Jitter-Robust LQG Control and Real-Time Scheduling Co-Design

In real-time control systems, varying task response times may lead to delays and jitter in the delays in the feedback control loops, which adversely affects both performance and robustness. Standard LQG control design does not give any guarantees on robustness, while robust control design methods often do not handle controller timing uncertainty. We propose a sampled-data controller synthesis method that minimizes an LQG cost function subject to a jitter margin constraint. By robustifying the LQG controller we are able to retain good stability margins under delay and jitter, while typically paying a small price in terms of nominal performance. We also present a co-design procedure that assigns optimal priorities and sampling periods to a set of controllers based on their performance characteristics and jitter sensitivity. The procedure is evaluated on randomized plant sets, showing an improvement over state-of-the-art methods.