This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-tostate stability (ISS) of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay’s inequality. Estimates on the set ...

We present an adaptive observer design for a first-order hyperbolic system of Partial Differential Equations with uncertain boundary parameters. The design relies on boundary measurements only, and is based on a backstepping approach. Using a Gradient Descent technique, we prove exponential convergence of the distributed system and estimation of the parameter. This method is applied to the esti...

This paper presents a smooth sliding mode control plus backstepping method for the motion/force control of a constrained robotic manipulator with flexible joints. The control scheme is presented based on that overall system parameters are with uncertainties whereas only the constrained force, positions and velocities of links and rotors are measurable. The smooth sliding controller can achieve ...

This paper describes how to use backstepping to develop control laws to perform trajectory tracking for a nonlinear, underactuated surface vessel. The research extends earlier backstepping designs for underactuated vessels by explaining how to select outputs when generalized forces act on the vessel. The resulting control law can correct orientation errors to track linear trajectories and can t...

In this paper we present a PID+ backstepping controller, as a solution to the problem of coordinated attitude control in spacecraft formations. The control scheme is based on quaternions and modified Rodriguez parameters as attitude representation of the relative attitude error. Utilizing the invertibility of the modified Rodriguez parameter kinematic differential equation, a globally exponenti...

Robust adaptive control of nonlinear systems with unknown state delay A robust dynamic inversion technique for asymptotic tracking control of an aircraft Non-linear control of variable-speed wind turbines with permanent magnet synchronous generators: a robust backstepping approach A new robust nonlinear control algorithm for the regulation of blood glucose in diabetic patients Robust backsteppi...

The position tracking control of induction motors with parameter uncertainties and load torque disturbance is addressed. Neural networks are employed to approximate the nonlinearities and an adaptive backstepping technique is used to construct controllers. The proposed adaptive neural controllers guarantee that the tracking error converges into a small neighborhood of the origin. Compared with ...

. On considère une classe de systèmes non-linéaires pour lesquels la technique de synthèse par backstepping n’est pas applicable. On présente un critère pour la synthèse d’une commande hybride faisant l’union d’une commande par backstepping et d’une commande locale. Cette commande hybride rend le système bouclé globalement asymptotiquement stable. Le critère de sélection repose sur le choix de ...