Reach Controllability of Single Input Affine Systems on a Simplex

Author

Semsar-Kazerooni, Elham ; Broucke, Mireille E.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada

Volume

59

Issue

3

fYear

2014

fDate

Mar-14

Firstpage

738

Lastpage

744

Abstract

We study the reach control problem (RCP) for a single input affine system with a simplicial state space. We extend previous results by exploring arbitrary triangulations of the state space; particularly allowing the set of possible equilibria to intersect the interior of simplices. In the studied setting, it is shown that closed-loop equilibria, nevertheless, only arise on the boundary of simplices. This allows to define a notion of reach controllability which quantifies the effect of the control input on boundary equilibria. Using reach controllability we obtain necessary and sufficient conditions for solvability of RCP by affine feedback.

Keywords

closed loop systems; controllability; state-space methods; RCP; affine feedback; arbitrary triangulations; boundary equilibria; closed-loop equilibria; necessary conditions; reach control problem; simplicial state space; single input affine systems; sufficient conditions; Aerospace electronics; Controllability; Face; Indexes; State feedback; Trajectory; Vectors; Reach control problem (RCP);

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2274707

Filename

6567943