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Fault-Tolerant Output-Feedback Path Planning with Temporal Logic Constraints

In this paper, we consider searching for fault tolerant control strategies for linear systems to satisfy some high level requirements specified by linear temporal logic. By the term fault tolerant, we mean the obtained control strategy can respond to a fault that leads to a sudden change of the system dynamics. We first show how open-loop fault tolerant strategies (associated with each initial state) can be synthesized by leveraging Mixed Integer Linear Programming (MILP) based encodings used for linear temporal logic. These open-loop strategies, however, are not robust to the disturbances because of two reasons. First, since the disturbed system cannot be predicted precisely, the fault will be detected with a delay. Secondly, even if the faulty status is known, the true system trajectory may still deviate from the planned trajectory as the impact of the disturbance accumulates. To solve the two problems, we present a MILP formulation of the problem that incorporates finite detection delays, the open-loop strategy defined by the MILP's solution is then robustified with additional linear regulation.