Data-driven invariant set for nonlinear systems with application to command governors
For control engineers dealing with nonlinear systems without accurate models, this work provides a data-driven way to ensure constraint satisfaction, though it is incremental as it builds on existing invariant set and command governor concepts.
This paper introduces a data-driven method to synthesize positive invariant sets for unmodeled nonlinear systems, using a sum-of-squares Lyapunov-like function learned via a semi-definite program reformulated as a linear program. The approach is validated on an analytical example and an autonomous driving scenario, showing constraint enforcement without a system model.
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 data-driven 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.