Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices

Abstract

In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.

An approximate method for solving fractional optimal control problems by the hybrid of block‐pulse functions and Taylor polynomials

“…Examples 3 and 4 were also considered in the work of Keshavarz et al by applying Bernoulli polynomials. Example 5 is an FOCP with inequality constraints and was studied in the work of Alipour et al by using Bernstein polynomials. Examples 1 to 5 were also considered in the work of Mashayekhi and Razzaghi by applying the hybrid of block‐pulse functions and Bernoulli polynomials.…”

“…Although the optimal control theory is an area in mathematics that has been under development for many years, the fractional optimal control theory is a very new area in mathematics …”

Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials

“…For more details about the definition, properties and the convergence analysis of Bernstein polynomials see [2].…”

Approximate Analytical Solution of a Coupled System of Fractional Partial Differential Equations by Bernstein Polynomials

“…The applications of B Mohsen Alipour m.alipour2323@gmail.com; m.alipour@nit.ac.ir 1 fractional calculus have caught the attention of scientists in different disciplines round the world, see for examples [1][2][3][4][5][6][7]9,11,12,14,15,17,21,22].…”

“…We have been influenced by the recent contributions of the scientists [1,4,6,15,21,22] and have aimed to get the numerical solution of the following PDEFO by the help of operational matrices of BPs:…”