Journal of Systems Engineering and Electronics ›› 2010, Vol. 21 ›› Issue (6): 1090-1094.doi: 10.3969/j.issn.1004-4132.2010.06.024

• CONTROL THEORY AND APPLICATION • Previous Articles     Next Articles

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

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

  1. 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
  • Online:2010-12-20 Published:2010-01-03

Abstract:

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.

Key words: constrained optimal predictive control, multi-parametric quadratic programming, dynamic programming, receding horizon control, positively invariant set