In this thesis, a system-theoretic approach is utilized to improve the reliability of a discrete event dynamic system (DEDS) from the fault-tolerance viewpoint. We discuss decentralized optimal fault-tolerant supervisory control issues on the basis of failure analysis and diagnosis from the angle of DEDSs. The development of theory includes : state identification, failure analysis, fault-tolerant supervisory control, failure diagnosis, layered optimal supervisory control, nonhomogeneous decentralized supervisory control, stability analysis, and robust supervisory control.
First, we address the detectability problem for state identification and the observability problem for achievable legal languages. We also propose a systematic way for analyzing DEDSs to classify faults and failures quantitatively and to find tolerable fault event sequences embedded in the system. An automated failure diagnosis scheme with respect to the nominal normal operating event sequences and the supervisory control for tolerable fault event sequences are presented. Moreover, the supervisor failure diagnosis with respect to the tolerable fault event sequences is considered. Then a fault-tolerant supervisory control framework with partial observations is presented. Applications of the results to semiconductor manufacturing systems including the case study of a photolithographic process and a plasma etching process are described.
Next, we consider the optimal supervisory control problem here. A complete mincut of the flow network induced from the finite state machine of a DEDS is introduced so that the soluting of the optimal supervisory control problem, which is transformed into an optimal state space partitioning problem, also includes the marked languages. In addition, the procedure for finding the achievable or nonachievable layered optimal legal sublanguages is suggested for a preferential option among the reachable states in the controlled plant. A layered optimal supervisory control framework is proposed upon these and the previous plasma etching systme example is revisited to illustrate the proposed methods.
For the flexibility and the reduced complexity in the supervisor synthesis, the idea of decentralized control was incorporated into this area resulting in decentralized supervisory control where the global control task is achieved by the concurrent action of local supervisors. In the line of extension of the decentralized approach for the enhanced applications, we consider the problem of compatible combination of decentralized with centralized control (nonhomogeneous decentralized control) in case pure decentralized control (homogeneous decentralized control) becomes inadequate. We introduce the concepts of locally controllable pair and its candidate along with some deriving conditions. Then several fundamental theorems are presented and a framework for nonhomogeneous decentralized supervisory control systems is proposed based upon the theorems.
Summing up the foregoing developments, we formulate the analytical framework of decentralized optimal fault-tolerant supervisory control systems.
Afterward, we consider the traditional but inevitalbe issue in control system fields, the stability analysis. For this purpose, we first present a general stability concept for DEDSs, stability in the sense of Lyapunov with resiliency, by incorporating Lyapunov stability concepts with the concept of stability in the sense of error recovery. We also provide algorithms for verifying stability and obtaining a domain of attraction. Relations between the notion of stability and the notion of fault-tolerance are established. The proposed stability analysis approach is illustrated by reconsidering the plasma etching system example in this respect.
Upon the proposed stability concepts, we address the issue of robust stability and stabilizability. We assume that the plant G is not known exactly but we only know that it belongs to a set of models. In robust stability, we analyze the stability of the common invariant states set of all possible plant models. Then we derive the necessary and sufficient conditions for the robust stabilizability, i.e., the existence of a supervisor which makes the uncertain system robustly stable. The example of an assembly robotic cell is provided.
