Conventional Backstepping Approach Research Articles

Neuro-adaptive path following control of autonomous ground vehicles with input deadzone

This article investigates the path-following control problem of an autonomous ground vehicle (AGV) with unknown external disturbances and input deadzones. Neural networks are used to estimate unknown external disturbances, dead zones, and nonlinear functions. The minimum learning parameter scheme is employed to adjust the neural network to reduce the computational load. A backstepping control is proposed to facilitate the tracking of the target path. The steady-state path-following error is decreased by adding an integral error term to the backstepping controller. Command filtering is employed to address the explosion of the complexity issue of the conventional backstepping approach, and the filtering error is compensated via an auxiliary signal. Lyapunov stability study indicates that the AGV closed-loop system is bounded by the proposed control with reasonable accuracy. At last, simulations are given to demonstrate the potential of the proposed scheme in path-following control.

Time-varying gain extended state observer-based adaptive optimal control for disturbed unmanned helicopter

In this paper, the robust adaptive optimal tracking control problem is addressed for the disturbed unmanned helicopter based on the time-varying gain extended state observer (TVGESO) and adaptive dynamic programming (ADP) methods. Firstly, a novel TVGESO is developed to tackle the unknown disturbance, which can overcome the drawback of initial peaking phenomenon in the traditional linear ESO method. Meanwhile, compared with the nonlinear ESO, the proposed TVGESO possesses easier and rigorous stability analysis process. Subsequently, the optimal tracking control issue for the original unmanned helicopter system is transformed into an optimization stabilization problem. By means of the ADP and neural network techniques, the feedforward controller and optimal feedback controller are skillfully designed. Compared with the conventional backstepping approach, the designed anti-disturbance optimal controller can make the unmanned helicopter accomplish the tracking task with less energy. Finally, simulation comparisons demonstrate the validity of the developed control scheme.

Prescribed performance event-triggered fuzzy optimal tracking control for strict-feedback nonlinear systems

The prescribed performance event-triggered optimal tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with external disturbances. First, the disturbance observers are constructed to estimate external disturbances. Then, the controller contains an adaptive fuzzy controller and an optimal compensation term, in which the unknown nonlinearities and cost function are approximated by the fuzzy logic systems. An adaptive fuzzy controller is established by the dynamic surface control (DSC) technique, which is addressed to handle “computation complexity” issue occurred in conventional backstepping approach. Based on adaptive dynamic programming (ADP) method, an optimal compensation term is developed by minimizing the cost function. Furthermore, communication load is reduced via embedding event-triggered mechanism. In addition, the tracking error can be restricted in the prescribed region with the aid of the prescribed performance control. Thus, the whole control scheme can not only ensure that the tracking error converges to a boundary but also achieve optimization, reduce the communication burden and avoid “computation complexity” issue. The boundedness of all signals in the closed-loop is proved. Finally, the simulation examples illustrate the validity of the designed control scheme.

Robust neuro-adaptive attitude control for high-precision Sun-pointing on a halo orbit

A novel neuro-adaptive control design approach is presented to maintain a high-precision Sun-pointing attitude of a spacecraft on a Sun–Earth L1 halo orbit. In the presence of parametric inaccuracies and unknown disturbances, the proposed method effectively learns the modeling uncertainty and adapts the control action to achieve its objective. First, large attitude errors are driven towards zero by applying a conventional back-stepping approach that uses the standard quadratic Lyapunov function (QLF). Once the errors are within the required error bounds, a barrier Lyapunov function-based (BLF) approach is excited, ensuring that the attitude errors remain constrained from thereon. Moreover, following the philosophy of meta-cognition, learning is purposefully stopped when the attitude error becomes too small but excited again whenever it grows large. The robustness of the proposed control law is illustrated by carrying out several simulations incorporating modeling uncertainties and disturbance torques, including high-magnitude solar flares. Finally, the effectiveness of the proposed BLF-based adaptive control law is demonstrated by comparing it with a QLF-based adaptive control law following the same philosophy.

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

In this technical note, a combined discrete-time controller, consisting of a partial feedback linearization controller and a backstepping controller, is proposed to manage the stabilization for a class of underactuated nonlinear mechanical systems. The traditional backstepping control method is impracticable to directly apply it to underactuated systems since they are generally not in the lower triangular form. First, a feedback controller that partially linearizes the underactuated mechanical systems is derived to facilitate the backstepping controller design. In the design, discrete-time system dynamics obtained utilizing the Euler approximation are considered. Afterward, a novel coordinate transformation is introduced for a class of underactuated systems that transform the mathematical model of the partially linearized underactuated mechanical systems into the strict-feedback form. After these steps, the conventional backstepping approach is structured in discrete-time setting. The stability of the closed-loop system dynamics with the proposed combined discrete-time controller is shown utilizing Lyapunov theory. Several computer-based simulations are executed to depict the performance and the applicability of the proposed method on the Cart–Pole system and the Inertia Wheel Pendulum. Moreover, the effectiveness of the proposed nonlinear controller is verified by numerical simulation results in comparison with a discrete-time chattering-free sliding-mode controller.

Fixed-Time Sliding Mode Disturbance Observer-Based Nonsmooth Backstepping Control for Hypersonic Vehicles

This paper presents a novel fixed-time sliding mode disturbance observer (SMDO)-based robust backstepping cruise tracking control scheme with closed-loop finite-time convergence for flexible air-breathing hypersonic vehicles (FAHVs). In order to enhance the control system's robustness, a fixed-time SMDO is designed to compensate for the flexibility effects, model uncertainties, and external disturbances in FAHVs. In consequence, fixed convergence time of disturbance observation is achieved independently of initial estimation errors. Furthermore, velocity and altitude continuous finite-time tracking controllers are constructed by incorporating the SMDO and nonsmooth backstepping technique. To solve the problem of “explosion of complexity” in the conventional backstepping approach, nonsmooth filters are specifically constructed to generate the derivatives of virtual control laws. A Lyapunov-based stability analysis is conducted to show the finite-time convergence of the closed-loop FAHV control system. Finally, several representative numerical simulations are given to illustrate the effectiveness and superiority of the proposed control strategy.

Adaptive NN control for nonlinear systems with uncertainty based on dynamic surface control

The problem of adaptive neural network (NN) control and the dynamic surface control (DSC) method for a series of nonlinear systems with uncertainty is discussed in this paper. Unknown smooth functions can be approximated by radial basis function-neural networks (RBF-NNs) with arbitrary accuracy in nonlinear systems. The DSC scheme is introduced for nonlinear systems with uncertainty to overcome the “explosion of complexity” compared with the conventional backstepping approach. Meanwhile, the global asymptotic stability of nonlinear systems is manifested via the Lyapunov stability theory, which indicates the uniform boundedness of all closed-loop signals is ensured and dynamic surface errors are arbitrarily small in the compact set by selecting proper parameters. Finally, the effectiveness of the proposed control technique is validated by two simulation examples.

Uncertainty and Disturbance Estimator-Based Backstepping Control for Nonlinear Systems With Mismatched Uncertainties and Disturbances

This paper proposes an uncertainty and disturbance estimator (UDE)-based controller for nonlinear systems with mismatched uncertainties and disturbances, integrating the UDE-based control and the conventional backstepping scheme. The adoption of the backstepping scheme helps to relax the structural constraint of the UDE-based control. Moreover, the reference model design in the UDE-based control offers a solution to address the “complexity explosion” problem of the backstepping approach. Furthermore, the strict-feedback form condition in the conventional backstepping approach is also relaxed by using the UDE-based control to estimate and compensate “disturbance-like” terms including nonstrict-feedback terms and intermediate system errors. The uniformly ultimate boundedness of the closed-loop system is analyzed. Both numerical and experimental studies are provided.

Decentralized Dynamic Surface Control of Large-Scale Interconnected Systems in Strict-Feedback Form Using Neural Networks With Asymptotic Stabilization

A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the "explosion of complexity" problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach.

Power System Stabilization Using Adaptive Neural Network-Based Dynamic Surface Control

In this paper, the power system with an excitation controller is represented as a class of large-scale, uncertain, interconnected nonlinear continuous-time system in strict-feedback form. Subsequently, dynamic surface control (DSC)-based adaptive neural network (NN) controller is designed to overcome the repeated differentiation of the control input that is observed in the conventional backstepping approach. The NNs are utilized to approximate the unknown subsystem and the interconnection dynamics. By using novel online NN weight update laws with quadratic error terms, the closed-loop signals are shown to be locally asymptotically stable via Lyapunov stability analysis, even in the presence of NN approximation errors in contrast with other NN techniques where a bounded stability is normally assured. Simulation results on the IEEE 14-bus power system with generator excitation control are provided to show the effectiveness of the approach in damping oscillations that occur after disturbances are removed. The end result is a nonlinear decentralized adaptive state-feedback excitation controller for damping power systems oscillations in the presence of uncertain interconnection terms.

Robust Adaptive Backstepping Motion Control of Linear Ultrasonic Motors Using Fuzzy Neural Network

A robust adaptive fuzzy neural network (RAFNN) backstepping control system is proposed to control the position of an X-Y-Theta motion control stage using linear ultrasonic motors (LUSMs) to track various contours in this study. First, an X-Y-Theta motion control stage is introduced. Then, the single-axis dynamics of LUSM mechanism with the introduction of a lumped uncertainty, which includes cross-coupled interference and friction force, is derived. Moreover, a conventional backstepping approach is proposed to compensate the uncertainties occurred in the motion control system. Furthermore, to improve the control performance in the tracking of the reference contours, an RAFNN backstepping control system is proposed to remove the chattering phenomena caused by the sign function in the backstepping control law. In the proposed RAFNN backstepping control system, a Sugeno-type adaptive fuzzy neural network (SAFNN) is employed to estimate the lumped uncertainty directly and a compensator is utilized to confront the reconstructed error of the SAFNN. In addition, the motions at the X axis, Y axis, and Theta axis are controlled separately. The experimental results show that the contour tracking performance is significantly improved and the robustness to parameter variations, external disturbances, cross-coupled interference, and friction force can be obtained, as well using the proposed RAFNN backstepping control system.