Safety Verification of Output Feedback Controllers for Nonlinear Systems

TL;DR

This paper develops a method for verifying safety in nonlinear systems using output feedback controllers and high-gain observers, ensuring safety properties are maintained despite partial state information.

Contribution

It introduces a novel approach to synthesize safety-preserving controllers for nonlinear systems using high-gain observers and derives bounds on trajectory deviations.

Findings

Bound on trajectory difference converges to zero with observer gain

Safety properties can be recovered under output feedback and control saturation

Maximal safety-invariant set can be constructed for nonlinear systems

Abstract

A high-gain observer is used for a class of feedback linearisable nonlinear systems to synthesize safety-preserving controllers over the observer output. A bound on the distance between trajectories under state and output feedback is derived, and shown to converge to zero as a function of the gain parameter of an observer. We can therefore recover safety properties under output feedback and control saturation constraints by synthesizing a controller as if the full state were available. We specifically design feedback linearising controllers that satisfy certain properties, such as stability, and then construct the associated maximal safety-invariant set, namely the largest set of all initial states that are guaranteed to produce safe trajectories over a given (possibly infinite) time horizon.