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The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler–Lagrange equations. An iterative method is also proposed to numerically solve the obtained equations from the necessary optimality conditions. Two illustrative examples are considered and simulated in order to show the applicability and efficiency of the proposed method. Numerical simulations show that the used method presents some satisfying results regarding the absolute error values. [ABSTRACT FROM AUTHOR]

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results. [ABSTRACT FROM AUTHOR]

In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement. [ABSTRACT FROM AUTHOR]