Active Fault Diagnosis via Reachable Set Separation using Interval Methods

This paper presents an optimization-based approach for active fault isolation in linear time invariant systems subject to additive disturbances which are bounded in intervals. We model the evolution of the system states and outputs using interval dynamics with the input signals also bounded within given intervals. The proposed approach is based on determining a sequence of control actions to minimize a function which quantifies the overlap of output intervals, while taking into account the prescribed input bounds. The resulting optimization problem is nonconvex, yet the cost function has Lipschitz-continuous gradient and the constraints are simple, which allows us to solve them efficiently. A numerical example is used to illustrate the implementation and suitability of the proposed optimization approach for active fault isolation.