Gaussian inference for data-driven state-feedback design of nonlinear systems

TL;DR

This paper introduces a data-driven method for nonlinear control using polynomial representations and Bayesian inference to design stabilizing state-feedback laws with performance guarantees, reducing computational complexity.

Contribution

It presents a novel polynomial-based control design framework that leverages Bayesian inference for noisy data, enabling tractable stability and performance guarantees.

Findings

Sum-of-squares optimization simplifies control design.

Bayesian inference effectively handles Gaussian noise.

Global asymptotic stability achieved with quadratic performance.

Abstract

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium point globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a single sum-ofsquares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.