Design and Stability Analysis for Anytime Control via Stochastic Scheduling

In this paper, we consider the problem of designing controllers for linear plants to be implemented in embedded platforms under stringent real-time constraints. These include preemptive scheduling schemes, under which the execution time allowed for control software tasks is uncertain. In a conservative Hard Real-Time (HRT) design approach, only a control algorithm that (in the worst case) is executable within the minimum time slot guaranteed by the scheduler would be employed. In the spirit of modern Soft Real-Time (SRT) approaches, we consider here an ”anytime control” design technique, based on a hierarchy of controllers for the same plant. Higher controllers in the hierarchy provide better closed-loop performance, while typically requiring longer execution time. Stochastic models of the scheduler and of algorithm execution times are used to infer probabilities that controllers of different complexity can be executed at different periods. We propose a strategy for choosing among executable controllers, maximizing the usage of higher controllers, which affords better exploitation of the computational platform than the HRT design while guaranteeing stability (in a suitable stochastic sense). Results on the robustness with respect to uncertainties affecting the scheduler model, and on bumpless transfer for tracking problems are also reported. Simulation results on the control of two prototypical mechanical systems show that performance is substantially enhanced by our anytime control technique w.r.t. worst case-based scheduling.