Optimal control for linear-rate multi-mode systems

Authors:
Dominik Wojtczak
Affiliations:
University of Liverpool, Liverpool, UK
Venue:
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
Year:
2013

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Abstract

Linear-Rate Multi-Mode Systems is a model that can be seen both as a subclass of switched linear systems with imposed global safety constraints and as hybrid automata with no guards on transitions. We study the existence and design of a controller for this model that keeps at all times the state of the system within a given safe set. A sufficient and necessary condition is given for such a controller to exist as well as an algorithm that finds one in polynomial time. We further generalise the model by adding costs on modes and present an algorithm that constructs a safe controller which minimises the peak cost, the average-cost or any cost expressed as a weighted sum of these two. Finally, we present numerical simulation results based on our implementation of these algorithms.