In this study, we propose a secure communication scheme based on the synchronization of two identical fractional-order chaotic systems. The fractional-order derivative is in Caputo sense, and for synchronization, we use a robust sliding-mode control scheme. The designed sliding surface is taken simply due to using special technic for fractional-order systems. Also, unlike most manuscripts, the ...

‎In this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (PMSM) system. The necessary condition for the existence of chaos in the fractional-order PMSM system is deduced and an active controller is developed based on the stability theory for fractional systems. The presented control scheme  is simple and flexible, and it is suitable both fo...

This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operat...

The paper presents an error estimate for RungeKutta direct discretizations of terminal optimal control problems for linear systems. The optimal control for such problems is typically discontinuous, and Lipschitz stability of the solution with respect to perturbations does not necessarily hold. The estimate (in terms of the optimal controls) is of first order if certain recently obtained suffici...

the aim of this paper is to design a fractional order sliding mode controllers (fosmc)for a class of dc-dc converters such as boost and buck converters. firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. secondly, themathematical proof of the stabilit...

We investigate a class of fractional neutral evolution equations on Banach spaces involving Caputo derivatives. Main results establish conditions for the controllability fractional-order system and existence solution to an optimal control problem minimum energy. The are proved with help fixed-point semigroup theories.

In this article, we discuss fractional order optimal control problems (FOCPs) and their solutions by means of rational approximation. The methodology developed here allows us to solve a very large class of FOCPs (linear/nonlinear, time-invariant/time-variant, SISO/MIMO, state/input constrained, free terminal conditions etc.) by converting them into a general, rational form of optimal control pr...

We introduce a formulation for the time-optimal control problems of systems displaying fractional dynamics in the sense of the Riemann-Liouville fractional derivatives operator. To propose a solution to the general time-optimal problem, a rational approximation based on the Hankel data matrix of the impulse response is considered to emulate the behavior of the fractional differentiation operato...

This paper present the development of new tuning method and performance for Genetic Algorithm based Fractional order PID controller ,fractional order PID controller include the conventional order PID controller parameter. The tuning of the PID controller is mostly done using Zeigler and Nichols tuning method. All the parameters of the controller, namely p K (Proportional gain), i K (integral ga...