On the control of discrete-event dynamical systems

Cover title.Includes bibliographical references.Supported by the Army Research Office. DAAL03-86-K-0171 Supported by a NSF PYI Award with matching funds from Bellcore, Inc.John N. Tsitsiklis

Language stability and stabilizability of discrete event dynamical systems

Abstract This paper studies the stability and stabilizability of Discrete Event Dynamical Systems (DEDS's) modeled by state machines. We define stability and stabilizability in terms of the behavior of the DEDS's, i.e. the language generated by the state machines (SM's). This generalizes earlier work where they were defined in terms of legal and illegal states rather than strings. The notion of reversal of languages is used to obtain algorithms for determining the stability and stabilizability of a given system. The notion of stability is then generalized to define the stability of infinite or sequential behavior of a DEDS modeled by a Büchi automaton. The relationship between the stability of finite and stability of infinite behavior is obtained and a test for stability of infinite behavior is obtained in terms of the test for stability of finite behavior. We present an algorithm of linear complexity for computing the regions of attraction which is used for determining the stability and stabilizability of a given system defined in terms of legal states. This algorithm is then used to obtain efficient tests for checking sufficient conditions for language stability and stabilizability

Stochastic Approximation Methods for Systems Over an Infinite Horizon

The paper develops efficient and general stochastic approximation (SA) methods for improving the operation of parametrized systems of either the continuous- or discrete-event dynamical systems types and which are of interest over a long time period. For example, one might wish to optimize or improve the stationary (or average cost per unit time) performance by adjusting the systems parameters. The number of applications and the associated literature are increasing at a rapid rate. This is partly due to the increasing activity in computing pathwise derivatives and adapting them to the average-cost problem. Although the original motivation and the examples come from an interest in the infinite-horizon problem, the techniques and results are of general applicability in SA. We present an updating and review of powerful ordinary differential equation-type methods, in a fairly general context, and based on weak convergence ideas. The results and proof techniques are applicable to a wide variety of applications. Exploiting the full potential of these ideas can greatly simplify and extend much current work. Their breadth as well as the relative ease of using the basic ideas are illustrated in detail via typical examples drawn from discrete-event dynamical systems, piecewise deterministic dynamical systems, and a stochastic differential equations model. In these particular illustrations, we use either infinitesimal perturbation analysis-type estimators, mean square derivative-type estimators, or finite-difference type estimators. Markov and non-Markov models are discussed. The algorithms for distributed/asynchronous updating as well as the fully synchronous schemes are developed

Sensor configuration selection for discrete-event systems under unreliable observations

Algorithms for counting the occurrences of special events in the framework of partially-observed discrete event dynamical systems (DEDS) were developed in previous work. Their performances typically become better as the sensors providing the observations become more costly or increase in number. This paper addresses the problem of finding a sensor configuration that achieves an optimal balance between cost and the performance of the special event counting algorithm, while satisfying given observability requirements and constraints. Since this problem is generally computational hard in the framework considered, a sensor optimization algorithm is developed using two greedy heuristics, one myopic and the other based on projected performances of candidate sensors. The two heuristics are sequentially executed in order to find best sensor configurations. The developed algorithm is then applied to a sensor optimization problem for a multiunit- operation system. Results show that improved sensor configurations can be found that may significantly reduce the sensor configuration cost but still yield acceptable performance for counting the occurrences of special events

Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

Generalised verification of the observer property in discrete event systems

The observer property is an important condition to be satisfied by abstractions of Discrete Event Systems (DES) models. This paper presents a generalised version of a previous algorithm which tests if an abstraction of a DES obtained through natural projection has the observer property. The procedure called OP-verifier II overcomes the limitations of the previously proposed verifier while keeping its computational complexity. Results are illustrated by a case study of a transfer line system