Data-driven stabilization of nonlinear polynomial systems with noisy data

Abstract

In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system.

References in corpus (2)

• Robust data-driven state-feedback design
• Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction

Cited by in corpus (6)

• Linear tracking MPC for nonlinear systems Part II: The data-driven case
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• Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics
• Nonlinear Data-Enabled Prediction and Control
• Direct data-driven control of LTV systems
• Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis