Stochastic stability analysis for fault tolerant control systems with multiple failure processes

Abstract

A new dynamical model is developed here to study the stochastic stability of Fault Tolerant Control Systems (FTCS) with multiple failure processes. In particular, two independent failure processes with Markovian characteristics are considered: one for plant component failures and the other for actuator failures. In this model, the Fault Detection and Isolation (FDI) process is also formulated as a Markov process with transition probabilities conditioned on the current state transition probabilities of the two failure processes. It is shown that the exponential stability in the mean square is su cient for almost sure asymptotic stability. In addition, a necessary and su cient condition for exponential stability in the mean square for FTCS is derived. Some previously known results are shown to be special cases of this new result. Failures in actuators with internal dynamics are also considered. A numerical example is included to demonstrate the theoretical analysis.

Active Fault Tolerant Control Systems

“…The vital issue of environmental noises and how they a ect the overall performance of FTCSMP was studied in 128 . FTCSMP with multiple fault processes was de ned to account for independent faults in di erent system components in 122, 129 . Imperfections in the performanceof the FDI algorithms including detection delays, false alarm and errors in detection were also considered in 125 .…”

Stability conditions for discrete time fault tolerant control systems with state delays

“…This unique modeling allows the consideration of practical implementation issues and physical limitations of a particular FTCSMP. Stability properties of FTCSMP in the presence of noise, detection errors, detection delays, parameter uncertainties and actuator saturation were studied in [8], [9] and [10]. A comprehensive review of the stochastic stability and stabilization of continuous Mufeed Mahd@uml.edu AFTCSMP using Lyapunov function approach can be found in [11].…”

Stability analysis of discrete fault tolerant control systems with parameter uncertainties

“…This unique modeling allows the consideration of practical implementation issues and physical limitations for a particular system to be controlled. were studied in [8], [9] and [10]. A comprehensive review of the stochastic stability and stabilization of continuous FTCSMP using Lyapunov function approach can be found in [11].…”