Input Design for Guaranteed Fault Diagnosis Using Zonotopes

An input design method is presented for guaranteeing the diagnosability of faults from the outputs of a system. Faults are modeled by discrete switches between linear models with bounded disturbances and measurement errors. Zonotopes are used to efficiently characterize the set of inputs that are guaranteed to lead to outputs that are consistent with at most one fault scenario. Provided that this set is nonempty, an element is then chosen that is minimally harmful with respect to other control objectives. This approach leads to a nonconvex optimization problem, but is shown to be equivalent to a mixed-integer quadratic program that can be solved efficiently. Methods are given for reducing the complexity of this program, including an observer-based method that drastically reduces the number of binary variables when many sampling times are required for diagnosis.