Switching controller synthesis for time-delayed hybrid systems
Xue Bai, Jiao Li, Yunjun Bai, Gan Ting, Naijun Zhan · Scientia Sinica Mathematica · 2020
How to design safe and reliable safety-critical cyber-physical systems (CPSs) so thatwe can bet our daily lives on them is a grand challenge to computer science and control theory. Delays in feedback control are ubiquitous, i.e., the behavior evolution of a system depends not only on its current state, but also on its execution history. Obviously, delays may invalidate the stability/safetycertificates obtained by abstracting them away as in the design of modern CPSs normally. In this paper, we study the switching controller synthesis problem of time-delayed hybrid systems, and propose an invariant-based approach by extending the corresponding approach to the design of CPSs without delays. To this end, based on spectral analysis and linearization, we first show that the differential invariant generation problem of delayed dynamical systems can be reduced to computing reachable sets over bounded time horizons; we then propose an abstract-based algorithm to over-approximate the reachable set over a given time bound; finally, we implement a prototypical tool of our approach and illustrate it with examples.