Control
Yunes Mohamadi; Maryam Alipour; Akbar Hashemi Borzabadi
Abstract
The present paper proposes a novel numerical approach for approximating solutions to optimal control problems with parabolic constraints. Utilizing Laguerre polynomials as a novel basis set, a method was developed to address a class of this problem. The employment of these basis functions in conjunction ...
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The present paper proposes a novel numerical approach for approximating solutions to optimal control problems with parabolic constraints. Utilizing Laguerre polynomials as a novel basis set, a method was developed to address a class of this problem. The employment of these basis functions in conjunction with the collocation method facilitates the transformation of optimal control problems governed by parabolic constraints into a system of nonlinear algebraic equations. The present study proposes an efficient discretization and transformation of complex optimal control problems governed by parabolic equations into lower-dimensional algebraic systems by leveraging the unique properties of Laguerre polynomials.Convergence analysis has been demonstrated to ascertain the optimal value approximations of the proposed method. In order to provide a comprehensive illustration of the reliability and applicability of the proposed method, two illustrative examples are presented. The findings underscore the efficacy and precision of the implemented methodology. This work makes a significant contribution to the field by offering a robust framework for solving complex parabolic control problems, thereby demonstrating the potential of spectral methods in the context of optimal control theory.
Optimization
Maryam Alipour; Samaneh Soradi zeid
Abstract
This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these functions, product variable-order operational matrices have been ...
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This paper deals with a general form of fractional optimal control problems involving variable-order fractional integro differential equation using orthonormal Laguerre wavelets expansions. By effectively employing these functions, product variable-order operational matrices have been obtained. By using these fractional operational matrices and collocation points, the study transforms the original continuous-time optimal control problems of variable-order fractional integro-differential equations into a system of linear or non-linear algebraic equations. Attempts have been made to use the collocation method with a joint application of Lagrange multiplier technique, to obtain the approximate cost function based on determining the state and control functions. The main components for applying these wavelets is to have viable solutions due to their orthogonality. In addition, the convergence analysis is presented with respect to the operational matrices of this scheme. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort.
Control
Maryam Alipour; Pooneh Omidiniya
Abstract
This paper, proposes an approximate analytical method to solvea class of optimal control problems. This method is an enhancementof the variational iteration method (VIM) which is called modifi ed variational iteration method (MVIM) and eliminates all additional calculations in VIM, thus requires less ...
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This paper, proposes an approximate analytical method to solvea class of optimal control problems. This method is an enhancementof the variational iteration method (VIM) which is called modifi ed variational iteration method (MVIM) and eliminates all additional calculations in VIM, thus requires less time to do the calculations. In thisapproach, first, the optimal control problem is converted into a non-linear two-point boundary value problem via the Pontryagins maximum principle, and then we applied the MVIM method to solve this boundary value problem. This suggested method is suitable for a large class of non-linear optimal control problems that for the non-linear part of the problem, we used the Taylor series expansion. In the end, three examples are provided to demonstrate the simplicity and efficiency of the method. The numerical results of the proposed method versus other methods are presented in tables. All calculations were carried out using Mathematica software.
