Data-driven abstraction-based control synthesis

doi:10.1016/j.nahs.2024.101467

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Data-driven abstraction-based control synthesis

2024-05-01

DOI：10.1016/j.nahs.2024.101467

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Abstract

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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.

Keywords:

Abstraction-based methods

Data-driven synthesis

Formal controller synthesis

Sample complexity

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