Abstract
We propose a new technique for controlled system synthesis on non-deterministic automata for requirements in modal logic. Synthesis, as defined in this paper, restricts a behavioral specification of the uncontrolled system such that it satisfies a given logical expression, while adhering to the rules dictated by supervisory control such as maximal permissiveness and controllability. The applied requirement formalism extends Hennessy-Milner logic with the invariant and reachability modalities from Gödel-Löb logic, and is therefore able to express a broad range of control requirements, such as marker state reachability and deadlock-freeness. This paper contributes to the field of control synthesis by achieving maximal permissiveness in a non-deterministic context for control requirements in modal logic, and treatment of controllability via partial bisimulation. We present a well-defined and complete derivation of the synthesis result, which is supported further by computer-verified proofs created using the Coq proof assistant. The synthesis method is also presented in algorithmic form, including an analysis of its computational complexity. We show that the proposed synthesis theory allows full expressibility of Ramadge-Wonham supervisory control theory and we illustrate its applicability in two small industrial case studies, including an analysis with regard to scalability.
Highlights
This paper concerns the controlled system synthesis on non-deterministic automata for requirements in modal logic
The automated generation, or synthesis, of such a restricted behavioral model incorporates a number of concepts from supervisory control theory (Ramadge and Wonham 1987), which guarantees that the generated model is a proper controlled system with regard to the original plant specification
We find the same omission of maximal permissiveness in Moor and Davoren (2001), where safety and liveness properties in μ-calculus are synthesized for hybrid automata, in Wolff et al (2013) where LTL-requirements are synthesized for non-deterministic plant models, and in (Ostroff 1989), where safety properties in real-time temporal logic are synthesized for non-deterministic plants
Summary
This paper concerns the controlled system synthesis on non-deterministic automata for requirements in modal logic. The contribution of this paper is two-fold It presents a new technique for maximally permissive controlled system synthesis in a non-deterministic context. We consider non-determinism in conjunction with maximal permissiveness; a property which states that all non-invalidating behavior should be preserved, while achieving the control objective This ensures that the controlled behavior stays as close as possible to the intended operation of the system. We combined the invariant ( f ) and reachable (♦ f ) modalities from GodelLob logic (Alberucci and Facchini 2009) with the universal ([e]f ) and existential (f ) lookahead from Hennessy-Milner logic (Hennessy and Milner 1985) We restrict this requirement formalism to state-based properties for the reachability operator, and we apply the same restriction to one side of a disjunction. Formal definitions and proofs for most of the theoretical work in this paper are presented in computer-verified form by means of Coq proofs
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