Receding-horizon control for max-plus linear systems with discrete actions using optimistic planning

Conference paper (2016)

Authors

J. Xu Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
L Busoniu Technical University of Cluj-Napoca
A.J.J. van den Boom Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
B.H.K. De Schutter Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2016 J. Xu, L Busoniu, A.J.J. van den Boom, B.H.K. De Schutter
DOI: https://doi.org/10.1109/WODES.2016.7497879
Linear programming Planning Optimal control Linear systems Algorithm design and analysis Aerospace electronics
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Published Date

2016

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

This paper addresses the infinite-horizon optimal control problem for max-plus linear systems where the considered objective function is a sum of discounted stage costs over an infinite horizon. The minimization problem of the cost function is equivalently transformed into a maximization problem of a reward function. The resulting optimal control problem is solved based on an optimistic planning algorithm. The control variables are the increments of system inputs and the action space is discretized as a finite set. Given a finite computational budget, a control sequence is returned by the optimistic planning algorithm. The first control action or a subsequence of the returned control sequence is applied to the system and then a receding-horizon scheme is adopted. The proposed optimistic planning approach allows us to limit the computational budget and also yields a characterization of the level of near-optimality of the resulting solution. The effectiveness of the approach is illustrated with a numerical example. The results show that the optimistic planning approach results in a lower tracking error compared with a finite-horizon approach when a subsequence of the returned control sequence is applied.

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