Feedback Stabilization of Polynomial Systems: From Model-based to Data-driven Methods

TL;DR

This paper introduces new global stabilization methods for polynomial systems, expanding applicability in model-based and data-driven contexts by allowing broader Lyapunov functions and handling noisy data.

Contribution

It develops a novel stabilization approach that broadens Lyapunov function choices and extends to data-driven scenarios with noise, enhancing robustness and flexibility.

Findings

Proposes a new global stabilization method for polynomial systems.

Extends stabilization to data-driven settings with noisy data.

Uses sum-of-squares relaxation for computational tractability.

Abstract

In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system only when the Lyapunov function is radially unbounded, which limits its applicability. To overcome this limitation, we develop a new global stabilization approach that allows a broader class of Lyapunov function candidates. Furthermore, we extend this approach to the data-driven setting, considering Lyapunov function candidates with the same functional structure. Using data corrupted by bounded noise, we derive conditions for constructing globally stabilizing controllers for unknown polynomial systems. Beyond handling noise, the proposed data-driven approach can be readily adapted to incorporate further prior knowledge of system parameters to reduce conservatism. In both approaches, sum-of-squares relaxation is used to ensure computational tractability of the involved conditions.