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A Matrix Approach for the Static Correction Problem of Asynchronous Sequential Machines

Biao Wang and Jun-e Feng*
International Journal of Control, Automation, and Systems, vol. 18, no. 2, pp.477-485, 2020

Abstract : This paper investigates the static correction problem of asynchronous sequential machines (ASMs) via semi-tensor product (STP) of matrices. For an input/state ASM, the static correction problem is to find a static state feedback controller to solve model matching. This controller contains no memory units and consists of only some logic gates. First, by STP method, two algebraic forms are derived to describe the dynamics of an input/state ASM and the function of a static state feedback controller, respectively. Then, as two special cases, the static state feedback controllers for no mismatch and only one mismatch are given. Based on these two cases and analyzing reachability of an ASM, a static state feedback controller design for model matching is presented. Moreover, the number of working points this controller contains is the least. Finally, the proposed method is applied to a simple home security system.

Keyword : Asynchronous sequential machines, model matching, semi-tensor product, static feedback.

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