Toward a Convex Design Framework for Online Active Fault Diagnosis of LPV Systems
Junbo Tan, Sorin Olaru, Feng Xu, Xueqian Wang
Abstract
This article focuses on the design of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">online</i> optimal input sequence for robust active fault diagnosis of discrete-time linear parameter-varying systems using set-theoretic methods. Instead of the traditional set-separation constraint conditions leading to the design of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offline</i> input sequence, the proposed approach focuses on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">online</i> (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 diagnosability of system has potential to be further improved. The criterion on the design of optimal input is characterized based on a nonconvex fractional programming problem at each time instant, which is shown to be efficiently solved within a convex optimization framework. In addition to 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.