Large Deviations for the Reliability Assessment of Redundant Multi-Channel Systems

In this paper, we are concerned with the reliability assessment of redundant multi-channel systems having multiple controllers with overlapping functionality -- where all controllers are required to respond optimally to the non-faulty controllers so as to ensure or maintain some system properties. In particular, for such redundant systems with small random perturbation, we study the relationships between the exit probabilities with which the state-trajectories exit from a given bounded open domain and the value functions corresponding to a family of stochastic exit-time control problems on the boundary of the given domain. Moreover, as the random perturbation vanishes, such relationships provide useful information concerning the reliability of the redundant multi-channel systems arising from the large deviations problem in connection with the asymptotic estimates of exit probabilities with respect to some portions of the boundary of the given domain. Finally, we briefly comment on the implication of our results on a co-design technique using multi-objective optimization frameworks for evaluating the performance of the redundant multi-channel systems.