A Semi-Algebraic Optimization Approach to Data-Driven Control of Continuous-Time Nonlinear Systems

Tianyu Dai, Mario Sznaier

Abstract: This letter considers the problem of designing state feedback data-driven controllers for nonlinear continuous-time systems. Specifically, we consider a scenario where the unknown dynamics can be parametrized in terms of known basis functions and the available measurements are corrupted by unknown-but-bounded noise. The goal is to use this noisy experimental data to directly design a rational state-feedback control law guaranteed to stabilize all plants compatible with the available information. The main result of this letter shows that, by using Rantzer's Dual Lyapunov approach, combined with elements from convex analysis, the problem can be recast as an optimization over positive polynomials, which can be relaxed to a semi-definite program through the use of Sum-of-Squares and semi-algebraic optimization arguments. Three academic examples are considered to illustrate the effectiveness of the proposed method.