Lyapunov-Based Reset Control

Abstract

More than 50 years ago, J.C. Clegg proposed a modified version of the analog integrator introducing suitable state resets and showing improved performance in terms of phase lag, at least as seen from a describing function analysis of the intricate nonlinear phenomenon behind state resets. With certain modern tools arising from recent hybrid dynamical systems representations, it is now possible to revisit that strategy, provide Lyapunov-based (therefore robust) guarantees of its stability and performance, and reach beyond stable linear filters involving resets. This talk covers 15 years of research activity within this framework, emphasizing the advantages and the challenges. A number of reset control strategies, stemming from generalizations of the original paradigm of Clegg, will be discussed. Among other things, we will emphasize the suggestive idea of homogeneous closed loops with reset controllers whose solutions converge exponentially to zero by way of exponentially unstable branches. The talk will be mostly focused on stabilization, but will hopefully also touch upon set-point regulation and reference tracking. Theoretical results will be discussed, together with some experimental and industrial validations within the automotive field.