Changyan Zhou

Semantic Translation of Simulink Diagrams to Input/Output Extended Finite Automata

We develop a semantic translation approach for Simulink diagrams. Simulink is a graphical tool for representing and simulating dynamical systems. We propose a recursive approach for translating a class of Simulink diagrams to input/output-extended finite automata (I/O-EFA). An I/O-EFA model of a Simulink diagram can be used for further analysis such as test generation and formal verification. We show that the translation approach is sound and complete: The input-state-output behavior of an I/O-EFA model, as defined in terms of a step-trajectory, preserves the input-state-output behavior of the corresponding Simulink diagram at each sample time (assuming the same integration method for any of the continuous blocks with dynamics).

Polynomial synthesis of supervisor for partially observed discrete-event systems by allowing nondeterminism in control

We study the supervisory control of discrete-event systems (DESs) under partial observation using nondeterministic supervisors. We formally define a nondeterministic control policy and also a control & observation compatible nondeterministic state machine and prove their equivalence. The control action of a nondeterministic supervisor is chosen online, nondeterministically from among a set of choices determined offline. Also, the control action can be changed online nondeterministically (prior to any new observation) in accordance with choices determined offline. The online choices, once made, can be used to affect the set of control action choices in future. We show that when control is exercised using a nondeterministic supervisor, the specification language is required to satisfy a weaker notion of observability, which we define in terms of recognizability and achievability. Achievability serves as necessary and sufficient condition for the existence of a nondeterministic supervisor, and it is weaker than controllability and observability combined. When all events are controllable, achievability reduces to recognizability. We show that both existence, and synthesis of nondeterministic supervisors can be determined polynomially. (For deterministic supervisors, only existence can be determined polynomially.) Both achievability and recognizability are preserved under union, and also under intersection (when restricted over prefix-closed languages). Using the intersection closure property we derive a necessary and sufficient condition for the range control problem for the prefix-closed case. Unlike the deterministic supervisory setting where the complexity of existence is exponential, our existence condition is polynomially verifiable, and also a supervisor can be polynomially synthesized.

Decentralized modular diagnosis of concurrent discrete event systems

The problem of decentralized modular fault diagnosis of concurrent discrete event systems, that is composed of a set of component modules, is formulated and studied. In the proposed decentralized modular framework, diagnosis is performed by the local diagnosers, located at the component sites, using their own local observations. This is to ensure the scalability of the approach with respect to the number of component modules, and we require that the local diagnosers be ldquomodularly computablerdquo, i.e., their computation should be based on the local models, and not the global models. It is also required that there are no missed-detections (every fault is detected within a bounded number of transitions) and no false-alarms (a fault detection report is issued only when a fault has occurred). We formally define the decentralized modular diagnosis problem and introduce the notion of modular diagnosability as a key property for the existence of desired decentralized modular diagnosers. We show that under this property, the complexity for constructing the local diagnosers is polynomial in the number of local modules. We present a method for testing the modular diagnosability property by reducing it to an instance of a certain codiagnosability property for which known verification techniques exist.

Control of nondeterministic discrete-event systems for bisimulation equivalence

This paper studies supervisory control of discrete event systems subject to specifications modeled as nondeterministic automata. The control is exercised so that the controlled system is simulation equivalent to the (nondeterministic) specification. Properties expressed in the universal fragment of the branching-time logic can equivalently be expressed as simulation equivalence specifications. This makes the simulation equivalence a natural choice for behavioral equivalence in many applications and it has found wide applicability in abstraction-based approaches to verification. While simulation equivalence is more general than language equivalence, we show that existence as well as synthesis of both the target and range control problems remain polynomially solvable. Our development shows that the simulation relation is a preorder over automata, with the union and the synchronization of the automata serving as an infimal upperbound and a supremal lowerbound, respectively. For the special case when the plant is deterministic, the notion of state-controllable-similar is introduced as a necessary and sufficient condition for the existence of similarity enforcing supervisor. We also present conditions for the existence of a similarity enforcing supervisor that is deterministic.

Computation of Diagnosable Fault-Occurrence Indices for Systems with Repeatable-Faults

We study discrete-event systems prone to such faults which can occur repeatedly. For the diagnosis of re- peatable faults, [5] introduced the notion of l-diagnosability requiring the diagnosis of the lth occurrence of a fault within a bounded delay. The present paper studies the identification of the set of all indices a for which the system is l-diagnosable. (These are precisely the occurrence indices for which a repeatable-fault can be diagnosed.) We first present a test to verify whether a fault is diagnosable for each occurrence index, i.e., whether it is “∀l-diagnosable”. For systems that fail this test, we further present a method to compute the set of all indices l for which the system is not l-diagnosable.

Control of Nondeterministic Discrete Event Systems for Simulation Equivalence

Most prior work on supervisory control of discrete event systems is for achieving deterministic specifications, expressed as formal languages. In this paper we study supervisory control for achieving nondeterministic specifications. Such specifications are useful when designing a system at a higher level of abstraction so that lower level details of system and its specification are omitted to obtain higher level models that may be nondeterministic. Nondeterministic specifications are also meaningful when the system to be controlled has a nondeterministic model due to the lack of information (caused for example by partial observation or unmodeled dynamics). Language equivalence is not an adequate notion of behavioral equivalence for nondeterministic systems, and instead we use the finest known notion of equivalence, namely the bisimulation equivalence. Choice of bisimulation equivalence is also supported by the fact that bisimulation equivalence specification is equivalent to a specification in the temporal logic of /spl mu/-calculus that subsumes the complete branching-time logic CTL*. Given nondeterministic models of system and its specification, we study the design of a supervisor (possibly nondeterministic) such that the controlled system is bisimilar to the specification. We obtain a small model theorem showing that a supervisor exists if and only if it exists over a certain finite state space, namely the power set of Cartesian product of system and specification state spaces. Also, the notion of state-controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor. In the special case of deterministic systems, we provide an existence condition that can be verified polynomially in both system and specification states, when the existence condition holds.

Finite bisimulation of reactive untimed infinite state systems modeled as automata with variables

Some discrete event systems such as software are typically infinite state systems, and a commonly used technique for performing formal analysis such as automated verification is based on their finite abstractions. In this paper, we consider a model for reactive untimed infinite state systems called input-output extended finite automaton (I/O-EFA), which is an automaton extended with discrete variables such as inputs, outputs, and data. Using I/O-EFA as a model many value-passing processes can be represented by finite graphs. We study the problem of finding a finite abstraction that is bisimilar to a given I/O-EFA. We present a sufficient condition under which the underlying transition system of an I/O-EFA admits a finite bisimilar quotient. This sufficient condition is existential as it relies on the existence of a suitable partition of the state space. We then identify a class of I/O-EFAs for which a partition satisfying our sufficient condition can be constructed by inspecting the structure of the given I/O-EFA.

Decentralized modular control of concurrent discrete event systems

The paper studies decentralized modular control of concurrent discrete event systems that are composed of multiple interacting modules. A modular supervisor consists of a set of local supervisor modules, one for each plant module and which determines its control actions based on the locally observed behaviors. No communication among local supervisor modules occurs in the setting of decentralized modular control. In this paper we introduce the notion of separable-controllability, a property strictly stronger than controllability and separability combined, as a condition for the existence of a decentralized modular control, and present a way to verify this property. We show that non-unique maximal separably- controllable sublanguages and the unique minimal closed and separably-controllable superlanguage of a specification language exist. These serve as an upper bound (resp., the lower bound) for a restrictive (resp., relaxive) decentralized modular control. We present modular computations for synthesizing a restrictive as well as a relaxive decentralized modular control. When appropriate we also compare our results with the existing ones.

Modeling Simulink Diagrams Using Input/Output Extended Finite Automata

We develop a modeling approach for Simulink diagrams. Simulink is a commercial graphical representation tool for representing and simulating dynamical systems. We propose a recursive approach for modeling a class of Simulink diagrams as input/output-extended finite automata (I/O-EFA). A model of a Simulink diagram can be used for further analysis such as test generation and formal verification. The modeling approach is sound and complete: The input-output behavior of an I/O-EFA model, as defined in terms of a step-trajectory, preserves the input-output behavior of the corresponding Simulink diagram at each sample time.

Bisimilarity Enforcement for Discrete Event Systems Using Deterministic Control

For discrete event systems, the control to enforce bisimilarity with respect to a given specification has been studied in , , . In this note we consider the case when the control is required to be deterministic. While a deterministic control is restrictive compared to a nondeterministic one, the case of deterministic control has its own practical significance as it is easier to implement and computationally less expensive to verify. We provide a necessary and sufficient condition for the existence of a bisimilarity enforcing deterministic control, and discuss its computational complexity. We also study properties related to the synthesis of “subspecification” and “superspecification”.