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Model abstraction for discrete-event systems by binary linear programming with applications to manufacturing systems.

Lihong Cheng1,2, Lei Feng2, Zhiwu Li1

  • 1School of Electro-Mechanical Engineering, Xidian University, Xi'an, China.

Science Progress
|July 22, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to simplify complex discrete-event systems by reformulating state space reduction as a binary linear programming problem. This approach enhances computational efficiency and understanding for verification and control synthesis.

Keywords:
Discrete-event systemsdeterministic finite automatamodel abstractionnatural projectionquasi-congruence relation

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Area of Science:

  • Control Theory
  • Computer Science
  • Operations Research

Background:

  • Model abstraction simplifies discrete-event systems (DES) for verification and control synthesis.
  • Supremal quasi-congruence equivalence is a known method for state space reduction in DES.
  • Existing algorithms for supremal quasi-congruence are graph-theory based.

Purpose of the Study:

  • To propose a new method for computing supremal quasi-congruence.
  • To convert the supremal quasi-congruence problem into a binary linear programming (BLP) problem.
  • To optimize the state-to-coset allocation for coarsest quasi-congruence.

Main Methods:

  • Formulating supremal quasi-congruence computation as a binary linear programming problem.
  • Solving the optimal partitioning problem as an optimal state-to-coset allocation problem.
  • Implementing solutions using mixed integer linear programming (MILP) in MATLAB and BLP in CPLEX.

Main Results:

  • The proposed method successfully converts supremal quasi-congruence computation into a solvable optimization problem.
  • Optimized translation process reduces computation time by simplifying variables and constraints.
  • Computational efficiency and correctness verified using two distinct solvers.
  • Applied to simplify a large-scale manufacturing system model.

Conclusions:

  • The novel approach provides an effective alternative for computing the coarsest quasi-congruence.
  • This method offers a more intuitive understanding of quasi-congruence relations in supervisory control.
  • Future work includes exploring more efficient solvers for optimal state-to-coset allocation.