Set-based guaranteed active fault diagnosis for LPV systems with unknown bounded uncertainties

Abstract This paper focuses on designing, via the minimization of a suitable cost function, an input sequence to guarantee active fault diagnosis (AFD) of discrete-time linear parameter-varying systems regardless of how the scheduling variables change in the scheduling set. Convex polyhedrons are used to characterize the sets of system uncertainties such that the designed input sequence leads to outputs which are consistent with a unique fault mode or healthy mode. Considering the smoothness and energy of the input sequence simultaneously, the optimal input sequence is obtained by solving a family of linear constrained quadratic programming (LCQP) problems in a brute-force way, which will lead to inefficiency when the number of facets of the interest region becomes large. In order to handle this problem, by analyzing a geometric property of the objective function, the original optimization problem is shown to be equivalent to the minimization of the radius of a hypersphere containing the origin based on a simple linear mapping, which is much more efficient than the brute force-based resolution. At the end of this paper, a numerical example and a vehicle model are used to illustrate the effectiveness of the proposed method.