Active Input Design to Balance Fault Diagnosis and Tracking Control Performance

The fault diagnosis module is usually integrated as a key component of active fault-tolerant control systems. However, the classical methods usually design fault diagnosis and control modules, separately, which ignore the existing interactions between the two key modules in active fault-tolerant control systems. In order to deal with this problem, this paper establishes a framework for integrated design of active fault diagnosis (AFD) and control while ensuring the performance of tracking control. In particular, the input is designed to balance the goal of AFD with the reference output tracking performance. The design of inputs is formulated to minimize the sum of a quadratic function and a non-convex quadratic fractional function at each step, whose global optimality can be obtained under the tighten condition of convex relaxation characterized by Frobenius norm of matrix. Furthermore, despite the global optimal condition is not always achieved, an enough satisfactory suboptimal solution could still be obtained, and the bound of suboptimality can be strictly guaranteed theoretically. At the end, a practical four-tank system example is used to verify the effectiveness of our proposed method.