The paper presents a new method of performing integrator backstepping in systems that are discontinuous, either due to their inherent structure or because of the applied control input. The proposed technique is applied to the stabilization problem of the dynamic system of a nonholonomic mobile robot. Simulation studies indicate that the methodology can also help alleviate the problem of chatter...

A nonlinear feedback path controller for a differential drive mobile robot is presented in this paper. First, a kinematic model in error coordinates expressed in a moving reference frame partially linked to the robot is developed. The control law is designed using backstepping method yielding exponential stability of the closed-loop system. Stability analysis is performed via Lyapunov stability...

The problem of course control for underactuated surface ship is addressed in this paper. Firstly, neural networks are adopted to determine the parameters of the unknown part of ideal virtual backstepping control, even the weight values of neural network are updated by adaptive technique. Then uniform stability for the convergence of course tracking errors has been proven through Lyapunov stabil...

This paper deals with the problem of suppression of stick-slip oscillations in oil well drill-strings. The backstepping technique is used to design two control schemes for the system. The first controller is a typical backstepping controller; the second controller is a sliding back-stepping controller. Moreover, a reduced order observer is proposed to estimate the unmeasurable states of the sys...

Abstract: This paper presents the backstepping nonlinear control applied to induction motor with on-line adaptation of rotor resistance using a backstepping observer type. This type of control proposed an analysis based primarily on the stability of the system from the Lyapunov theory. This approach takes into account the nonlinearity of the system when designing the control law. The effectiven...

In this paper, the authors derive a Dirichlet boundary control law that stabilizes a reaction-diffusion equation (a more general one than what is usually understood by``heat equation'') with arbitrary number of unstable modes in open-loop. Although interesting in its own right, this result is not as important as the technique used, which, the authors claim, generalizes backstepping/feedback lin...

In this paper, a new synchronization scheme, combination synchronization, is used to realize reduced order function projective synchronization among three chaotic Josephson junction systems using backstepping technique. In the first case, function projective synchronization of two (2) third order drive systems with a single second order Josephson junction is considered while in the second case,...

Abstract: In this paper, we show that adaptive controllers designed using the standard backstepping technique proposed in Krstic [1995] globally stabilize a class of uncertain systems with unknown input time delay and unmodeled dynamics. As such systems belong to nonminimum phase systems and thus our result extends the class of systems stabilizable from minimum phase systems when the standard b...

We introduce a new method for the design of observers for nonlinear systems using backstepping. The method is applicable to a class of nonlinear systems slighter larger than those treated by Gauthier, Hammouri, and Othman [IEEE Trans. Automat. Control, 27 (1992), pp. 875– 880]. They presented an observer design method that is globally convergent using high gain. In contrast to theirs, our obser...

Many real-world systems are governed by the timedependent, nonlinear differential equations. Dynamics of an electrical system are also best described using the very equations. Being one of the preferred machines when using advanced control algorithms for electric drives, DC motor has been selected for position tracking. Defining dynamic equations of the motor derived from the theory of nonlinea...