Convex Data-Driven Contraction With Riemannian Metrics

Andreas Oliveira, Jian Zheng, Mario Sznaier

Abstract: The growing complexity of dynamical systems and advances in data collection necessitate robust data-driven control strategies without explicit system identification and robust synthesis. Data-driven stability has been explored in linear and nonlinear systems, often by turning the problem into a linear or positive semidefinite program. This letter focuses on contractivity, which refers to the exponential convergence of all system trajectories toward each other under a specified metric. Data-driven closed-loop contractivity has been studied for the case of weighted $\ell _{2}$ -norms and assuming nonlinearities are Lipschitz bounded in subsets of $\mathbb {R}^{n}$ . We extend the analysis by considering Riemannian metrics for polynomial dynamics. The key to our derivation is to leverage the convex criteria for closed-loop contraction and duality results to efficiently check infinite dimensional membership constraints. Numerical examples demonstrate the effectiveness of the proposed method for both linear and nonlinear systems.

External IDs:doi:10.1109/lcsys.2025.3578275