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A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and response networks tend to zero asymptotically under the control. The proposed scheme is numerically implemented in the synchronization of two networks with the Fisher–Kolmogorov and the Burgers spatiotemporal chaotic systems as the nodes.

A backstepping nonsingular fast terminal sliding mode control with the extended state observer (ESO) is proposed for the uncertain factors of nonlinear spinning missile. Based on Lyapunov stability theory, the virtual control as sliding mode is taken in the backstepping design and then the tracking differentiator (TD) is employed to eliminate the “explosion of terms”. In the last step of the backstepping design, nonsingular fast terminal sliding mode control is utilized to drive the angular velocity tracking error to converge to the origin in a finite period of time. To estimate the chattering phenomenon caused by disturbance influence variable in the system, an ESO is applied to estimate and compensate the impact from uncertainties and disturbances. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed control method and the stability of the controller.

This paper considers the stabilization problem of Inertia Wheel Pendulum, a widely studied benchmark nonlinear system. It is a classical example of a flat underactuated mechanical system, for which the design of control law becomes a challenging task owing to its underactuated nature. A novel nonlinear controller design, fusing the recently introduced Dynamic Surface Control and the Control Lyapunov Function method, is presented as the solution. Stability is analyzed using concepts from Singular Perturbation Theory. The proposed design procedure is shown to be simpler and more intuitive than existing designs. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and verified using numerical simulations.

This paper focuses on parameter convergence and precise modeling for fractional-order nonlinear systems with functional uncertainties via using adaptive backstepping neural network control (ABNNC) and composite learning adaptive backstepping neural network control (CLABNNC). In the ABNNC design, a command filter is proposed, and the neural network approximation system is considered to deal with the unknown function, where an adaptation law is designed to ensure tracking errors converge to an arbitrarily small region near the origin under a strict persistent excitation condition that is too strict for the convergence of adaptive parameters. In order to relax this condition, a composite learning adaptation law is established by taking advantage of the tracking error and the prediction error to update the free parameter of the neural network system. The proposed CLABNNC method can not only ensure the convergence of tracking errors, but also achieve the accurate approximation of functional uncertainties under a weaker interval excitation condition. Finally, a numerical simulation example is put forward to demonstrate the effectiveness of our method.

This paper proposes Interval type-2 Fuzzy sliding mode controller based on Backstepping (IT2FBSMC), to control the speed of a dual star induction machine (DSIM), in order to get a robust performance machine. An appropriate control strategy based on the coupling of three methods (Backstepping, sliding mode and type-2 Fuzzy controller) is used to build a robust controller used to approximate the discontinuous control eliminating the chattering phenomenon and guaranteeing the stability of the machine. Moreover, it forces the rotor angular speed to follow a desired reference signal. The simulation results obtained using Matlab/Simulink behavior are presented and discussed. The obtained results show that the controller can greatly alleviate the chattering effect and enhance the robustness of control systems with high accuracy.

In this paper, a novel robust backstepping-based fault-tolerant control is designed, implemented and validated experimentally on a quadrotor unmanned aerial vehicle testbed under actuator fault conditions for tracking control. Backstepping is known as a robust method to maintain system performance and keep it insensitive to disturbances. The proposed nonlinear controller is mainly based on the advanced robust backstepping method to solve the system uncertainties caused by disturbances and actuator faults, which appear in the motor part of the system and are compensated without diagnostics or fault identification. The various parameters of the proposed approach are optimized using the particle swarm optimization (PSO) method. Owing to the minimized control effort to accommodate uncertainties compared to the conventional backstepping, the proposed approach can still maintain the system performance when severer faults occur. The proposed approach is validated, first, in a simulation using the nonlinear model of the quadrotor, then experimentally, using the Quanser 3DOF Hover quadrotor. Both theoretical and experimental analyses have demonstrated that the effectiveness of the proposed improved backstepping fault-tolerant control strategies faces significant loss of actuator efficiency.

This paper focuses on trajectory tracking, robustness and stabilization of a golf swing robot which has been recently developed to simulate the ultra-high-speed swing motions of a golfer. The proposed control strategies are based on the Lyapunov stability theory and include Backstepping and Sliding-Mode Control based techniques. To attenuate the chattering phenomena caused by a discontinuous switching function and improve the dynamic response of the manipulator, a fuzzy system is used in this research; a Backstepping Sliding-Mode Controller (BSMC), a Backstepping Fuzzy Sliding-Mode Controller (BFSMC) and a Super-twisting Backstepping Sliding-Mode Controller (STBSMC) are used to evaluate the proposed hybrid controller’s BFSMC performance. The Lyapunov stability theory is used to guarantee the stability of the proposed closed-loop robot technique. Numerical simulations show the effectiveness of the proposed strategy based on the fuzzy logic mechanism under different disturbances and uncertainties.