Towards a Convex Design Framework for Online Active Fault Diagnosis of LPV Systems

This paper focuses on the design of on-line optimal input sequence for robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems using set-theoretic methods. Instead of the traditional set-separation constraint conditions leading to the design of off-line input sequence, the proposed approach focuses on on-line (re)shaping of the input sequence based on the real-time information of the output to discriminate system modes at each time instant such that the conservatism of robust AFD has the potential to be further reduced. The criterion on the design of optimal input is characterized based on a non-convex fractional programming problem at each time instant, which is shown to be efficiently solved within a convex optimization framework. Aside this main contribution, by exploiting Lagrange duality, the optimal input is explicitly obtained by solving a characteristic equation. At the end, a physical circuit model is provided to illustrate the effectiveness of the proposed method.