Finite Horizon Control Design for Optimal Discrimination between Several Models

Multiple-model fault detection is a powerful method for detecting changes, such as faults, in dynamic systems. In many cases, the ability of such a detection scheme to distinguish between possible models for the system dynamics depends critically on the control inputs applied to the system. Prior work has therefore aimed to design control inputs in order to improve fault detection. We previously developed a new method that uses constrained finite horizon control design to create control inputs that minimize an upper bound on the probability of model selection error. This method is limited, however, to the problem of selection between two models. In this paper we describe a new method that extends this approach to handle an arbitrary number of models. By optimizing subject to hard constraints, the new method can ensure that a defined task is fulfilled, while optimally discriminating between models. This means that the discrimination power of the designed control input can be much greater than that created by other approaches, which typically design ´auxiliary´ signals with limited power so that the effect on the system state is small. Furthermore, the optimization criterion, which is an upper bound on the probability of model selection error, has a more meaningful interpretation than alternative approaches that are based on information gain, for example. We demonstrate the method using an aircraft fault detection scenario and show that the new method significantly reduces the bound on the probability of error when compared to a manually generated identification sequence and a fuel-optimal sequence