Integration of Prior Knowledge into Direct Learning for Safe Control of Linear Systems

TL;DR

This paper presents a method to incorporate prior knowledge into data-driven safe control design for linear systems, ensuring safety constraints are met while leveraging system and disturbance information.

Contribution

It introduces a formal framework using matrix zonotopes to integrate prior knowledge into the learning process for safe control of linear uncertain systems.

Findings

The proposed approach guarantees safety by set inclusion conditions.

Matrix zonotopes effectively characterize system explainability.

The method accommodates both polytope and zonotope safe sets.

Abstract

This paper integrates prior knowledge into direct learning of safe controllers for linear uncertain systems under disturbances. To this end, we characterize the set of all closed-loop systems that can be explained by available prior knowledge of the system model and the disturbances. We leverage matrix zonotopes for data-based characterization of closed-loop systems and show that the explainability of closed-loop systems by prior knowledge can be formalized by adding an equality conformity constraint to the matrix zonotope. We then leverage the resulting constraint matrix zonotope and design safe controllers that conform with both data and prior knowledge. This is achieved by ensuring the inclusion of a constrained zonotope of all possible next states in a {\lambda}-scaled level set of the safe set. We consider both polytope and zonotope safe sets and provide set inclusion conditions using linear programming.