Semidefinite programming relaxation of optimum active input design for fault detection and diagnosis: Model-based finite horizon prediction

This paper establishes optimal/suboptimal active fault detection and diagnosis (FDD) methods in which semidefinite programming relaxation is used and the optimality criteria are information theoretic measures of the statistical distance between probability distributions. The design problems are formulated as optimizations in which an optimal sequence of inputs within a prediction horizon is computed for maximizing the statistical discrimination of different models of fault scenarios. Three different measures for the degree of statistical distinguishability between two hypothesized stochastic dynamical system models are considered and their mathematical properties that are related to Bayesian hypothesis tests are studied. The resulting input design problems are non-convex and we propose associated convex relaxation methods that can be solved in polynomial time using interior point methods. Numerical simulations with an aircraft model are provided to illustrate and demonstrate the presented methods of optimal input design for FDD.