In supervisory control of timed discrete-event systems (TDESs), a conceptually well founded finitary control synthesis framework is developed, and it requires specifications to be prescribed as finite (-trace) automata in the form of timed transition graphs (TTGs). However, prescribing real-time specifications as TTGs is a nontrivial task that must be resolved before the formal framework could expect to become widely used. In addressing this specification problem, metric temporal logic (MTL) is proposed in this paper as a control specification language for use with the TTG-based control synthesis framework. MTL is a designer-friendly formalism due to its human or natural language expressiveness and readability, and is well suited for specifying real-time control specifications. In automating TTG prescription, this paper proposes an MTL interface to the control synthesis framework. The interface is proved to be a correct and complete translation algorithm that converts finitary control specifications written in state-based MTL formulas for a given TDES model into deterministic finite TTGs. Integrated, the MTL interface and the control synthesis framework combine the human expressiveness and readability of MTL with the algorithmic computability of TTGs, and together provide a new and convenient MTL specification-based design tool for automated prescription of TTGs and real-time control synthesis. Illustrative examples demonstrate the utility of the MTL interface.
In control of discrete-event systems (DESs), specifying control requirements in automata is not a trivial task. For many DES applications, designers are often confronted with the long-standing problem of uncertainty in specification, namely, how do we know that a specification automaton does indeed model the intended control requirement? Toward a formal framework that helps mitigate this uncertainty for designer comprehensibility, in this paper, we introduce and develop a new specification concept of automaton transparency and investigate the problem of maximizing the transparency of specification automata for DESs. In a transparent specification automaton, events that are irrelevant to the specification but can occur in the system are "hidden" in self-loops. Different automata of the same specification on a DES can be associated with different sets of such irrelevant events, and any such automaton is said to be the most transparent if it has an irrelevant event set of maximal cardinality. The transparency maximization problem is theoretically formulated, and a provably correct solution algorithm is obtained. Given a specification automaton for a DES, the transparent specification automaton produced by the algorithm is a more comprehensible structure, essentially showing the precedence ordering among events from a minimal cardinality set that is relevant in modeling some requirement for the DES, and should aid designers in clarifying if the requirement prescribed is the one intended.
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