Passive soft-reset controllers for nonlinear systems

TL;DR

This paper introduces passive soft-reset controllers as a continuous-time approximation to hard-reset controllers, analyzing their stability and implementation advantages in nonlinear systems.

Contribution

It presents a novel class of passive soft-reset controllers that approximate hard-reset controllers, with stability analysis and practical implementation insights.

Findings

Soft-reset controllers can approximate hard-reset controllers effectively.

Interconnection of passive soft-reset controllers with passive plants is asymptotically stable.

Soft-reset controllers are easier to understand and implement than hybrid hard-reset controllers.

Abstract

Soft-reset controllers are introduced as a way to approximate hard-reset controllers. The focus is on implementing reset controllers that are (strictly) passive and on analyzing their interconnection with passive plants. A passive hard-reset controller that has a strongly convex energy function can be approximated as a soft-reset controller. A hard-reset controller is a hybrid system whereas a soft-reset controller corresponds to a differential inclusion, living entirely in the continuous-time domain. This feature may make soft-reset controllers easier to understand and implement. A soft-reset controller contains a parameter that can be adjusted to better approximate the action of the hard-reset controller. Closed-loop asymptotic stability is established for the interconnection of a passive soft-reset controller with a passive plant, under appropriate detectability assumptions. Several examples are used to illustrate the efficacy of soft-reset controllers.