Sampled-Data Stabilization with Control Lyapunov Functions via Quadratically Constrained Quadratic Programs

TL;DR

This paper develops a method to design sampled-data controllers for nonlinear systems using Control Lyapunov Functions, ensuring stability and improved performance in digital implementations compared to continuous-time designs.

Contribution

It introduces a novel QCQP-based approach to synthesize sampled-data CLF controllers, bridging the gap between continuous-time design and discrete implementation.

Findings

Enhanced stability guarantees for sampled-data systems.

Simulation results show improved performance over continuous-time controllers.

Method applicable to feedback linearizable systems with stable zero-dynamics.

Abstract

Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system's continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation.