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The problem of rigid-body attitude tracking in the presence of exogenous disturbances is addressed. Attitude is parameterized using the rotation matrix, an element of the Special Orthogonal Group SO(3), as it provides a singularity-free and unambiguous attitude description. The closed-loop stability and robustness properties of a PD-type state-feedback control law, proposed in literature for attitude tracking using rotation matrices, are investigated using the nonlinear H∞ control framework. Starting from a dissipation inequality, sufficient conditions are derived which ensure that the closed-loop energy gain from bounded, finite-energy exogenous disturbances to a specified error signal respects a given upper bound. Then, the sufficient conditions are reformulated using the state and input matrices for the translational double integrator, and recast as linear matrix inequalities (LMIs). Lastly, the reformulated LMIs are used to synthesize controller gains for the proportional and derivative state-feedback terms in the original SO(3) control law. The controller synthesis problem for a microsatellite is considered as a case study. The controller gains are obtained using the proposed LMI-based procedure, and the tracking and disturbance rejection capabilities of the SO(3) controller are illustrated.

This paper deals with the design of an Active Fault Tolerant Control (AFTC) approach for polytopic uncertain Linear Parameter-Varying (LPV) systems subject to uncertainties and actuator faults. First, a fault estimation method is developed by integrating robust observer design with zonotopic techniques. The proposed observer is developed using L∞ norm to attenuate the effects of the uncertainties and to improve the accuracy of the estimation. Then, an AFTC strategy is used to compensate actuator fault effect and maintain system stability. Finally, the effectiveness of the proposed method is demonstrated by a case study on a 4.8MW wind turbine benchmark system.

•The problem of square-rooting in high-degree cubature Kalman filters is addressed for nonlinear continuous-discrete stochastic systems.•The overall SR solution in the realm of the unscented and cubature Kalman filters is devised by means of hyperbolic QR decompositions.•The new square-root fifth-degree cubature Kalman filter implementations are examined in estimating an aircraft executing a coordinated turn in the presence of Gaussian noise and ill-conditioned measurements. This paper addresses the problem of square-rooting in the Cubature Kalman Filtering (CKF) originated from Arasaratnam and Haykin in 2009. Presently, this technique has been accommodated to various cubature rules, including high-degree ones. Since its discovery the CKF has become one of the most powerful state estimation methods because of outstanding performance and robustness in numerous engineering applications. Its high-degree versions are shown to be accurate and even comparable to particle filters, which are considered to be among the most effective algorithms for treating nonlinear stochastic systems. However, the lack of square-root implementations within high-degree CKFs makes them vulnerable to round-off and other errors committed because of a potential covariance matrix positivity loss, which may encounter in practice. This shortcoming affects severely and fails high-degree CKFs since the Cholesky factorization of predicted and filtering covariances underlying the filters in use may not be fulfilled for indefinite matrices. Here, we resolve it by means of hyperbolic QR transforms applied for yielding J-orthogonal square roots. Our novel square-root algorithms are justified theoretically and examined and compared numerically to the existing non-square-root CKF and some other available filters in a simulated flight control scenario, including that with ill-conditioned measurements.

This work deals with the robustness analysis of LPV (Linear Parameter-Varying) systems. The degree of robustness of a system makes possible to know if the defined level of performance is guaranteed or not. The robustness of a system is characterized by its capacity to reject perturbations, by criterion of speed, of precision or by taking into account a certain degree of imprecision of the model, often introduced during a necessary phase of linearization. It is then necessary to manipulate relatively sophisticated models in order to take all these parameters into account. The representation of the LPV systems is such a sophisticated modeling. Fuzzy Takagi–Sugeno, polytopic and norm-bounded representations are often used to describe the behavior of nonlinear dynamics of the system. This paper proposes a generic model that encompasses these representations (fuzzy TS, polytopic and norm-bounded). This generic model is denoted uncertain BPV (Bi-linear Parameter Varying). A robustness analysis technique, allowing the generation of a robustness criterion, is then proposed. It can be applied to the case of state or output feedback, as well as to paremeter-dependent controllers. The concept of D-stability is considered and the tools are expressed in terms of LMI.