Semi-definite programs for online control of nonlinear systems with stability guarantees

TL;DR

This paper introduces a semidefinite programming approach for online nonlinear system control, providing stability guarantees and performance bounds through time-varying SDPs.

Contribution

It presents a novel SDP-based method for stabilizing nonlinear systems online with stability certificates and recursive feasibility guarantees.

Findings

Numerical examples demonstrate the method's effectiveness on nonlinear systems.

The approach provides stability certificates and estimates of the region of attraction.

The method is flexible and applicable to various nonlinear control problems.

Abstract

This paper develops a semidefinite-programming-based method for online feedback control of nonlinear systems using a state-dependent representation. We formulate sequences of time-varying SDPs whose optimal solutions jointly yield a stabilizing feedback controller and a Lyapunov certificate satisfying stability conditions and quadratic performance specifications. We further establish compact conditions certifying recursive feasibility of the resulting SDP sequences and derive estimates of the region of attraction. Numerical examples on representative nonlinear systems illustrate the flexibility and effectiveness of the proposed method.