Data-driven abstraction-based control synthesis

• Published in: Nonlinear analysis. Hybrid systems Vol. 52; p. 101467
• Main Authors: Kazemi, Milad, Majumdar, Rupak, Salamati, Mahmoud, Soudjani, Sadegh, Wooding, Ben
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2024
• Subjects: Abstraction-based methods; Data-driven synthesis; Formal controller synthesis; Sample complexity; Abstraction-based methods; Sample complexity; Formal controller synthesis; Data-driven synthesis
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2024.101467

This paper studies formal synthesis of controllers for continuous-space systems with unknown dynamics to satisfy requirements expressed as linear temporal logic formulas. Formal abstraction-based synthesis schemes rely on a precise mathematical model of the system to build a finite abstract model, which is then used to design a controller. The abstraction-based schemes are not applicable when the dynamics of the system are unknown. We propose a data-driven approach that computes a growth bound of the system using a finite number of trajectories. The computed growth bound together with the sampled trajectories are then used to construct the abstraction and synthesise a controller. Our approach casts the computation of a growth bound as a robust convex optimisation program (RCP). Since the unknown dynamics appear in the optimisation, we formulate a scenario convex program (SCP) corresponding to the RCP using a finite number of sampled trajectories. We establish a sample complexity result that gives a lower bound for the number of sampled trajectories to guarantee the correctness of the growth bound computed from the SCP with a given confidence. Our sample complexity result requires knowing a possibly conservative bound on the Lipschitz constant of the system. We also provide a sample complexity result for the satisfaction of the specification on the system in closed loop with the designed controller for a given confidence. Our data-driven synthesised controller can provide guarantees on satisfaction of both finite and infinite-horizon specifications. We show that our data-driven approach can be readily used as a model-free abstraction refinement scheme by modifying the formulation of the system’s growth bounds and providing similar sample complexity results. The performance of our approach is shown on three case studies.