrete-time linear systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2003.816984 – ident: 10.1016/j.automatica.2011.05.001_br000025 doi: 10.23919/ECC.2001.7076033 – ident: 10.1016/j.automatica.2011.05.001_br000120 doi: 10.1016/S1474-6670(17)34180-0 – volume: 26 start-page: 175 year: 2002 ident: 10.1016/j.automatica.2011.05.001_br000095 article-title: On-line optimization via off-line parametric optimization tools publication-title: Computers & Chemical Engineering doi: 10.1016/S0098-1354(01)00739-6 – volume: 152 start-page: 443 issue: 4 year: 2005 ident: 10.1016/j.automatica.2011.05.001_br000130 article-title: Explicit solutions to optimal control problems for constrained continuous-time linear systems publication-title: IEE Proceedings: Control Theory and Applications – ident: 10.1016/j.automatica.2011.05.001_br000090 – volume: 34 start-page: 2097 year: 2010 ident: 10.1016/j.automatica.2011.05.001_br000050 article-title: Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2010.07.032 – year: 1986 ident: 10.1016/j.automatica.2011.05.001_br000135 – volume: Vol. 1 year: 2007 ident: 10.1016/j.automatica.2011.05.001_br000110 – volume: 41 start-page: 1709 year: 2005 ident: 10.1016/j.automatica.2011.05.001_br000045 article-title: Dynamic programming for constrained optimal control of discrete-time linear hybrid systems publication-title: Automatica doi: 10.1016/j.automatica.2005.04.017 – ident: 10.1016/j.automatica.2011.05.001_br000060 doi: 10.1109/CDC.2002.1184260 – ident: 10.1016/j.automatica.2011.05.001_br000075 doi: 10.1109/CDC.2004.1428785 – ident: 10.1016/j.automatica.2011.05.001_br000020 doi: 10.1109/ACC.2000.876688 – year: 2005 ident: 10.1016/j.automatica.2011.05.001_br000040 – ident: 10.1016/j.automatica.2011.05.001_br000100 – volume: 38 start-page: 3 year: 2002 ident: 10.1016/j.automatica.2011.05.001_br000035 article-title: The explicit linear quadratic regulator for constrained systems publication-title: Automatica doi: 10.1016/S0005-1098(01)00174-1 – volume: 40 start-page: 189 year: 2004 ident: 10.1016/j.automatica.2011.05.001_br000125 article-title: Design of robust model-based controllers via parametric programming publication-title: Automatica doi: 10.1016/j.automatica.2003.08.011 – ident: 10.1016/j.automatica.2011.05.001_br000015 doi: 10.1109/CDC.2003.1273110 – volume: 42 start-page: 371 issue: 3 year: 2006 ident: 10.1016/j.automatica.2011.05.001_br000070 article-title: Characterization of the solution to a constrained h-infty optimal control problem publication-title: Automatica doi: 10.1016/j.automatica.2005.10.015 – volume: Vol. 2 year: 2007 ident: 10.1016/j.automatica.2011.05.001_br000105 – volume: 39 start-page: 489 year: 2003 ident: 10.1016/j.automatica.2011.05.001_br000140 article-title: An algorithm for multi-parametric quadratic programming and explicit MPC solutions publication-title: Automatica doi: 10.1016/S0005-1098(02)00250-9 – year: 2009 ident: 10.1016/j.automatica.2011.05.001_br000115
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Snippet	This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant...
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SubjectTerms	Algorithms Applied sciences Computer science; control theory; systems Control theory. Systems Dynamic programming Dynamical systems Dynamics Exact sciences and technology Explicit Model Predictive Control Mathematical models Model Predictive Control Multi-parametric control Multi-parametric programming Optimal control Optimization Predictive control Programming
Title	Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming
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