Sahar Mohajerani

A Framework for Compositional Synthesis of Modular Nonblocking Supervisors

This paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modeled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds.

Compositional synthesis of discrete event systems using synthesis abstraction

This paper proposes a general method to synthesize a least restrictive supervisor for a large discrete event system model, consisting of a large number of arbitrary automata representing the plants and specifications. A new type of abstraction called synthesis abstraction is introduced and three rules are proposed to calculate an abstraction of a given automaton. Furthermore, a compositional algorithm for synthesizing a supervisor for large-scale systems of composed finite-state automata is proposed. In the proposed algorithm, the synchronous composition is computed step by step and intermediate results are simplified according to synthesis abstraction. Then a supervisor for the abstracted system is calculated, which in combination with the original system gives the least restrictive, nonblocking, and controllable behaviour.

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.

Nondeterminism avoidance in compositional synthesis of discrete event systems

This paper proposes a framework for compositional synthesis of least restrictive controllable and nonblocking supervisors for modular discrete event systems models. The problem of state-space explosion is mitigated by abstracting individual components using synthesis abstraction before computing too large synchronous products. The paper improves and generalises previous work by introducing renaming to avoid nondeterministic intermediate results, making it possible to use more means of abstraction. Four classes of abstraction rules are discussed in the generalised framework, and an example demonstrates the feasibility of the method for practical problems.

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 10^12 reachable states.

Compositional synthesis of supervisors in the form of state machines and state maps

This paper investigates the compositional abstraction-based synthesis of least restrictive, controllable, and nonblocking supervisors for discrete event systems that are given as a large number of finite-state machines. It compares a previous algorithm that synthesises modular supervisors in the form of state machines, with an alternative that records state maps after each abstraction step and uses these to control the system. The state map-based algorithm supports all abstraction methods used previously, and in addition allows for nondeterminism, hiding, and transition removal. It has been implemented in the software tool Supremica and applied to several large industrial models. The experimental results and the complexity analysis show that state maps can be computed efficiently and in many cases require less memory than state machine-based supervisors.

Compositional nonblocking verification for extended finite-state automata using partial unfolding

This paper describes a framework for compositional nonblocking verification of discrete event systems modelled as extended finite-state automata. Compositional verification is shown in previous work to be efficient to verify the nonblocking property of large discrete event systems. Here, these results are applied to extended finite-state automata communicating via shared variables and events. The model to be verified is composed gradually, partially unfolding variables as needed. At each step, symbolic observation equivalence is used to simplify the resultant components in such a way that the final verification result is the same as it would have been for the original model. The paper concludes with an example showing the potential of compositional verification to achieve substantial state-space reduction.

An Algorithm for Compositional Nonblocking Verification of Extended Finite-State Machines

This paper describes an approach for compositional nonblocking verification of discrete event systems modelled as extended finite-state machines (EFSM). Previous results about finite-state machines in lock-step synchronisation are generalised and applied to EFSMs communicating via shared variables. This gives rise to an EFSM-based conflict check algorithm that composes EFSMs gradually and partially unfolds variables as needed. At each step, components are simplified using conflict-equivalence preserving abstraction. The algorithm has been implemented in the discrete event systems tool Supremica. The paper presents experimental results for the verification of two scalable manufacturing system models, and shows that the EFSM-based algorithm verifies some large models faster than previously used methods.

Transition removal for compositional supervisor synthesis

This paper investigates under which conditions transitions can be removed from an automaton while preserving important synthesis properties. The work is part of a framework for compositional synthesis of least restrictive controllable and nonblocking supervisors for modular discrete event systems. The method for transition removal complements previous results, which are largely focused on state merging. Issues concerning transition removal in synthesis are discussed, and redirection maps are introduced to enable a supervisor to process an event, even though the corresponding transition is no longer present in the model. Based on the results, different techniques are proposed to remove controllable and uncontrollable transitions, and an example shows the potential of the method for practical problems.

On Initialization of Iterative Algorithms For Nonlinear ARX Models

A challenging issue with parameter estimation for models that are nonlinear in parameters, is that in excess to the global minimum they may have local minima as well. As iterative algorithms are commonly used for identification of such models, finding proper initial values for these algorithms decreases the risk of ending up in local minima. In this contribution an algorithm to obtain a suitable candidate for initial values of an iterative algorithm when the model is nonlinear autoregressive model with exogenous (NARX model) is suggested. The algorithm is based on linearizing the nonlinear model structure and solving the mapping equations between the parameters of the corresponding linear model and nonlinear model. Note that since the method relies on the identification of a linearized model, the data must be selected so that a linear approximation works. In this way, an estimation of the unknown parameters of the nonlinear model can be obtained. The mapping between the linear and the nonlinear models may have one unique solution, no solution, or multiple solutions, and the paper explains and investigates these possible outcomes.