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The present paper proves chaos phenomenon for a range of parameters in attitude dynamic of a satellite and designs an appropriate nonlinear controller, while ensuring optimal system performance, the controller guarantees control of a chaotic state. As the dynamic equations of a three-axis satellite are defined as a nonlinear non-autonomous system, a technique is offered for calculating the Lyapunov exponents of such systems that may express the system’s chaotic state. Using the technique, the chaotic behavior of a system is proved within a range of parameters. Then a back-stepping sliding mode controller is proposed based on the desired performance and the closed-loop system stability is proved based on the Lyapunov’s theorem. Moreover, converting the system into a compatible form with the conditions of the Melnikov theorem using this analytical method ensures removing chaos phenomenon in the controlled system. Calculating Lyapunov exponents of the closed system confirms this issue. Finally, the simulation results obtained from the proposed controlling actions for different work fields are presented.

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The dynamic equations of an autonomous underwater vehicle (AUV) are described as a nonlinear system with multiple hydrodynamic coefficients which strongly affect the performance, maneuverability and controllability of AUV. On the other hand, the values of these coefficients depend on the vehicle speed and the geometric properties. In this paper, the nonlinear model identification problem of NPS AUV II, as a six degree-of-freedom (DOF) autonomous underwater vehicle, is addressed by using the nonlinear continuous-time extended Kalman filter (EKF) observer with guaranteed convergence. To this end, the hydrodynamic coefficients of AUV are considered as the augmented state variables of a six DOF nonlinear model. Based on the input-output data at the presence of the measurement noise of sensors, the state variables and the hydrodynamic coefficients of the nonlinear model in a (path) helical maneuver, are suitably estimated by using the EKF observer. In order to analyze the numerical performance of the proposed method, the dynamic equations of the vehicle are introduced, and a comparison is made between the identified model outputs and those of the real model.

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In this paper, the problem of robust stabilization of uncertain and perturbed switched nonlinear systems has been investigated. It’s well-known that the solution of H_∞ control problem may not exist for switched systems with a common storage function for all subsystems. On the other hand, by adopting multiple storage functions, different Hamilton-Jacobin inequalities need to be solved. Hence, the robust control problem is addressed here based on passivity, in two cases. First, it is assumed that there is at least one passive subsystem in the whole state space, and the problem is solved based on the average dwell time approach. In this case, by defining the concept of system passivity rate, the admissible range of average dwell time is obtained. In the second case, none of subsystems is passive and the H_∞ control problem is solved by using the feedback passification. In addition to theoretical analysis of the design algorithms, the performance of the theorems for uncertain switched nonlinear systems has been investigated by providing two simulation examples and numerical analysis.