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Abstract: This paper designs an optimal controller for the simultaneous determination of physical model parameters and LQR controller parameters. In some systems, it is possible to determine some of the model parameters by the designer. In conventional methods of optimal controller design for this group of systems, first, the model parameters are determined by the designer, and then in a separate step, the controller is designed for the definite model. In this paper, a method for the simultaneous determination of these two sets of parameters is presented for continuous-time linear systems. Simultaneous parameter determination is a nonlinear and non-convex optimization problem that in this paper a new method is considered to solve this problem. The non-convex optimization problem is transformed into a convex optimization problem by performing simplifications and then solved by the CVX toolbox of MATLAB software. The result is a controller with less control cost in comparison to conventional methods for this group of systems. By providing a simulation example, the performance improvement of the proposed method is shown.

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In this paper, the problem of stabilization and synchronization of Lorenz and Chua chaotic in the presence of uncertainty using fractional order sliding mode control strategy based on nonlinear adaptation law has been investigated. Lorenz and Chua systems denote third order dynamics models which are chaotic for certain parameters. The proposed control law is composed of two prats sliding mode control and adaptive control law. Firstly, by supposing that instantaneous information of nonlinear part of chaotic system is not available, a linear regressor equation including an unknown section has been used. Using Lyapunov stability theorem and based on fractional calculus, adaptation law is developed to instantaneous estimation of unknown part. Moreover, by defining based on error signals and realizing exponential reaching law for insuring closed-loop stability, the sliding mode control law including equivalent and switching control has been derived. Eventually, the final control law has been derived by synthesizing sliding mode control and adaptive laws. The important aspect of the proposed approach is ability to encounter unstructured uncertainties and nonlinear effects of chaotic systems dynamic and guiding the state variables into sliding surface for arbitrary initial conditions. The performance of the proposed algorithm has been evaluated by realizing the stabilization problem of chaotic Lorenz system and synchronization of chaotic Lorenz and Chua systems.