Backstepping Design for Incremental Input-to-State Stabilization of Unknown Systems

TL;DR

This paper introduces a new incremental stability concept called { extdelta}-ISpS, develops a backstepping control method using Gaussian Processes to stabilize unknown systems, and demonstrates its effectiveness through case studies.

Contribution

It presents a novel incremental Lyapunov function class and a backstepping control scheme for unknown systems utilizing Gaussian Process learning.

Findings

The proposed controller achieves { extdelta}-ISpS in unknown systems.

Effectiveness demonstrated through two case studies.

New stability notion and control design method successfully applied.

Abstract

Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class of incremental Lyapunov functions, an incremental stability notion known as Incremental Input-to-State practical Stability ({\delta}-ISpS). Using Gaussian Process, we learn the unknown dynamics of a class of control systems. We then present a backstepping control design scheme that provides state-feedback controllers that render the partially unknown control system {\delta}-ISpS. To show the effectiveness of the proposed controller, we implement it in two case studies.