| This thesis develops a reliability-based framework for the analysis and design of Fault Tolerant Control Systems (FTCS's). The proposed reliability index is defined based on control objectives and hard deadline. For analysis purpose, a semi-Markov model is built from dynamical model, and stochastic transitions of Markov states describe degradation of system conditions among a finite set of states. This reliability index incorporates the characteristics of FTCS's, and can be used as a probabilistic criterion on overall system performance in long term.;The proposed reliability index and evaluation method are based on the Markov modeling of fault occurrence and Fault Detection & Isolation (FDI) schemes. But Markov models accept only the exponential distribution, which causes a memoryless restriction. To remove this restriction, a semi-Markov description is adopted as a general model for cyclic FDI schemes. Furthermore, the reliability modeling and evaluation method are extended for this general model of FTCS's.;In the last part, a reliability monitoring scheme is developed. The reliability index is defined based on system dynamical responses and a safety boundary; FDI history data is used to update its transition characteristics and reliability model. This method provides an up-to-date reliability index as demonstrated on an aircraft model.;Two reliability-based design methods are developed using this new reliability index as an optimization objective. The design difficulty lies in the fact that the index can be evaluated from a numerical procedure only but lacks analytical expressions. To address this problem, the first method considers stabilizing controller parameterization and randomized algorithm techniques to find the statistically optimal controller with respect to reliability. The second design method is based on a two-stage design scheme: A gradient-based search is first carried out on probabilistic Hinfinity performance characteristics for reliability requirement; a sequential randomized algorithm with a weighted violation function is then developed for controller design to satisfy the required Hinfinity , performance, and its convergence is guaranteed with probability 1. |
