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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.05.001