Reach control problem for a class of convex differential inclusions on simplices

Author:

Lv Dejing1,Ge Bin2,Wu Mingze3

Affiliation:

1. College of Intelligent Systems Science and Engineering , Harbin Engineering University, 150001 Harbin , China

2. College of Intelligent Systems Science and Engineering , Harbin Engineering University, 150001 Harbin, China, College of Mathematical Sciences, Harbin Engineering University, 150001 Harbin , China

3. College of Underwater Acoustic Engineering , Harbin Engineering University, 150001 Harbin , China

Abstract

Abstract This paper focuses on the reach control problem for systems expressed as a class of convex differential inclusions. The purpose is to find affine feedback for the trajectories of the systems to reach and leave an unrestricted facet of a given simplex in a finite time. It is proved that the condition for strong reachability is sufficient and necessary. The sufficient condition for weak reachability is obtained based on the solvability of the reach control problem for linear affine systems. At last, algorithms are designed and numerical examples are given to verify the validity of the results.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Control and Optimization,Control and Systems Engineering

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