Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

Abstract

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.

Optimal Control of Non-linear Volterra Integral Equations with Weakly Singular Kernels Based on Genocchi Polynomials and Collocation Method

“…method based on Genocchi Polynomials involves the discretization of both the cost function (1) and the controlled integral equation with weakly singular kernels (2). Firstly, we implement a spectral approach based on the Genocchi polynomials to solve equation (2).…”

“…method based on Genocchi Polynomials involves the discretization of both the cost function (1) and the controlled integral equation with weakly singular kernels (2). Firstly, we implement a spectral approach based on the Genocchi polynomials to solve equation (2). We compute the following integral for m = 0, 1, … to apply the propounded approach for approximating the system dynamics in (2) We assume…”

“…Firstly, we implement a spectral approach based on the Genocchi polynomials to solve equation (2). We compute the following integral for m = 0, 1, … to apply the propounded approach for approximating the system dynamics in (2) We assume…”

“…Spectral methods have been widely employed to solve mathematical models that arise in various fields, such as heat conduction, quantum mechanics, and fluid dynamics [1]. These methods use different infinitely differentiable orthogonal functions as trial functions, which lead to various spectral approaches [1,2]. The high accuracy of these approaches has led to their widespread use in solving many Asiyeh Ebrahimzadeh and Elham Hashemizadeh have contributed equally to this work.…”