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This paper addresses the robust filtering problem of joint fault and state estimation for uncertain systems from the viewpoint of regularized least-square estimation. The method is based on the assumption that no prior knowledge about the dynamical evolution of the fault is available. Compared with earlier studies the robust criterion for least-square designs incorporate simultaneously both regularization and weighting and applies to a large class of uncertainties. The solution to the regularized least-square problem yields robust filter equations that perform regularization as opposed to de-regularization. The proposed filter is tested by an illustrative example.

No abstract

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.