This paper presents an improved backstepping control implementation scheme for a n-dimensional strictfeedback uncertain nonlinear system based on command filtered backstepping and adaptive neural network backstepping. In this approach, n command filters and one neural network are applied to reconstruct the approximations of unknown nonlinearities which are related to the system uncertainties including the system's unmodeled dynamics and external disturbances. Then, one can use the negative feedback of these approximations to compensate the system uncertainties. Moreover, convex optimization and soft computing technique are adopted to design the update law of the weights of the neural network, and Lyapunov stability criterion is used to prove the stability of the closedloop system. Finally, simulation results are given to show the effectiveness of the proposed methods.

This paper presents an adaptive neural network backstepping control design for an experimental helicopter with three rotational degrees-of-freedom. The helicopter system is described by a state-space model with unmodeled dynamics and external disturbances. By resorting to radial basis function neural networks with on-line gradient descent training, such unmodeled dynamics and external disturbances can be compensated in real time. With the help of Lyapunov stability criteria, it is proved that the desired trajectories can be boundedly tracked by the corresponding attitude angles of the helicopter under the proposed adaptive neural network backstepping controller. Compared with robust adaptive integral backstepping technique, our approach has smaller root-mean-squared-error. Finally, four sets of contrastive experiment results are respectively given to show the effectiveness and advantages of the proposed control scheme.

In this paper, the swing-up and stabilization control problems for a rotary inverted pendulum system are solved via new control schemes, in which the swing-up strategy is designed by using trajectory planning and inertia effect such that the pendulum can be swung to a desired position to trigger the stabilization controller, and the stabilization scheme is implemented by resorting to the nonlinear adaptive neural network control method and linear matrix inequation technique. By using Lyapunov stability theory, it can be proved that the target trajectory can be boundedly tracked by the arm section, and the pendulum section can be balanced in the upright position with a small error. Finally, two experimental results are given to show the effectiveness of the proposed swing-up and stabilization methods, respectively.

This paper investigates the problem of position tracking control for an electro-hydraulic servo system with parameter uncertainty. Superior to some existing results based on parameter estimation or fuzzy modeling, our proposed control scheme can guarantee the bounded tracking performance without parameter identification and model approximation. This is accomplished by using a novel differentiator-based backstepping control scheme, in which finite-time-convergent second-order differentiators are introduced to get the differential estimations of the system states. Then, the obtained differentials can be used to deal with the system uncertainties since such differentials contain the information relating to the system uncertainties. Moreover, in backstepping control design procedure, the derivatives of the virtual control functions can also be approximated via the second-order differentiator, which can overcome the difficulty of calculating the derivatives of the virtual control functions. Finally, a design experiment is given to show the effectiveness of the proposed method.