In this paper we propose a Fractional Order Controller for an under-actuated system (POAC). This system has two degrees-of-freedom and one control input. The model of the system is derived using Euler Lagrange method and the stabilization is achieved with constraints using Fractional Order Controller. To validate the control law, simulation are performed and compared with Integer Order Controll...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong t...

In this paper a fractional order PI controller (FOPI) is proposed for the speed control of Permanent Magnet Synchronous Motor(PMSM). Fractional calculus is introduced into the PI controller, and proposes a robust fractional order PI controller (FOPI) for the speed control of a PMSM .PMSM drive system is a nonlinear system which is sensitive to load disturbance, parameter variation, unmodelled a...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

This article deals with the optimal control of fractional stochastic nonlocal semilinear system in Hilbert space. The existence and uniqueness results for mild solution are derived using Banach fixed point theorem. is proved minimizing sequence approach Mazur?s lemma. For better understanding theory, we have included one example.

In this paper, a fractional order universal high gain adaptive stabilizer is proposed which guarantees the Lp stability of fractional order multiple–input and multiple–output (MIMO) systems with finite control effort. The boundedness of the control gain for the fractional order universal adaptive strategy is discussed for fractional order MIMO systems, and an upper bound of the control gain is ...