A sub-optimal solution for optimal control of linear systems with unmeasurable switching delays
For control engineers dealing with networked control systems, this work offers a practical algorithm to handle unmeasurable delays, though the solution is sub-optimal.
The paper addresses optimal control for discrete-time LTI systems with unmeasurable switching delays, modeling them as switching linear systems and providing an algorithm for a sub-optimal solution.
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.