Integration of Prior Knowledge into Direct Learning for Safe Control of Linear Systems
Amir Modares, Bahare Kiumarsi, Hamidreza Modares
TL;DR
This work tackles safe control of linear discrete-time systems under disturbances by marrying prior model knowledge with direct data-driven learning. It introduces a constrained matrix zonotope framework to exactly characterize all closed-loop models consistent with data and prior knowledge, then enforces safety via a set-inclusion condition that guarantees ${\lambda}$-contractivity of a robust invariant safe set. The proposed method yields tractable, LP/LP-like conditions for both constrained zonotope and polytope safe sets, enabling practical safe controller synthesis of the form ${u(t) = Kx(t)}$. Simulation demonstrates that incorporating prior information increases disturbance tolerance and reduces conservatism without sacrificing stability guarantees. Overall, the paper provides a principled, set-based integration of prior knowledge into direct learning for safe, data-driven control of linear systems.
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 λ-scaled level set of the safe set. We consider both polytope and zonotope safe sets and provide set inclusion conditions using linear programming.