A sub-optimal solution for optimal control of linear systems with unmeasurable switching delays

TL;DR

This paper addresses the challenge of designing sub-optimal control strategies for discrete-time linear systems with unmeasurable switching delays, using a worst-case optimization approach and a novel modeling technique.

Contribution

It introduces a new modeling method for systems with unmeasurable delays and provides an algorithm to compute sub-optimal control solutions.

Findings

Modeling of systems as pure switching linear systems.

Development of an algorithm for sub-optimal control.

Application to systems with unmeasurable switching delays.

Abstract

We consider the optimal control design problem for discrete-time LTI systems with state feedback, when the actuation signal is subject to unmeasurable switching propagation delays, due to e.g. the routing in a multi-hop communication network and/or jitter. In particular, we set up a constrained optimization problem where the cost function is the worst-case $\mathcal{L}_2$ norm for all admissible switching delays. We first show how to model these systems as pure switching linear systems, and as main contribution of the paper we provide an algorithm to compute a sub-optimal solution.