Region-Based Self-Triggered Control for Perturbed and Uncertain Nonlinear Systems

Abstract: In this work, we derive a region-based self-triggered control (STC) scheme for nonlinear systems with bounded disturbances and model uncertainties. The proposed STC scheme is able to guarantee different performance specifications (e.g. stability, boundedness, etc.), depending on the event-triggered control (ETC) triggering function that is chosen to be emulated. To deal with disturbances and uncertainties, we employ differential inclusions (DIs). By introducing ETC/STC notions in the context of DIs, we extend well-known results on ETC/STC to perturbed uncertain systems. Given these results, and adapting tools from our previous work, we derive inner-approximations of isochronous manifolds of perturbed uncertain ETC systems. These approximations dictate a partition of the state-space into regions, each of which is associated to a uniform inter-sampling time. At each sampling time instant, the controller checks to which region the measured state belongs and correspondingly decides the next sampling instant.