Lazy Controller Synthesis using Three-valued Abstractions for Safety and Reachability Specifications

TLDR: A new way to tackle the lack of scalability of control software synthesis by adopting a lazy controller synthesis approach, where the abstraction is computed lazily as needed for safety and reachability specifications.

Abstract: The synthesis of correct-by-design control software is a promising direction to address the well known difficulties in formally verifying complex cyber-physical systems. Despite the promise of this approach, it is currently limited to small systems since it typically requires the computation of a finite-state abstraction whose size grows exponentially with the number of continuous states. In this paper we present a new way to tackle the lack of scalability of control software synthesis by adopting a lazy controller synthesis approach. Instead of synthesizing a controller using a precomputed abstraction of the full system, the abstraction is computed lazily as needed for safety and reachability specifications. We illustrate, through different examples, how this lazy approach significantly reduces the total time required for the synthesis of correct-by-design controllers.