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In this paper the goal is to identify the parameters of the Lorenz chaotic system, based on synchronization of identical systems using fractional calculus. The method which is used for synchronization is come from Lyapunov stability theorem and then by using fractional dynamics, control laws are improved. To this end, a Lyapunov function is presented and based on the Lyapunov stability theory and asymptotic stability criteria, some adaptation laws to estimate unknown parameters of the system are proposed. The introduced method is applied to the Lorenz chaotic system and since the goal is identification, all the parameters of the system are taken unknown. Using invariant set theory, it is proved that the parameter estimation errors converge to zero. Then the results of numerical simulations are shown and discussed and it is observed that fractional calculus has an essential effect on reducing fluctuations and settling time of the parameters convergence. At the end, the stability of the system by using fractional adaptation law is discussed. It is shown that the asymptotic stability of the synchronization error dynamics is proved using the fractional adaptation law, and this is confirmed through simulation.

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In this study, the control problem of a knee rehabilitation robot is examined. The main drawback of rehabilitation facilities, such as continuous passive motion, is the lack of feedback from the interaction force between the robot and patient leg. This means that if during the exercises, an unvoluntary motion by patient is generated, the increased interaction force can then damage the patient leg. The interaction force is increased because the robot tries to hold the patient leg along the prescribed reference path. In the current paper, to realize the compliant behavior of the robot, the concept of admittance along with two control methods including adaptive model reference and integral backstepping will be utilized. Adopting admittance control method, the robot will deviate the prescribed path so that the interaction force can be decreased. The obtained simulation results reveal the good performance of the robot even in the presence of noisy sensory data. Additionally, it has been shown that the proposed combined admittance and backstepping controller has better performance, in terms of tracking error and decrease of interaction force, as compared with the model adaptive reference model.