Minimal Representation of Finite Automata for Hybrid Systems Control

This paper discusses a new approach to representing a finite automaton as a linear state equation with the smallest number of binary input variables to reduce the computational time for solving the model predictive control problem of a class of hybrid systems. Our method for modeling a finite automaton, which has been proposed in our previous paper, is explained at first. Then an open question on the minimality of the dimension of binary input variables in the state equation is described. Thus the purpose of this paper is to give a solution to a kind of minimal representation problem of finite automata. Using the implicit system expression on the binary field GF(2)9 it is proven that, for a given implicit system model on GF{2) of expressing a finite automaton, its state equation representation on the field of real numbers R obtained via our method is minimal in the sense that the dimension of the input variables is minimal for all linear equivalence transformations on GF(2)