Backstepping is a technique developed for designing stabilizing controls for a special class of nonlinear dynamical systems. It is built from subsystems that radiate out from an irreducible system which can be stabilized using some other method. This method is based directly on the mathematical model of the examined system. It is developed by introducing new variables into it in a form dependin...

This paper proposes a fuzzy-identification-based adaptive control scheme for the chaotic dynamic systems using backstepping control approach, which is referenced as adaptive fuzzy backstepping control (AFBC). The proposed AFBC offers a design approach to drive the chaotic trajectory to track a desired trajectory, and it is comprised of a fuzzy backstepping controller and a robust controller. Th...

At present, robotic manipulators are commonly used in manufacturing industry. In many cases, their end-effectors are required to move from one place to the other and follow some desired trajectories. This paper develops a nonlinear backstepping control design scheme with velocity observers for the trajectory tracking control of robotic manipulators. In fact, most of robot manipulator controller...

Promulgated by some with religious-like fervor, viewed with skepticism by others, adaptive control has for almost forty years been one of the most alluring, intriguing, and often misunderstood areas within the eld of automatic control. In truth, despite its present shortcomings fe.g., its failure to adequately address performance issuesg adaptive control has come quite a long way since rst conc...

The problem under study is a synthesis of position and heading control system for low frequency model of surface vessel described by 3 DOF mathematical model. The recursive vectorial backstepping control design was used to keep fixed position and heading in presence of wave disturbances. The controller has been simulated on computer model of scaled supply vessel. It has been assumed that the ac...

A novel Lyapunov function, which contains a concept of transfer function, was constructed to prove the rightness of a new kind of robust backstepping filter derivative control method. Meanwhile, the relationship between Lyapunov function and transfer function was established, which is an important concept that can be applied in a large family of control systems. Also, the backstepping design te...

We solve both the global practical stabilization and tracking problem for an underactuated ship, using a combined integrator backstepping and averaging approach. Exponential convergence to an arbitrarily small neighbourhood of the origin and of the reference trajectory, respectively, is proved. Simulation results are included. R esum e: Nous r esolvons a la fois la stabilisation globale et le p...

In this paper, we study the tracking control problem for a nonlinear system in which the zero dynamics may be unstable. The objective here is to approximate the nonlinear system by another singularly perturbed system by using a small singular perturbation parameter  . The proposed approach is based on the methodology of exact input output linearization control, the integrator backstepping appr...

| This paper addresses the control problem of hydraulic robot manipulators. The backstepping design methodology is adopted to develop a novel nonlinear position tracking controller. The tracking errors are shown to be exponentially stable under the proposed control law. The controller is further augmentedwith adaptation laws to compensate for parametric uncertainties in the system dynamics. Acc...

We consider a problem of stabilization of the linearized Schrödinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control desig...