Finite Horizon Control Design for Optimal Model Discrimination

In many fault detection and system identification problems, it is essential to be able to discriminate between a number of competing models of a system based on observed system outputs. For example, in a fault detection scenario we may wish to determine whether a system is best modeled by a known nominal model, or a known failure model. The probability of detecting the true system model can be enhanced by design of the control inputs applied to the system. In this paper we present a method by which a finite sequence of control inputs is designed automatically in order to minimize an upper bound on the probability of model selection error between any two linear, discrete-time systems. We are able to solve this problem efficiently by showing that it is an instance of a Quadratic Program. In addition, linear equality and inequality constraints can be applied to the control inputs and expected system state. These constraints can be used to ensure that a certain task is fulfilled, make sure the system stays within a valid linearization region, or to guarantee safe operation. Experimental results for the case of an aircraft actuator failure scenario show that the method significantly reduces the upper bound on the probability of model selection error when compared to a manually generated sequence and a fuel-optimal sequence.