In this paper, we present a new method for solving fractional optimal control problems with delays in state and control. This method is based upon Bernstein polynomials basis and feedback control. The main advantage of feedback or closed-loop control is that one can monitor the effect of such control on the system and modify the output accordingly. In this work, we use Bernstein polynomials to ...

Abstract Nonorthogonal polynomials have many useful properties like being used as a basis for spectral methods, generated in an easy way, having exponential rates of convergence, fewer terms and reducing computational errors comparison with some others, producing most important basic polynomials. In this regard, paper deals new indirect numerical method to solve fractional optimal control probl...

In this paper, we are concerned with the minimization problem of an integral functional integrand that is not convex in control on solutions a Riemann-Liouville fractional differential system mixed nonconvex feedback constraints control. At First, existence results for semilinear systems discussed by using Schauder's fixed point theorem. Under some reasonable assumptions, prove relaxation has o...

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The solution takes the form product consisting unknown coefficients and polynomials. Our main task is compute numerical values coefficients. To achieve goal, apply initial condition problem, Tau Lagrange multiplier methods. We do error ana...

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noetherlike theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define...

An efficient algorithm based on the wavelet collocation method is introduced in order to solve nonlinear fractional optimal control problems (FOCPs) with inequality constraints. By using interpolation properties of Hermite cubic spline functions, we construct an operational matrix Caputo derivative for first time. Using this matrix, reduce problem a programming that can be solved some suitable ...