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Max-plus-linear model-based predictive control for constrained hybrid systems:linear programming solution
引用本文:Yuanyuan ZOU,Shaoyuan LI. Max-plus-linear model-based predictive control for constrained hybrid systems:linear programming solution[J]. 控制理论与应用(英文版), 2007, 5(1): 71-76. DOI: 10.1007/s11768-005-5278-2
作者姓名:Yuanyuan ZOU  Shaoyuan LI
作者单位:Institute of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
基金项目:This work was supported by the National Science Foundation of China (No. 60474051) and the program for New Century Excellent Talents in University of China (NCET).
摘    要:In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.

关 键 词:约束混合系统  最大加线性系统  模式预测控制  线性规划
收稿时间:2005-10-28
修稿时间:2006-09-29

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution
Yuanyuan ZOU,Shaoyuan LI. Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution[J]. Journal of Control Theory and Applications, 2007, 5(1): 71-76. DOI: 10.1007/s11768-005-5278-2
Authors:Yuanyuan ZOU  Shaoyuan LI
Affiliation:Institute of Automation,Shanghai Jiao Tong university Shanghai 200240,China
Abstract:In this paper, a linear programming method is proposed to solvemodel predictive control for a class of hybrid systems. Firstly,using the (max, +) algebra, a typical subclass of hybrid systemscalled max-plus-linear (MPL) systems is obtained. And then, modelpredictive control (MPC) framework is extended to MPL systems. Ingeneral, the nonlinear optimization approach or extended linearcomplementarity problem (ELCP) were applied to solve the MPL-MPCoptimization problem. A new optimization method based on canonicalforms for max-min-plus-scaling (MMPS) functions (using theoperations maximization, minimization, addition and scalarmultiplication) with linear constraints on the inputs is presented.The proposed approach consists in solving several linear programmingproblems and is more efficient than nonlinear optimization. Thevalidity of the algorithm is illustrated by an example.
Keywords:Hybrid systems   Max-plus-linear systems   Model predictive control  Canonical form   Max-min-plus-scaling function   Linear programming
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