# Approximately global optimal control for max-plus linear systems and its application on load distribution

INTERNATIONAL JOURNAL OF CONTROL（2023）

Abstract

This paper considers the approximation problem of global optimal control of max-plus linear systems with real affine equality constrains. The approximate model that makes feasible values closest to the greatest lower bound is set up by introducing the distance between max-plus vectors. The existence of approximately optimal solutions is proved, and a criterion for the uniqueness of such solutions is presented. A general formula with polynomial time complexity is given to compute all the approximately optimal solutions. Furthermore, the proposed approximation technique is used to minimise the overall completion time of a distributed system without accurate optimal solution. The examples and simulations are provided to demonstrate the applicability of the results.

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Key words

Max-plus linear system, global optimal control, approximately optimal solution, general formula, load distribution, polynomial complexity

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