This paper extends the application of continuous Chebyshev wavelet expansions to find the optimal solution of linear timevarying systems using two different approaches. By using the product of two time functions together with the operational matrix of integration, the system of state equations are changed into a set of algebraic equations which can be solved using a digital computer. In addition, the Chebyshev wavelets are more successful to find the optimal solution of linear time-varying systems when compared with the other existing mentioned algorithms. Finally, the main feature of this paper over similar possible works is that the use of the Lagrange multipliers approach gives more accurate results in comparison with the results of the Riccati approach. The given examples support these claims.
In the present research, Iterative Feedback Tuning (IFT) algorithm is employed to tune a type of fractional order Proportional-Integral-Derivative (PID) [Formula: see text] controller. For this purpose, fractional order calculus is introduced and some important principles are represented. Then, IFT algorithm is presented in a general form. Following it, IFT algorithm is derived to tune the specific type of PID. The relevant update law is calculated for the fractional order controller. Finally, the proposed algorithm is tested on a Hardware in Loop (HIL) system, that is, Ball Levitation (BL) system, and the efficiency of the proposed method is verified via experiments.
In this paper, a suitable hybrid iterative scheme for solving a class of non-linear optimal control problems (NOCPs) is proposed. The technique is based upon homotopy analysis and parametrization methods. Actually an appropriate parametrization of control is applied and state variables are computed using homotopy analysis method (HAM). Then performance index is transformed by replacing new control and state variables. The results obtained from the given method are compared with the results which are obtained using the spectral homotopy analysis method (SHAM), homotopy perturbation method (HPM), optimal homotopy perturbation method (OHPM), modified variational iteration method (MVIM) and differential transformations. The existence and uniqueness of the solution are presented. The comparison and ability of the given approach is illustrated via two examples.
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