Among the methods of the multi-source navigation filter, as a distributed method, the federated filter has a small calculation amount with Gaussian state noise, and it is easy to achieve global optimization. However, when the state noise is time-varying or its initial estimation is not accurate, there will be a big difference with the true value in the result of the federated filter. For the systems with time-varying noise, adaptive filter is widely used for its remarkable advantages. Therefore, this paper proposes a federated Sage–Husa adaptive filter for multi-source navigation systems with time-varying or mis-estimated state noise. Because both the federated and the adaptive principles are different in updating the covariance of the state noise, it is required to weight the two updating methods to obtain a combined method with stability and adaptability. In addition, according to the characteristics of the system, the weighting coefficient is formed by the exponential function. This federated adaptive filter is applied to the SINS/CNS/GNSS integrated navigation, and the simulation results show that this method is effective.

An integral sliding mode fault‐tolerant control method is proposed to deal with faults with matched uncertainties, unmatched uncertainties, and input saturation. Integral sliding mode, control allocation, and parameter identification are included in this method. The Lyapunov stability conditions of the integral sliding mode control for uncertainties and input saturation, respectively, are obtained, which denote the robustness extent of the controller. The direct method for control allocation is improved by adding a judgement before calculating for each facet. Finally, the fault‐tolerant scheme is applied to a six‐wheel spacecraft and simulations are given to show its effectiveness.

This article addresses the quantitative fault diagnosability evaluation for dynamic systems without distribution knowledge. The system dynamics in different cases are first characterized by mean vectors and covariance matrices. Then, fault detectability and isolability are defined based on the constructed characteristics. On this basis, the Mahalanobis distance (MD) is employed to propose a fault diagnosability analysis measure. Furthermore, model-based and data-driven algorithms for fault diagnosability evaluation are given according to the MD-based measure. In addition, the reliabilities of the evaluation results are considered by taking advantage of ambiguity sets of mean vectors and covariance matrices of the system dynamics. Finally, two examples are employed to verify the effectiveness of the proposed algorithms.

This note addresses reconfiguration-based fault-tolerant control with robust guaranteed performance for nonlinear uncertain systems under actuator faults. A PAssive/ACTive combined fault-tolerant control method is proposed based on reliable control, which synthesizes the advantages of the active and passive fault-tolerant control and strikes a balance between the performance and complexity of the method. Moreover, the reliability overcost of this method is reduced to balance the system nominal performance and reconfigurability. In this procedure, the $\theta$ -D method is used to solve the Hamilton-Jacobi-Bellman and generalized Hamilton-Jacobi-Bellman equations. Effectiveness of the proposed method is verified by a numerical example.

Weak fault signals, high coupling data, and unknown faults commonly exist in fault diagnosis systems, causing low detection and identification performance of fault diagnosis methods based on $T^2$ statistics or cross entropy. This paper proposes a new fault diagnosis method based on optimal bandwidth kernel density estimation (KDE) and Jensen–Shannon (JS) divergence distribution for improved fault detection performance. KDE addresses weak signal and coupling fault detection, and JS divergence addresses unknown fault detection. Firstly, the formula and algorithm of the optimal bandwidth of multidimensional KDE are presented, and the convergence of the algorithm is proved. Secondly, the difference in JS divergence between the data is obtained based on the optimal KDE and used for fault detection. Finally, the fault diagnosis experiment based on the bearing data from Case Western Reserve University Bearing Data Center is conducted. The results show that for known faults, the proposed method has $10\%$ and $2\%$ higher detection rate than $T^2$ statistics and the cross entropy method, respectively. For unknown faults, $T^2$ statistics cannot effectively detect faults, and the proposed method has approximately $15\%$ higher detection rate than the cross entropy method. Thus, the proposed method can effectively improve the fault detection rate.