Safe Self-Triggered Control Based on Precomputed Reachability Sequences

Self-triggered controllers have the potential to improve the state-of-the-art of Cyber-Physical Systems (CPSs) by enhancing the performance of the underlying closed-loop control systems. However, a major concern in deploying a self-triggered controller in a safety-critical CPS is that the stabilizing self-triggered controller may not always guarantee the satisfaction of the safety constraints. We propose a self-triggered control scheme that deals with the safe scheduling of control tasks for uncertain continuous-time linear systems. We derive a computationally efficient scheduling function that computes an upper bound on the next sampling period as a function of the current state in the presence of additive disturbance. To reduce the computational complexity of online reachability analysis and increase accuracy, we compute a large sequence of reachable sets offline and use these precomputed sets to derive a low-complexity online scheduling function that computes sufficiently large bounds in real time. We evaluate our algorithm on three high-dimensional benchmark control systems, where two of the examples have a twelve-dimensional joint state plus feedback input. Experimental results demonstrate that our self-triggered control algorithm guarantees the safety of the closed-loop control system through negligible online computation, establishing the feasibility of its practical implementation.