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...

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether’s theorem to fractional optima...

A control problem for a linear stochastic system with an arbitrary fractional Brownian motion and a cost functional that is quadratic in the system state and the control is solved. An optimal control is given explicitly as the sum of a prediction of the future fractional Brownian motion and the well known linear feedback control for the associated deterministic linear-quadratic control problem....

Abstract: This study aims to generate a model for the problem of beamforming in fractional Fourier domain, through which a general solution for obtaining weighted beamforming in fractional Fourier domain for different criteria might be delivered. In order to generate this model, a description of fractional delay concept is presented, through which the string vector in fractional Fourier domain ...

Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonline...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

Abstract We study the optimal feedback control for fractional evolution equations with a nonlinear perturbation of time-fractional derivative term involving Caputo derivatives arbitrary kernels. Firstly, we derive mild solution in terms semigroup operator generated by resolvents and kernel from general operators establish existence uniqueness solutions systems. Then, feasible pairs applying Fil...