Data-driven Invariance for Reference Governors

TL;DR

This paper introduces a data-driven method for synthesizing positive invariant sets for nonlinear systems, enabling constraint enforcement and robust reference design without explicit models.

Contribution

It develops a novel data-driven approach using kernel functions and semi-definite programming to compute invariant sets and design reference governors for nonlinear systems.

Findings

Validated on an analytical example comparing invariant sets

Demonstrated effectiveness in an autonomous driving scenario

Ensured robustness to plant uncertainty

Abstract

This paper presents a novel approach to synthesizing positive invariant sets for unmodeled nonlinear systems using direct data-driven techniques. The data-driven invariant sets are used to design a data-driven reference governor that selects a reference for the closed-loop system to enforce constraints. Using kernel-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 as well as reference inputs. Leveraging Lipschitz properties of the system, we prove that tightening the model-based design ensures robustness of the data-driven 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.