Feedback Synthesis for Nonlinear Systems Via Convex Control Lyapunov Functions

TL;DR

This paper presents efficient methods for synthesizing explicit piecewise affine feedback laws for nonlinear systems, ensuring robustness and performance through convex control Lyapunov functions, demonstrated on a Van der Pol oscillator.

Contribution

It introduces a novel convex optimization approach to synthesize PWA controllers with guaranteed stability and performance for nonlinear discrete-time systems.

Findings

Synthesized PWA controller with certified ergodic performance.

Controller maintains robustness over large operational domains.

Framework achieves configurable complexity and evaluation times.

Abstract

This paper introduces computationally efficient methods for synthesizing explicit piecewise affine (PWA) feedback laws for nonlinear discrete-time systems, ensuring robustness and performance guarantees. The approach proceeds by optimizing a configuration-constrained PWA approximation of the value function of an infinite-horizon min-max Hamilton-Jacobi-Bellman equation. Here, robustness and performance are maintained by enforcing the PWA approximation to be a generalized control Lyapunov function for the given nonlinear system. This enables the generation of feedback laws with configurable storage complexity and pre-determined evaluation times, based on a selected configuration template. The framework's effectiveness is demonstrated through a constrained Van der Pol oscillator case study, where an explicit PWA controller with certified ergodic performance and specified complexity is synthesized over a large operational domain.