Michael Heymann

Supervisory control of concurrent discrete-event systems

Abstract When a discrele-event system P consists of several subsystems P1,...,Pn which operate concurrently, a natural approach to the supervisory control problem is to synthesize a ‘local’ controller Si , for each subsystem Pi , and operate the individually controlled subsystems Si/Pi concurrently. Such an approach is called concurrent supervisory control and is closely related to decentralized supervisory control as studied by Cieslak et al. (1988) and Lin and Wonham (1988). In the present paper simple and easily computable conditions are developed which guarantee that concurrent supervisory control can achieve the optimal behaviour achievable by a global supervisor. To achieve this, two specific concurrent control strategies are introduced.

Concurrency and discrete event control

Much of discrete event control theory has been developed within the framework of automata and formal languages. An alternative approach inspired by the theories of process-algebra as developed in the computer science literature is presented. The framework, which rests on a new formalism of concurrency, can adequately handle nondeterminism and can be used for analysis of a wide range of discrete event phenomena.<<ETX>>

Linear feedback : an algebraic approach

The algebraic theory of linear input–output maps is reexamined with the objective of accomodating the concept of (state) feedback in this theory. The concepts of extended and restricted linear i/o maps (and linear i/s maps) are introduced and investigated. It is shown how “fraction representations” of transfer matrices arise naturally in this new theoretical framework.Conditions are given for when the change caused to a linear input-output map by an (open loop) “cascade compensator” can also be accomplished by utilization of (closed loop) state feedback. In particular, it is shown that the change caused to a linear input-output map by cascading (composing) it with an input space isomorphism, can also be effected by feedback, provided the input space isomorphism in “bicausal”, i.e. it does not change the causal structure of the input-output map. Further detailed characterizations of feedback are also given especially in connection with the newly introduced concepts of degree chain and degree list.

FORMAL VERIFICATION OF HUMAN-AUTOMATION INTERACTION

This paper discusses a formal and rigorous approach to the analysis of operator interaction with machines. It addresses the acute problem of detecting design errors in human-machine interaction and focuses on verifying the correctness of the interaction in complex and automated control systems. The paper describes a systematic methodology for evaluating whether the interface provides the necessary information about the machine to enable the operator to perform a specified task successfully and unambiguously. It also addresses the adequacy of information provided to the user via training material (e.g., user manual) about the machines behavior. The essentials of the methodology, which can be automated and applied to the verification of large systems, are illustrated by several examples and through a case study of pilot interaction with an autopilot aboard a modern commercial aircraft. The expected application of this methodology is an augmentation and enhancement, by formal verification, of human-automation interfaces.

Linear feedback decoupling--Transfer function analysis

The problem of linear system decoupling is examined based on recent results on linear feedback. New insight is obtained, through which resolution of the decoupliug problem is accomplished by calculations, performed directly on the given transfer matrix. Computation of the decoupling compensators follows by easy constructions. The problem of feedback block decoupling with internal stability, is also formulated and resolved.

Stabilization of discrete-event processes

Discrete-event processes are modelled by state-machines in the Ramadge-Wonham framework with control by a feedback event disablement mechanism. In this paper concepts of stabilization of discrete-event processes are defined and investigated. We examine the possibility of driving a process (under control) from arbitrary initial states to a prescribed subset of the state set and then keeping it there indefinitely. This stabilization property is studied also with respect to ‘open-loop’ processes (i.e. uncontrolled processes) and their asymptotic behaviour is characterized. To this end, such well known classical concepts of dynamics as invariant sets and attractors are redefined and characterized in the discrete-event control framework. We provide polynomial time algorithms for verifying various types of attraction and for the. synthesis of attractors.

Comments "On pole assignment in multi-input controllable linear systems"

It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenbergers type for asymptotic state identification.

Discrete-event control of nondeterministic systems

Nondeterminism in discrete-event systems occurs in many practical situations and often as a result of partial observability of events. For the adequate description of nondeterministic systems and nondeterministic phenomena, the trajectory-model formalism was introduced by Heymann (1991) and Heymann et al. (1991). This formalism has been used in by Shayman et al. (1995) for obtaining various results on supervisory control of nondeterministic systems subject to language specifications. In the present paper we develop a theory of supervisory control for nondeterministic discrete-event systems subject to both language and trajectory-model specifications. We further show how well-known algorithms for supervisory control (of deterministic systems) under partial observation can be adapted for synthesis of supervisors for nondeterministic systems subject to both language and trajectory-model specifications.

On-Line Control of Partially Observed Discrete Event Systems

It is well known that the design of supervisors for partially observed discrete-event systems is an NP-complete problem and hence computationally impractical. Furthermore, optimal supervisors for partially observed systems do not generally exist. Hence, the best supervisors that can be designed directly for operation under partial observation are the ones that generate the supremal normal (and controllable) sublanguage. In the present paper we show that a standard procedure exists by which any supervisor that has been designed for operation under full observation, can be modified to operate under partial observation. When the procedure is used to modify the optimal full-observation supervisor (i.e., the one that generates the supremal controllable language), the resultant modified supervisor is at least as efficient as the best one that can be designed directly (that generates the supremal normal sublanguage). The supervisor modification algorithm can be carried out on-line with linear computational complexity and hence makes the control under partial observation a computationally feasible procedure.

Two-dimensional robot navigation among unknown stationary polygonal obstacles

The authors describe an algorithm for navigating a polygonal robot, capable of translational motion, in an unknown environment. The environment contains stationary polygonal obstacles and is bounded by polygonal walls, all of which are initially unknown to the robot. The environment is learned during the navigation process by use of a laser range-finding device, and new knowledge is integrated with previously acquired information. A partial map of the environment, containing parts of the obstacles that were seen by the robot and the free space between them, is obtained. The obstacles in the map are transformed into a new set of expanded polygonal obstacles, allowing the robot to be treated as a point, and the navigation problem is reduced to point navigation among unknown polygonal obstacles. A navigation graph is built from the transformed obstacles and used to search for a piecewise linear path to the destination. The algorithm is proved to converge to the desired destination in a finite number of steps provided a path to the destination exists. >