Applications of stochastic techniques to partially observed discrete event systems.
David Thorsley · Deep Blue (University of Michigan) · 2006
In order to address questions like fault diagnosis and optimization in large, complex systems, it is necessary to have a proper understanding of how information develops in such systems and what information is necessary in order to solve particular problems. Such a treatment of information is well developed in the theory of stochastic systems, but less so in the theory of discrete-event systems (DES). In this thesis we apply facets of stochastic systems theory to DES. Three distinct major problems are considered. The first is the question of diagnosability of stochastic DES. The notions of A- and AA-diagnosability are defined for stochastic automata and conditions for A- and AA-diagnosability are determined through the construction of a stochastic diagnoser. The second problem, the active acquisition of information problem, relates to how to optimally schedule measurements so as to minimize the observation cost necessary to control a system or diagnose a failure within it. A cost is incurred each instant a sensor is activated in an attempt to observe an event, and the objective is to minimize either the worst-case cost (for logical DES) or expected cost (stochastic DES) required in order to detect a failure. The solution of this problem requires properly defining an information state for DES and the construction of a proper sequence of information sigma-fields. Dynamic programming used the information sigma-fields to find an optimal solution. The final problem concerns intrusion detection in centralized and decentralized supervisory control systems. The control action implemented by a supervisor may fail as a result of an intruder interfering with the system's performance and, as a result, strings that the supervisor wished to disable may be executed. Conditions for ensuring that all illegal strings can be disabled in the presence of intrusion are presented. A language measure technique is used to assess the potential damage an intruder can cause. Optimal control specifications are determined by constructing appropriate information states and using dynamic programming.