In order to bridge between fractional-order and integer order nonlinear dynamical system, in this letter, we brings attention to synchronization and anti-synchronization between fractional-order chaotic system and integer-order chaotic system by using back-stepping method. And the sufficient conditions for achieving the synchronization and anti-synchronization of a class of fractional-order non...

Adaptive back stepping control (ABC) is originally applied to a linearized model of an active magnetic bearing (AMB) system. Our control goal is to regulate the deviation of the magnetic bearing from its equilibrium position in the presence of an external disturbance and system uncertainties. Two types of ABC methods are developed on the AMB system. One is based on full state feedback, for whic...

This article presents the motion control of nonholonomic two-wheeled differential drive portable robot in terms dynamic and kinematic model. The main problem lies demonstration a versatile behavior. controller is planned two sections, initially, linear configured utilizing PID strategy. In subsequent stage, algorithm designed back-stepping controller. An examination has been done between contro...

This paper address a novel method for nonholonomic Wheeled Mobile Robot (NWMR) trajectory tracking using a hybrid controller. In the essential of the proposed scheme, hybrid algorithm includes fuzzy logic based Regulation, Pole-Placement and Tracking (F-RST). The hybrid controller easily track the reference trajectory and linearize the nonlinear behavior of robot under the influence of uncertai...

In this paper, a robust forwarding control technique is introduced for a class of uncertain nonlinear systems admitting the so-called up-augmented structure. This technique gives a recur-sive design procedure which yields a smooth controller. Further, it can be combined with the well-known back-stepping technique to solve the robust stabilization problem for a large class of uncertain nonlinear...

In this paper, a feedback boundary controller for an unstable heat equation is designed. The boundary control law is designed in the form of an integral operator with a known, continuous kernel function which can be interpreted as a back stepping control law. This interpretation provides a Lyapunov function for proving stability of the system. The control is applied by insulating one end of the...