Combining LTL monitoring with model invalidation for improved fault detectability analysis for hybrid systems

Abstract

In this work, we consider detectability analysis for faults in systems governed by switched affine dynamics. By a fault, we mean a sudden and permanent change in the system dynamics. Given the model of the healthy system, such a fault can be detected via a model invalidation approach, i.e., by collecting historic observations over a finite horizon and checking whether these observations can be generated by the healthy system model. Whenever the faulty system model is also available, it is possible to find T, the minimum length of the horizon, with which the fault is guaranteed to be detected eventually (with a T-delay at most). The main contribution of this work is to show the possibility of reducing the value of T, by augmenting the fault detectability analysis with additional linear temporal logic (LTL) constraints on the switching signals, if any. We express the LTL constraints (restricted in a finite horizon) with a nondeterministic finite automaton (NFA), which is then transformed into a set of mixed integer linear constraints that can be easily integrated in the detectability analysis.