This paper proposes a new approach to reducing the computational time for solving the model predictive control problem of a class of hybrid systems, by representing a finite automaton with a smaller number of binary variables. First, the technical issue in the modeling on the field of real numbers is pointed out, and an implicit system expression on the binary field
GF(2) is presented. Next, a systematic method to transform this system model into the state equation on the field of real numbers by way of the state equation on
GF(2) is proposed, which thus enables us to reduce the original control problem into the mixed integer quadratic problem with a smaller number of binary variables. Finally, the effectiveness of the proposed method is shown by numerical examples.
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