Input design for model discrimination and fault detection via convex relaxation

This paper addresses the design of input signals for the purpose of discriminating among a finite set of models of a dynamic system within a given finite time interval. A motivating application is fault detection and isolation. We propose several specific optimization problems with objectives or constraints based on signal power, signal amplitude, and probability of successful model discrimination. Since these optimization problems are nonconvex, we suggest a suboptimal solution via a random search algorithm guided by the semidefinite relaxation (SDR) and analyze the accuracy of the suboptimal solution. We conclude with a simple example taken from a benchmark problem on fault detection for wind turbines.