A fast numerical algorithm based on alternative orthogonal polynomials for fractional optimal control problems

A fast numerical algorithm based on alternative orthogonal polynomials for fractional optimal control problems

In this paper, we focus on alternative Legendre polynomials (ALPs) in fractional calculus area and obtain the operational matrix of the Riemann-Liouville fractional integration for the first time. To solve the problem, first the fractional optimal control problem (FOCP) is transformed into an equivalent variational problem, then using the alternative Legendre polynomials basis, the problem is reduced to the problem of solving a system of algebraic equations. With the aid of an operational matrix of Riemann-Liouville fractional integration, Gauss quadrature formula and Newton’s iterative method for solving a system of algebraic equations, the problem is solved approximately. Some examples are given to demonstrate the validity and applicability of the our technique and a comparison is made with the existing results.

In this paper, we focus on alternative Legendre polynomials (ALPs) in fractional calculus area and obtain the operational matrix of the Riemann-Liouville fractional integration for the first time. To solve the problem, first the fractional optimal control problem (FOCP) is transformed into an equivalent variational problem, then using the alternative Legendre polynomials basis, the problem is reduced to the problem of solving a system of algebraic equations. With the aid of an operational matrix of Riemann-Liouville fractional integration, Gauss quadrature formula and Newton’s iterative method for solving a system of algebraic equations, the problem is solved approximately. Some examples are given to demonstrate the validity and applicability of the our technique and a comparison is made with the existing results.