Stabilization of Finite Automata with Application to Hybrid Systems Control

Authors:
Koichi Kobayashi;Jun-Ichi Imura;Kunihiko Hiraishi
Affiliations:
School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan 923-1292;Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan 152-8552;School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan 923-1292
Venue:
Discrete Event Dynamic Systems
Year:
2011

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Abstract

This paper discusses the state feedback stabilization problem of a deterministic finite automaton (DFA), and its application to stabilizing model predictive control (MPC) of hybrid systems. In the modeling of a DFA, a linear state equation representation recently proposed by the authors is used. First, this representation is briefly explained. Next, after the notion of equilibrium points and stabilizability of the DFA are defined, a necessary and sufficient condition for the DFA to be stabilizable is derived. Then a characterization of all stabilizing state feedback controllers is presented. Third, a simple example is given to show how to follow the proposed procedure. Finally, control Lyapunov functions for hybrid systems are introduced based on the above results, and the MPC law is proposed. The effectiveness of this method is shown by a numerical example.