Modular synthesis of discrete controllers

This paper presents supervisory control theory in a process-algebraic setting, and proposes a way of synthesising modular supervisors that guarantee nonblocking. The framework used includes the possibility of hiding actions which results in nondeterminism. As modularity crucially depends on the process equivalence used, the paper studies possible equivalences and points out that, in order to be consistent with respect to the nonblocking property and to supervisor synthesis, a conflict-preserving equivalence must be used. It applies the results to synthesise nonblocking modular supervisors for a manufacturing system

Attack-Resilient Supervisory Control of Discrete-Event Systems

In this work, we study the problem of supervisory control of discrete-event systems (DES) in the presence of attacks that tamper with inputs and outputs of the plant. We consider a very general system setup as we focus on both deterministic and nondeterministic plants that we model as finite state transducers (FSTs); this also covers the conventional approach to modeling DES as deterministic finite automata. Furthermore, we cover a wide class of attacks that can nondeterministically add, remove, or rewrite a sensing and/or actuation word to any word from predefined regular languages, and show how such attacks can be modeled by nondeterministic FSTs; we also present how the use of FSTs facilitates modeling realistic (and very complex) attacks, as well as provides the foundation for design of attack-resilient supervisory controllers. Specifically, we first consider the supervisory control problem for deterministic plants with attacks (i) only on their sensors, (ii) only on their actuators, and (iii) both on their sensors and actuators. For each case, we develop new conditions for controllability in the presence of attacks, as well as synthesizing algorithms to obtain FST-based description of such attack-resilient supervisors. A derived resilient controller provides a set of all safe control words that can keep the plant work desirably even in the presence of corrupted observation and/or if the control words are subjected to actuation attacks. Then, we extend the controllability theorems and the supervisor synthesizing algorithms to nondeterministic plants that satisfy a nonblocking condition. Finally, we illustrate applicability of our methodology on several examples and numerical case-studies

Compositional synthesis of discrete event systems via synthesis equivalence

A two-pass algorithm for compositional synthesis of modular supervisors for largescale systems of composed finite-state automata is proposed. The first pass provides an efficient method to determine whether a supervisory control problem has a solution, without explicitly constructing the synchronous composition of all components. If a solution exists, the second pass yields an over-approximation of the least restrictive solution which, if nonblocking, is a modular representation of the least restrictive supervisor. Using a new type of equivalence of nondeterministic processes, called synthesis equivalence, a wide range of abstractions can be employed to mitigate state-space explosion throughout the algorithm

On the use of observation equivalence in synthesis abstraction

In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor

Compositional synthesis of maximally permissive supervisors using supervision equivalence

This paper presents a general framework for efficient synthesis of supervisors for discrete event systems. The approach is based on compositional minimisation, using concepts of process equivalence. In this context, a large number of ways are suggested how a finite-state automaton can be simplified such that the results of supervisor synthesis are preserved. The proposed approach yields a compact representation of a least restrictive supervisor that ensures controllability and nonblocking. The method is demonstrated on a simple manufacturing example to significantly reduce the number of states constructed for supervisor synthesis

Three variations of observation equivalence preserving synthesis abstraction

In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor

Certainly Unsupervisable States

This paper proposes an abstraction method for compositional synthesis. Synthesis is a method to automatically compute a control program or supervisor that restricts the behaviour of a given system to ensure safety and liveness. Compositional synthesis uses repeated abstraction and simplification to combat the state-space explosion problem for large systems. The abstraction method proposed in this paper finds and removes the so-called certainly unsupervisable states. By removing these states at an early stage, the final state space can be reduced substantially. The paper describes an algorithm with cubic time complexity to compute the largest possible set of removable states. A practical example demonstrates the feasibility of the method to solve real-world problems

Hierarchical interface-based supervisory control using the conflict preorder

Hierarchical Interface-Based Supervisory Control decomposes a large discrete event system into subsystems linked to each other by interfaces, facilitating the design of complex systems and the re-use of components. By ensuring that each subsystem satisfies its interface consistency conditions locally, it can be ensured that the complete system is controllable and nonblocking. The interface consistency conditions proposed in this paper are based on the conflict preorder, providing increased flexibility over previous approaches. The framework requires only a small number of interface consistency conditions, and allows for the design of multi-level hierarchies that are provably controllable and nonblocking

An algorithm for weak synthesis observation equivalence for compositional supervisor synthesis

This paper proposes an algorithm to simplify automata in such a way that compositional synthesis results are preserved in every possible context. It relaxes some requirements of synthesis observation equivalence from previous work, so that better abstractions can be obtained. The paper describes the algorithm, adapted from known bisimulation equivalence algorithms, for the improved abstraction method. The algorithm has been implemented in the DES software tool Supremica and has been used to compute modular supervisors for several large benchmark examples. It successfully computes modular supervisors for systems with more than 1012 reachable states