Journal of Systems Engineering and Electronics 2010, 21(6) 1090-1094 DOI:   10.3969/j.issn.1004-4132.2010.06.024  ISSN: 1004-4132 CN: 11-3018/N

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constrained optimal predictive control
multi-parametric quadratic programming
dynamic programming
receding horizon control
positively invariant set

Stabilizing model predictive control scheme for piecewise affine systems with maximal positively invariant terminal set

Fu Chen1,2,*, Guangzhou Zhao1, and Xiaoming Yu1

1. College of System Science and Engineering, Zhejiang University, Hangzhou 310027, P. R. China;
2. Key Laboratory of Tobacco Processing Technology, Zhengzhou Tobacco Research Institute of CNTC,    Zhengzhou 450001, P. R. China


An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control (CFTOC) problem for discrete-time piecewise affine (PWA) systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.

Keywords�� constrained optimal predictive control   multi-parametric quadratic programming   dynamic programming   receding horizon control   positively invariant set  
Received  Revised  Online:  
DOI: 10.3969/j.issn.1004-4132.2010.06.024
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