Data-driven invariant set for nonlinear systems with application to

This paper presents a novel approach to synthesize positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a datadriven command governor that selects a command for the closed-loop system to enforce constraints. Using basis functions, we solve a semi-definite program to learn a sum-of-squares Lyapunov-like function whose unity level-set is a constraint admissible positive invariant set, which determines the constraint admissible states and input commands. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the invariant set to the inherent plant uncertainty in a data-driven framework. To mitigate the curse-of-dimensionality, we repose the semi-definite program into a linear program. We validate our approach through two examples: First, we present an illustrative example where we can analytically compute the maximum positive invariant set and compare with the presented data-driven invariant set. Second, we present a practical autonomous driving scenario to demonstrate the utility of the presented method for nonlinear systems. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.