Optimal Scheduling for Linear-Rate Multi-Mode Systems

TL;DR

This paper investigates optimal scheduling controllers for linear-rate multi-mode systems, providing necessary and sufficient conditions for safety, polynomial-time algorithms for controller synthesis, and cost minimization strategies with simulation validation.

Contribution

It introduces a comprehensive framework for safe and cost-efficient control of multi-mode systems, including new algorithms and theoretical conditions.

Findings

Existence of a safe controller characterized by a necessary and sufficient condition.

Polynomial-time algorithm for synthesizing safe controllers.

Algorithms for minimizing peak and average costs in control strategies.

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 the state of the system within a given safe set for the whole time. 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.