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

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  • Control Theory and Applications
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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.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, P. R. China

    Biao Wang & Jun-e Feng

Authors
  1. Biao Wang
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  2. Jun-e Feng
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Correspondence to Jun-e Feng.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Ding Zhai under the direction of Editor Guang-Hong Yang. This work was supported by the National Natural Science Foundation of China (61773371, 61877036), and the Natural Science Fund of Shandong Province (ZR2019MF002).

Biao Wang received his B.S. degree from Jilin Normal University in 2007, an M.S degree from Yanbian University in 2015, and a Ph.D. degree from Shandong University in 2019. Currently, he is a Postdoctoral Researcher at the School of Mathematics in Shandong University, China. His research interests include logical dynamic systems, discrete event systems, and finite automata, etc.

Jun-e Feng received her Ph.D. degree from Shandong University in 2003. She is currently a Professor of School of Mathematics at Shandong University, Jinan, China. She was a visiting scholar at MIT, USA, from 2006 to 2007, and a visiting scholar at the University of Hong Kong, Hong Kong, China, in 2008, 2009, and 2013. Her research interests include singular systems, Boolean networks, and robust control, etc.

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Wang, B., Feng, Je. A Matrix Approach for the Static Correction Problem of Asynchronous Sequential Machines. Int. J. Control Autom. Syst. 18, 477–485 (2020). https://doi.org/10.1007/s12555-019-0148-8

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  • DOI: https://doi.org/10.1007/s12555-019-0148-8

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