Data-driven stabilizer design and closed-loop analysis of general nonlinear systems via Taylor's expansion

TL;DR

This paper introduces a data-driven method for stabilizer design and stability analysis of nonlinear systems using Taylor's expansion, without requiring explicit basis functions, enabling local stability guarantees from input-state data.

Contribution

It proposes a novel approach combining Taylor's expansion with Lyapunov methods for stabilizer design without prior basis function knowledge.

Findings

Design of stabilizers using input-state data

Conditions for invariance of Lyapunov sublevel sets

Handling Taylor's remainder in stability analysis

Abstract

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system can be expressed or well-approximated by the basis functions and the experimental data. For a more general setting where explicit information on the basis functions is not available, this paper presents a data-driven approach for stabilizer design and closed-loop analysis via the Lyapunov method. First, based on Taylor's expansion and using input-state data, a stabilizer and a Lyapunov function are designed to render the known equilibrium locally asymptotically stable. Then, data-driven conditions are derived to check whether a given sublevel set of the found Lyapunov function is an invariant subset of the region of attraction. One of the main challenges is how to handle Taylor's remainder in the design of the local stabilizers and the analysis of the closed-loop performance.