Robustly Complete Reach-and-Stay Control Synthesis for Switched Systems via Interval Analysis
Yinan Li, Jun Liu · 2018
This paper proposes a formal synthesis algorithm for discrete-time switched systems with respect to reach-and-stay specifications. Fundamental to the proposed method is a fixed-point algorithm characterizing the initial states satisfying reach-and-stay specifications for continuous-state systems. Based on the interval branch-and-bound scheme, the original continuous state space is adaptively partitioned into a finite number of cells according to the given specification and system dynamics during the fixed-point iterations. Valid switching modes are recorded and a partition-based switching strategy can be extracted immediately after the algorithm terminates. In contrast with most of the abstraction-based methods, the proposed algorithm is guaranteed to return a switching strategy after a finite number of iterations, provided that the specification is robustly realizable. As illustrated in the numerical example, the adaptive partitioning framework effectively reduces the size of the finite partition, which offers a considerable advantage over abstraction-based methods that use a uniform partition.