Infinite horizon safety controller synthesis through disjunctive polyhedral abstract interpretation

Abstract

This paper presents a controller synthesis approach using disjunctive polyhedral abstract interpretation. Our approach synthesizes infinite time-horizon controllers for safety properties with discrete-time, linear plant model and a switching feedback controller that is suitable for time-triggered implementations. The core idea behind our approach is to perform an abstract interpretation over disjunctions of convex polyhedra to identify states that are potentially uncontrollable. Complementing this set yields the set of controllable states, starting from which, the safety property can be guaranteed by an appropriate controller feedback function. Since, a straightforward disjunctive domain is computationally inefficient, we present an abstract domain based on a state partitioning scheme that allows us to efficiently control the complexity of the intermediate representations. Next, we focus on the automatic generation of controller implementation from the abstract interpretation results. We show that a balanced tree approach can yield efficient controller code with guarantees on the worst-case execution time. Finally, we evaluate our approach on a suite of benchmarks, comparing different instantiations with related synthesis tools. The evaluation shows that our approach can successfully synthesize controller implementations for small to medium sized benchmarks.

Formal Policy Learning from Demonstrations for Reachability Properties

“…The idea of generating controllers from rich temporal property specifications underlies the field of formal synthesis. A variety of recent approaches consider this problem, including discretization-based techniques that abstract the dynamics to finite state machines and use automatatheoretic approaches to synthesize controllers [18], [21], [23], [27], formal parameter synthesis approaches that search for unknown parameters so that the overall system satisfies its specifications [33], [29], [9], [1], deductive approaches that learn controllers and associated certificates such as the Lyapunov function [24], [3], [30], [6]. Recent work [22], [32] presents approaches to controller synthesis for temporal logic based on the paradigm of counterexample-guided inductive synthesis (CEGIS) [28].…”

Deadlock-free discrete controller synthesis for infinite state systems

“…The use of other widening operators as those designed by Bagnara et al [21] would certainly be worth investigating. At last, the partitioned polyhedral disjunctive domains designed by Ravanbakhsh and Sankaranarayanan [26] in the setting of infinite horizon safety controller synthesis, could also be an interesting trail for improving our solution. x 5 (see Remark 6).…”