Analysis of fault tolerant control by using randomized algorithms

Active fault tolerant control systems (FTCS) can be modeled as stochastic systems with Markovian parameters. This paper addresses the modeling and analysis of such systems by using the randomized algorithms. Such algorithms are usually used to perform the robustness analysis or robust control synthesis based on a probabilistic notion. This paper extends the methods to jump linear systems (JLS) and stochastic FTCS for performance verification. It discusses how to set up a model for FTCS from the imperfect FDI parameters and how to transform it into a JLS model. Then, by combining the stationary distribution of the Markov process and specific performance at each state, it presents two algorithms to estimate probability given the performance requirement or estimate performance given the probability requirement. The performance analysis can reveal some valuable results on the influence of imperfect FDI and properties of integrated design, as illustrated in the examples.