Abstract-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 -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.
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-stateoutput 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).
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.
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