Application of NN-based backstepping adaptive controller for stabilized platform of shipborne weapons

To improve position tracking performance of servo systems, a position tracking control using adaptive back-stepping control(ABSC) scheme and recurrent fuzzy neural networks(RFNN) is proposed. An adaptive rule of the ABSC based on system dynamics and dynamic friction model is also suggested to compensate nonlinear dynamic friction characteristics. However, it is difficult to reduce the position tracking error of servo systems by using only the ABSC scheme because of the system uncertainties which cannot be exactly identified during the modeling of servo systems. Therefore, in order to overcome system uncertainties and then to improve position tracking performance of servo systems, the RFNN technique is additionally applied to the servo system. The feasibility of the proposed control scheme for a servo system is validated through experiments. Experimental results show that the servo system with ABS controller based on the dual friction observer and RFNN including the reconstruction error estimator can achieve desired tracking performance and robustness.

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

In this study, an adaptive backstepping control scheme using fuzzy neural networks is proposed for a class of nonlinear uncertain systems. Two kinds of fuzzy neural networks (FNNs) are used to estimate the unknown system functions. According to the estimated value of the FNNs, the control input can be chosen by backstepping design procedures, and then the system output follows the desired trajectory. Based on the Lyapunov approach, the adaptive laws and stability analysis were obtained. Finally, computer simulation results are shown to demonstrate the performances of our approach.

A nonlinear robust and adaptive backstepping control strategy is hierarchically proposed to solve the trajectory tracking problem of hexacopter UAVs. Due to the under-actuated and coupled properties of the hexacopter dynamics, the nominal backstepping control approach is fully designed as the main controller. Considering the model uncertainties and external disturbances perturbing the system stability, a robust 2 nd -order linear extended state observer (LESO) with more reliable velocity feedback is devised to observe and suppress the instabilities, and peaking phenomena in the observation are removed. Usually, large observer gains are selected to reduce the tracking errors but will amplify the measurement noise. To further enhance the system robustness, an adaptive switching function based compensator is introduced to eliminate the observation errors, through which the requirement on large observer gains is relaxed, and high gain behaviors of the LESO are avoided. Stability analysis proves that the nonlinear control scheme can ensure the hexacopter UAV asymptotic tracking along the designated trajectory. Comparative simulations under different controllers are carried out to demonstrate the efficiency and superiority of the proposed control scheme.

This study aims to address the inherent uncertainty in plug loads and load extraction, distributed generation, and the inevitable circulating current in a parallel structure. Therefore, in this paper, an adaptive backstepping control scheme with an online parameter estimator (OPE) for a plug-and-play parallel converter system in a four-port power switcher is proposed. The adaptive backstepping control method was designed in the dq0 coordinate system to suppress the circulating current in the zero-component; the circulating current can be suppressed by using an embedded algorithm and omitting the extra controller. An adaptive update law was designed to weaken the influence of the arbitrary plug and extraction operations in the DC and AC buses to realize the plug-and-play function. The transient tracking performance is governed by the limitation of maximum total errors in the voltage and current. As a result, the settling times of the voltage, current, and power decreased. Additionally, to further improve the system robustness, an online inductance and resistance estimator was established using an optimal algorithm that solves the weighted least squares problem. In the estimator, there are no additional voltage and current sensors needed, and the mean squared error (MSE) of the estimation can be minimized. Simulation studies on a two-converter parallel system with a plug-and-play function were conducted using MATLAB/SIMULINK (R2018b, MathWorks, Natick, MA, USA) to verify the effectiveness of the proposed adaptive backstepping control strategy. The results show that this strategy improves system performance over that of a system with unbalanced parameters among a parallel structure with AC and DC system disturbances caused by arbitrary plug and extraction operations.

In this paper, an adaptive backstepping control scheme is proposed for a class of nonlinear systems with unknown time delay. The unknown time delay in the system depends on all system states, which will inevitably destroy the triangular structure of the control system. Therefore, traditional backstepping can not be used to design the controller. In order to overcome the problem caused by “non-triangular structure”, we construct a linear projection between the state vector and its transform in controller design. Using inequality and adaptive backstepping control, we compensate the uncertainties caused by unknown time delays. Finally, the simulation results show that the proposed algorithm is effective.

Robust adaptive integral backstepping control for opto-electronic tracking system based on modified LuGre friction model

In this article, a fuzzy-approximation-based adaptive backstepping control method for dual-arm of a humanoid robot was proposed. The purpose of this control system is to provide coordinated movement assistance to enable the humanoid robot’s human-like forearm to grab objects coordinately (or track any continuous desired trajectory), even in the presence of environmental disturbances and parametric uncertainties. We analyze the proposed adaptive backstepping by mathematical modeling and actually measure the robot dual-arm motion information of a number of case when they simulate the trajectory to verify the model. We design the adaptive fuzzy-approximation control strategy and combining the synthesis of the robust design, backstepping control, and Lyapunov function method, the proposed adaptive fuzzy backstepping control does not need to know the humanoid robot’s arms model precisely. In the control system proposed here, once the desired trajectories of the robot’s dual-arm positions are given, the adaptive fuzzy system was closed to any unknown functions and to the derivative of the virtual control law of the humanoid robot system. In this case, a robust design scheme was utilized to compensate for any approximation errors. With the proposed trajectory tracking, not only able to generate the coordinate motions for a humanoid robot’s two arms, but it can also control the arms to move to the desired positions. The proposed closed-loop system under the adaptive fuzzy backstepping control design was effective and that asymptotic stability was successfully achieved. The adaptive fuzzy-approximation backstepping control strategy should be more complete and intelligent and more actual test should be conducted to further evaluate the effect of the proposed trajectory tracking. The instability of dual-arm of humanoid robot system is systematically analyzed and a backstepping control strategy based on the adaptive fuzzy-approximation to improve the continuity of trajectory tracking of the robot’s arms is proposed.

In this paper, a fuzzy-identification-based adaptive backstepping control (FABC) scheme is proposed. The FABC system is composed of a backstepping controller and a robust controller. The backstepping controller, which uses a self-organizing fuzzy system (SFS) with the structure and parameter learning phases to on-line estimate the controlled system dynamics, is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the SFS. The developed SFS automatically generates and prunes the fuzzy rules by the proposed structure adaptation algorithm and the parameters of the fuzzy rules and membership functions tunes on-line in the Lyapunov sense. Thus, the overall closed-loop FABC system can guarantee that the tracking error and parameter estimation error are uniformly ultimately bounded; and the tracking error converges to a desired small neighborhood around zero. Finally, the proposed FABC system is applied to a chaotic dynamic system to show its effectiveness. The simulation results verify that the proposed FABC system can achieve favorable tracking performance even with unknown controlled system dynamics.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

In this article, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.

Owing to nonlinear issues such as external disturbances and uncertain parameters within the semi-active suspension system (SASS), the vibration amplitude of the suspension system tends to increase, and the time required for the suspension system to reach a steady-state response is prolonged. Hence, this paper proposes an adaptive backstepping control strategy based on radial basis function neural networks (RBF-NNs). Firstly, the damping force characteristics of the magnetorheological (MR) damper are tested, and the experimental data are utilized for parameters identification and fitting of the Bouc-Wen model. To establish a connection between the controller and the forward model of the MR damper, the forward model of the MR damper, the inverse model of the MR damper, and the model of the MR-SASS are constructed. Secondly, the backstepping controller and the adaptive backstepping controller based on RBF-NNs are designed. The stability and reliability of the closed-loop suspension system are verified through stability analysis using Lyapunov function. Finally, the dynamic characteristics of the passive control, backstepping control, and adaptive backstepping control strategies based on RBF-NNs applied to MR-SASS are analyzed under B-Class road excitation and speed bump road excitation. The acceleration, suspension dynamic deflection, and tire dynamic load are selected as the evaluation indices. The results demonstrate that the adaptive backstepping controller based on RBF-NNs significantly enhances the ride comfort of the SASS.

A force/position hybrid adaptive control method based on radial basis function(RBF) neural network is proposed to solve the problem of difficulties to precisely describe the compliance and friction for robot terminal during trajectory tracking process.RBF neural network is an efficient feed-forward neural network with non-linear approximation and global optimization characteristics,which is not provided by other feed-forward networks,which is simple in network structure,and rapid in training speed.An adaptive controller is designed that relies on the nonlinear approximation ability of the RBF neural network to estimate the uncertainty factors in the models,the update rules for the weights of the controller neural network is provided and its finally uniform boundedness of the errors of the controller output force and position is proved.The controller is applied to a duct cleaning robot for simulation experiments.Simulation results shows that the adaptive controller demonstrates superior tracking precision and robustness compared with traditional adaptive controller.

International Journal of Adaptive Control and Signal ProcessingVolume 35, Issue 11 p. 2328-2328 RETRACTION STATEMENTFree Access Retraction: SCRIM drive system using adaptive backstepping control and mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization This article retracts the following: Retracted: SCRIM drive system using adaptive backstepping control and mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization Chih-Hong Lin, Kuo-Tsai Chang, Volume 33Issue 5International Journal of Adaptive Control and Signal Processing pages: 802-828 First Published online: April 10, 2019 First published: 12 October 2021 https://doi.org/10.1002/acs.3341AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat The above article from the International Journal of Adaptive Control and Signal Processing, published online on 10 April 2019 in Wiley Online Library (wileyonlinelibrary.com) and in Volume 33, pp. 802–828, has been retracted by agreement between the journal Editor in Chief, Mike Grimble, and John Wiley & Sons Ltd. The retraction has been agreed due to major overlap with a previously published article from the same group of authors. REFERENCE 1 Lin C-H, Chang K-T. SCRIM drive system using adaptive backstepping control and mended recurrent Romanovski polynomials neural network with reformed particle swarm optimization. Int J Adapt Control Signal Process. 2019; 33(5): 802- 828. https://doi.org/10.1002/acs.2990Wiley Online LibraryWeb of Science®Google Scholar Volume35, Issue11November 2021Pages 2328-2328 ReferencesRelatedInformation