Input design for discrimination between classes of LTI models

This paper addresses the design of input signals for the purpose of discriminating, within a given finite time interval, among a finite number of classes each of which represents a status of a system, e.g. a normal condition, fault type I, fault type II, etc. Each class contains a finite number of mathematical models that are designed to represent the system operating in the corresponding class. For given input-output data of the system, each class is evaluated by a hypothesis test and we search for an input signal that discriminates classes so that multiple classes cannot pass the test concurrently. This search, combined with other constraints on the input signal, is formulated as quadratic and nonconvex optimization problems. For a tractable computation of solutions to the optimization problems, we employ the semidefinite relaxation technique and identify the cases where this technique provides an optimal input signal. In other cases, we analyze the quality of suboptimal input signals produced by the technique.