Adaptive Observer Design for a Multi-State Reparable System

This paper is concerned with the problem of identification of both failure and repair rates of a multi-state reparable system. The mathematical model of such systems considered in this work is governed by coupled transport and integro-differential equations, which describe the probabilities of the system in good and failure modes. The failure and repair rates are two very important parameters associated with this type of systems, which are not always accessible, yet play critical roles in determining the system behaviors. The objective of this work is to utilize an adaptive observer to identify these parameters. Rigorous analysis on the convergence of the error dynamics is presented.