Approximate Evaluation of Reliability and Related Quantities via Perturbation Techniques

The evaluation of the reliability, stability, and performance of fault tolerant control systems (FTCS) is considered. New sufficient conditions for stochastic stability of FTCS with standard Markovian component failure behavior and Markovian failure detection decision behavior are derived. By specia...

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Bibliographic Details
Main Authors: Walker, Bruce K, Srichander, Ramaswamy
Format: Report
Language:English
Subjects:
CONFIGURATIONS
CONTROL SYSTEMS
DETECTION
FAILURE
FAULT TOLERANCE
FAULTS
INVARIANCE
LINEAR SYSTEMS
MARKOV PROCESSES
MEAN
NUMERICAL ANALYSIS
Numerical Mathematics
NUMERICAL METHODS AND PROCEDURES
Operations Research
PE61102F
PERTURBATIONS
RELIABILITY
SEQUENTIAL ANALYSIS
STABILITY
STATISTICAL TESTS
STOCHASTIC PROCESSES
SYSTEMS ANALYSIS
TEST AND EVALUATION
TIME
TOLERANCE
WUAFOSR2304A5
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Summary:The evaluation of the reliability, stability, and performance of fault tolerant control systems (FTCS) is considered. New sufficient conditions for stochastic stability of FTCS with standard Markovian component failure behavior and Markovian failure detection decision behavior are derived. By specializing these results to the class of linear time-invariant (LTI) FTCS with linear state feedback control laws that are reconfigured by switching the feedback gain matrix according to the identified failure configuration, the stability results are strengthened to necessary and sufficient conditions for stochastic stability of a special type (exponential in mean square) that implies a very strong sense of stability (a.s. in probability). An approximate feedback control design technique for LTI FTCS is then proposed and demonstrated on a simple numerical case. In addition, previous results on semi-Markov analysis of FTCS reliability are used to derive a numerical method for establishing approximately optimal failure detection test thresholds for sequential failure detection tests. This method, though approximate, is shown to yield thresholds that provide a considerable increase in system reliability relative to those provided by a method based on a rigorously derived reliability approximation for one numerical example.