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A new operational design for hierarchical control of discrete-event systems is proposed. The design brings the structure of command and control from concept to realization for online control operation. For a command reference input, a new concept for output control feasibility of a discrete-event system modeled by a Moore automaton is characterized; and a system decomposition of a suitably structured Moore automaton into a controllable subsystem and an uncontrollable subsystem is formulated. Based on these results, the new command and control design for controller operation is realized, examined, and discussed.Note to Practitioners-In the academic literature, the command and control theory of hierarchical control for discrete-event systems is well established for meeting control specifications of safety with nonblockingness. This paper proposes a new operational design that uses the two-level structure of high-level command and low-level control, hitherto only a theoretical concept, for online translation of command to control during runtime hierarchical control. The design is realized with a two-level control algorithm and a reusable "control technology" for the real discrete-event system at the low level, developed using the fresh theoretical findings in this paper. As the first steps in filling the theory-to-practice gap, the practical advantages of this new operational design include facilitating a deeper understanding of control with online causal clarity of command over control, and a significant reduction in offline synthesis complexity with fast online control computation. In laying an algorithmic foundation for online hierarchical control, the proposed design has potential applications for many engineering control problems, where command and control is the inherent mode of runtime operation, or is needed to provide operational clarity when subjecting the control system to validation tests by simulation and observation. Problems include the design of logical command and control systems for supervising smart grids, traffic light systems and mass rapid transit networks, where the manager in the central command center may issue high-level commands to the operators to control the low-level physical system. Index Terms-Discrete-event systems (DESs), formal languages and automata, hierarchical control, online supervision.

In the existing paradigm of formal languages and finite automata, the hierarchical control setup for untimed discrete-event systems (untimed DES's) is a standard high-level command and low-level control structure, and timed DES's (TDES's) can be modeled by a class of automata called timed transition graphs (TTG's) incorporated with time fidelity. In this paper, using the same hierarchical control setup, with the TDES at the low level modeled by a Moore TTG with time fidelity, supporting concepts are proposed for a timed version of the concept of output-control consistency for hierarchical control. Importantly, this new timed consistency concept also preserves the time fidelity of the resultant system model at the high level, and lays a time fidelity foundation for extending the consistency of hierarchical control in untimed DES's to TDES's.Index Terms-Hierarchical control, timed discrete-event systems, formal languages and finite automata.978-1-4799-5283-0/14/$31.00 ©2014 IEEE

The control framework of hierarchical consistency of timed discrete-event systems (TDES's) is investigated in a standard two-level hierarchy. Real-time concepts and the associated theoretical results supporting consistent TDES hierarchies are developed. Where the given low-level system model of the hierarchy possesses time fidelity, a consistency version that assures time fidelity of the high-level system model is also developed. Importantly, this version furnishes a sound real-time high-level specification design foundation for hierarchical control. An example illustrates the new time-fidelity control foundation. Given that in general, a given two-level TDES hierarchy is not hierarchically consistent between the levels, the structural existence and synthesis of the sufficiency structure for hierarchical consistency is investigated. Both the timed versions of hierarchical consistency -without and with output-time fidelity guarantee -are successively treated. The abstraction or output-system refinement procedures for the version without output-time fidelity guarantee are first developed for a class of TDES hierarchies under mild output-system design restrictions. The abstraction methods for the version with output-time fidelity are then developed for a subclass 'linearly' structured under further output-system design restrictions. A detailed example explains and illustrates the use of an overarching method developed.Keywords Hierarchical control ¨timed discrete-event systems ¨formal languages ¨finite automata. IntroductionUnder the general framework of formal languages and finite (or finite-state) automata, the seminal concept of hierarchical consistency for logical or untimed discrete-event systems (DES's) (Zhong and Wonham, 1990) is suitably extended to timed DES's (TDES's) in this paper. In a two-level, untimed hierarchical control setup, conceptualized in (Zhong and and algorithmically realized in (Ngo and Seow, 2014a), the system at the low level drives the system at the high level which is an abstraction of the former, via an information channel modeled by a hierarchical reporter map. Depicted in Fig. 1, this setup consists of two horizontal levels of standard feedback control which are vertically interconnected so that a manager at the high level (or high-level supervisor) can issue commands to an operator at the low level (or low-level supervisor) to control a real DES modeled by a Moore automaton (Eilenberg, 1974), in response to information of interest sent up from the low level to the high level. By hierarchical consistency between the levels (Zhong and , a low-level supervisor implementing feasible commands issued (or virtual controls) at the high level can fully realize a controllable prefix-closed specification task (Ramadge and Wonham, 1987) prescribed at the high level. The importance of hierarchical control stems from the fact that, in general, a hierarchical structure conforms better to practice and renders a given system more manageable for system specification and control in terms of large-sca...

for the structural existence and synthesis of the sufficiency structure for hierarchical consistency with no output-time fidelity guarantee are developed. It is then shown that a class of Moore TDES's exists whose structure can be refined to achieve hierarchical consistency with output-time fidelity, and is a linear subclass of a mildly restrictive class of TDES's whose structure can be refined to achieve hierarchical consistency with no output-time fidelity guarantee.