An improved algorithm for robust safety analysis of sampled data systems

Abstract

A sampled data model falls somewhere between continuous and discrete time models: The plant evolves in continuous time, but the controller receives feedback and can modify its control input(s) only at periodic points in time. In previous work we have demonstrated how to compute the discriminating kernel (also called the maximal robust control invariant set) for sampled data systems and how this kernel can be used to analyze and even synthesize safe feedback controllers for systems with state space safety constraints; however, the algorithm for computing the kernel was conservative. In this paper we provide an improved abstract algorithm whose computations are tight to the sampled data discriminating kernel. The improved algorithm can also take sample time jitter into account. A level set implementation is used to demonstrate that the new algorithm is tight and a conservative ellipsoidal implementation is used to demonstrate its practical benefits on a nonlinear quadrotor model.