Adaptive Radial Basis Function Research Articles

Robust fixed-time H∞ tracking control of UUVs with partial and full state constraints and prescribed performance under input saturation

In this paper, a fixed-time tracking control problem for an unmanned underwater vehicle (UUV) is investigated in the case of strong external sudden disturbances, model uncertainty, time-varying disturbances and specified performance constraints. First, a modified barrier Lyapunov function (QABLF) is proposed to increase applicability by introducing the standard quadratic Lyapunov function (QLF) and the logarithmic asymmetric barrier Lyapunov function (ABLF). The QALBF has two types and can be constructed to avoid violations of full and partial state constraints by parameter modification. Second, adaptive antisaturation appointed-time prescribed performance functions (APPFs) are introduced in the QABLF for the first time to relax the overshoot restriction and reduce the effect of input saturation on the performance constraint. Third, based on the backstepping method, a robust H∞ control strategy is developed to address strong, sudden disturbances. An auxiliary variable is designed to compensate for input saturation. Next, an improved adaptive radial basis function neural network (ARBFNN) is proposed to match the time-varying disturbances and model uncertainty. Finally, composite robust fixed-time control is achieved with high robustness and transient performance, which guarantees that the closed-loop system is fixed-time convergent. Moreover, the feasibility of the proposed controller is verified by Lyapunov analysis and numerical simulation.

Space Robot On-Orbit Operation of Insertion and Extraction Impedance Control Based on Adaptive Neural Network

The on-orbit operation of insertion and extraction of space robots is a technology essential to the assembly and maintenance in orbit, satellite fuel filling, failed satellite recovery, especially modular in-orbit assembly of micro-spacecraft. Therefore, the force/posture impedance control for the on-orbit operation of insertion and extraction is studied. Firstly, the dynamic model of space robots’ system in the form of uncontrolled carrier position and controlled attitude is derived by using the momentum conservation principle. Through the kinematic constraints of the replacement component plug, the Jacobi relationship of the plug motion in the base coordinate system is established. Secondly, to achieve the output force control of the plug during the on-orbit operation of insertion and extraction, a second-order linear impedance model is established based on the dynamic relationship between the plug posture and its output force and the impedance control principle. Then, in order to improve the stability, robustness, and adaptability of the controller, an adaptive Radial Basis Function Neural Network (RBFNN) is used to approximate the uncertainties in the dynamic model for the force/posture control of the plug. Finally, the stability of the system is verified by the Lyapunov principle. The simulation results show that the designed neural network impedance control strategy can achieve a control accuracy of less than 10−3 rad for the plug’s attitude tracking error, less than 10−3 m for its position tracking error, and less than 0.5 N for its output force tracking error.

Attitude tracking backstepping control for small unmanned helicopters based on adaptive neural network under unknown environment disturbances

To solve the attitude tracking control problem of small unmanned helicopters under unknown bounded disturbances, an attitude tracking backstepping controller based on adaptive radial basis function (RBF) neural network disturbance compensation is proposed in this paper. The unknown disturbance is estimated online and in real time through RBF neural network with a novel gradient descent weight update rate. A novel attitude tracking backstepping controller based on virtual control variables is designed, and the system stability is analyzed using the Lyapunov method. The experimental verification of the backstepping controller is carried out on the three-degrees-of-freedom helicopter. The experiments show the effectiveness and advancedness of the proposed adaptive neural network backstepping controller in suppressing unknown external disturbances compared with the robust adaptive integral backstepping.

Efficient adaptive deep gradient RBF network for multi-output nonlinear and nonstationary industrial processes

Due to the complexity of process operation, industrial process data are often nonlinear and nonstationary, high dimensional, and multivariate with complex interactions between multiple outputs. To address all these issues, this paper proposes a novel industrial predictive model that integrates deep feature extraction and fast online adaptation, and can effectively deal with multiple process outputs. Specifically, a multi-output gradient radial basis function network (MGRBF) with excellent predictive capacity of nonstationary data is first used to provide preliminary prediction of target outputs. This prior quality information is combined with the original process input for deep feature learning and dimensional reduction. Through layer-wise feature extraction by the stacked autoencoder (SAE), deep quality-enhanced features can be obtained, which is further fed into a MGRBF tracker for online prediction. In order to timely capture the fast-changing process characteristics, the first two modules, namely, preliminary MGRBF predictor and SAE feature extractor are frozen after training, while the structure and parameters of the MGRBF tracker are updated online in an efficient manner. Two industrial case studies demonstrate that the proposed adaptive deep MGRBF network outperforms existing state-of-the-art online modeling approaches as well as deep learning models, in terms of both multi-output modeling accuracy and online computational complexity.

Trajectory tracking control for unmanned helicopter based on RBFNN

This paper proposes a nonlinear adaptive radial basis function neural network (RBFNN) control method for Unmanned Helicopter. The control objective is to reduce the trajectory tracking error of the unmanned helicopter in the presence of system uncertainty and external disturbances. Based on the backstepping control technique, the controller of the unmanned helicopter are designed in order of position kinematics, position dynamics, attitude kinematics and attitude dynamics, and the block processing is used in the last three steps above.Then, RBFNN is added to compensate the error caused by external interference. Meanwhile, the derivatives of virtual controls are obtained by second-order command filter, and the stability of the system is analyzed by Lyapunov stability theorems. Finally, the simulation results verify the stability and robustness of the control method.

Adaptive NN state error PCH trajectory tracking control for unmanned surface vessel with uncertainties and input saturation

AbstractA novel robust state error port controlled Hamiltonian (PCH) trajectory tracking controller of an unmanned surface vessel (USV) subject to time‐varying disturbances, dynamic uncertainties and control input saturation is presented. The proposed control scheme combines the advantages of the high robustness and energy minimization of the state error PCH approach and the approximation capability of adaptive radial basis function neural networks (RBFNNs). Adaptive RBFNNs are used to the time‐varying disturbances of the environment and unknown dynamics uncertainties of the USV model. The state error PCH control approach is designed such that the system can optimize energy consumption, and the state error PCH technique makes the designed trajectory tracking controller be easy to implement in practice. To handle the effect of the control input saturation, a Gaussian error function model is employed. It has been demonstrated that the proposed approach can maintain the USV's trajectory at the desired trajectory, while the closed‐loop control system can guarantee the uniformly ultimate boundedness. The energy consumption model of the USV is constructed to reveal to the energy consumption. Simulation results demonstrate the effectiveness of the proposed controller.

Adaptive Robust RBF-NN Nonsingular Terminal Sliding Mode Control Scheme for Application to Snake Robot’s Head for Image Stabilization

Image stabilization is important for snake robots to be used as mobile robots. In this paper, we propose an adaptive robust RBF neural network nonsingular terminal sliding mode control to reduce swinging in the snake robot’s head while it is being driven. To avoid complex dynamic problems and reduce interference during driving, we propose a 2-DOF snake robot’s head system. We designed the control system based on the nonsingular terminal sliding mode control, which ensures a fast response and finite time convergence. To reduce chattering, we incorporated an RBF neural network that can compensate for disturbances. Additionally, we included an adaptive robust term to address the disadvantages of neural network-based control. The adaptive robust term generates control inputs based on the error and is used in conjunction with the reverse saturation function to eliminate chattering. The update law of the neural network and the adaptive robust term is designed based on Lyapunov’s theory. We proved the stability of the proposed controller by investigating finite time convergence before and after the reverse saturation function operation section. Finally, we verified the performance of the proposed controller through computer simulation. The simulation evaluates the controllers using a sinusoidal reference signal similar to snake robot movement and a mixed reference signal considering the controller’s waste case. The proposed controller has excellent tracking performance and improved chattering compared with the previous controller.

Adaptive neural networks-based integral sliding mode control for T-S fuzzy model of delayed nonlinear systems

This paper presents a method for designing adaptive neural networks (NNs) based on integral sliding mode control (ISMC) for delayed Takagi-Sugeno fuzzy systems with external disturbances. To do this, a fuzzy sliding surface is constructed with the information of the delayed states, and an adaptive radial basis function (RBF) NNs-based fuzzy ISMC is designed. Here, the RBF NN function is utilized to approximate the nonlinear perturbation term. The resulting stability criteria are derived based on suitable Lyapunov functionals with the help of generalized free-weight matrix-based inequality. The resulting conditions ensure the asymptotic stability with H∞ attenuation level. Moreover, the designed sliding motion achieved the reachability condition under the adaptive RBF NNs based on the sliding mode controller. To end with, a design and comparative examples are given to show the success of the nominated control scheme and less conservatism of the derived sufficient conditions.

Disturbance Observer based Dynamic Surface Sliding Mode Control for Manipulator Arm with Adaptive RBF Networks

For the rotation position control of automatic loading manipulator arm with uncertain problems of load change and external disturbances, an adaptive radial basis function networks (RBF) dynamic surface sliding mode control (DSMC) strategy based on disturbance observer (DOB) is proposed. The value of the external disturbance, which is estimated by the DOB on line, is added to the output of the proposed controller for feedforward compensation. The dynamic performance of the controller is ensured by introducing the adaptive RBF networks while the stability of the controller is verified by designing the Lyapunov function. Comparison between the results of the proposed control strategy and those of the conventional sliding mode control (SMC) shows that the controller has better dynamic tracking characteristics, steady-state accuracy and strong robustness under load changes.

Research on the Line of Sight Stabilization Control Technology of Optronic Mast under High Oceanic Condition and Big Swaying Movement of Platform

To realize high-performance line of sight (LOS) stabilization control of the optronic mast under high oceanic conditions and big swaying movements of platforms, a composite control method based on an adaptive radial basis function neural network (RBFNN) and sliding mode control (SMC) is proposed. The adaptive RBFNN is used to approximate the nonlinear and parameter-varying ideal model of the optronic mast, so as to compensate for the uncertainties of the system and reduce the big-amplitude chattering phenomenon caused by excessive switching gain in SMC. The adaptive RBFNN is constructed and optimized online based on the state error information in the working process; therefore, no prior training data are required. At the same time, a saturation function is used to replace the sign function for the time-varying hydrodynamic disturbance torque and the friction disturbance torque, which further reduce the chattering phenomenon of the system. The asymptotic stability of the proposed control method has been proven by the Lyapunov stability theory. The applicability of the proposed control method is validated by a series of simulations and experiments.

An Intelligence Attitude Controller Based on Active Disturbance Rejection Control Technology for an Unmanned Helicopter

To solve the problems of complex parameter tuning of traditional active disturbance rejection controller (ADRC) and low adaptive ability of extended state observer, this paper designs a novel intelligent attitude controller based on active disturbance rejection control technology. The adaptive radial basis function neural network can improve the adaptability of the extended state observer, and the fuzzy control can adjust the parameters of the state error nonlinear control law online. The intelligent ADRC controller can eliminate the influence of internal and external disturbances on the unmanned helicopter, and reduce the difficulty of controller parameter tuning. Based on the intelligent ADRC controller, this paper designs an intelligent attitude control system for a small unmanned helicopter and completes the attitude control test. The corresponding test results demonstrate that the intelligent attitude controller has excellent anti-disturbances, robustness and tracking ability, and the control effect is better than that of the traditional ADRC controller.

Finite-time suspension control based on GFTSM and RBFNN for low-wind-speed MVAWT

For low-wind-speed maglev vertical axis wind turbine (MVAWT), this paper proposes a finite-time suspension control strategy based on global fast terminal sliding mode (GFTSM) and adaptive RBF neural network (RBFNN). Due to the randomness of wind speed and wind direction, the actual working conditions of low-wind-speed wind farms are very complex. In order to ensure the stability of the maglev system in MVAWT and improve its anti-disturbance ability, a finite-time GFTSM controller with small chattering is firstly designed based on the dynamic suspension model considering external wind load disturbance. Secondly, the RBFNN is adopted to approximate system uncertainties and external disturbance, its network weight is adjusted according to the adaptive law, and the finite-time global fast convergence characteristic of GFTSM is also introduced into the adaptive law to improve the convergence speed of the RBFNN. Furthermore, in order to obtain the derivatives of input signals of controller and mitigate the effect of sensors’ noise, a finite-time differentiator is introduced. According to Lyapunov stability theory, the stability and finite-time convergence characteristics of the proposed control strategy are proved. Finally, simulation and experiment results show that the proposed strategy has faster dynamic response speed and stronger anti-disturbance ability.

Consensus Tracking for High-Order Uncertain Nonlinear MASs via Adaptive Backstepping Approach.

In this article, we focus on the problems of consensus control for nonlinear uncertain multiagent systems (MASs) with both unknown state delays and unknown external disturbances. First, a nonlinear function approximator is proposed for the system uncertainties deriving from unknown nonlinearity for each agent according to adaptive radial basis function neural networks (RBFNNs). By taking advantage of the Lyapunov-Krasovskii functionals (LKFs) approach, we develop a compensation control strategy to eliminate the effects of state delays. Considering the combination of adaptive RBFNNs, LKFs, and backstepping techniques, an adaptive output-feedback approach is raised to construct consensus tracking control protocols and adaptive laws. Then, the proposed consensus tracking scheme can steer the nonlinear MAS synchronizing to the predefined reference signal on account of the Lyapunov stability theory and inequality properties. Finally, simulation results are carried out to verify the validity of the presented theoretical approach.

Robust Control Based on Adaptive Neural Network for the Process of Steady Formation of Continuous Contact Force in Unmanned Aerial Manipulator

Contact force control for Unmanned Aerial Manipulators (UAMs) is a challenging issue today. This paper designs a new method to stabilize the UAM system during the formation of contact force with the target. Firstly, the dynamic model of the contact process between the UAM and the target is derived. Then, a non-singular global fast terminal sliding mode controller (NGFTSMC) is proposed to guarantee that the contact process is completed within a finite time. Moreover, to compensate for system uncertainties and external disturbances, the equivalent part of the controller is estimated by an adaptive radial basis function neural network (RBFNN). Finally, the Lyapunov theory is applied to validate the global stability of the closed-loop system and derive the adaptive law for the neural network weight matrix online updating. Simulation and experimental results demonstrate that the proposed method can stably form a continuous contact force and reduce the chattering with good robustness.

Attitude tracking control design of fixed-wing UAVs having uncertain dynamics and corrupted gyro sensor outputs

Flight performance of unmanned aerial vehicles (UAVs) strongly depends on implemented attitude tracking control. For designing better controllers, nonlinear control design techniques are often opted instead of control design based on linearized models. Uncertainty in nonlinear dynamics estimation may arise due to inaccuracies in aerodynamic derivatives and simplifications/assumptions made during the derivation of nonlinear models. This paper considers attitude tracking control of fixed-wing UAVs having uncertain dynamics and corrupted gyro sensor outputs. An integral chain differentiator (ICD) is used to provide the analytical redundancy to the gyros used to measure the angular rates. Two control design schemes are proposed, a neuro-fuzzy adaptive sliding mode control (NFASMC) and an ICD approximation-based fuzzy adaptive sliding mode control (ICD-FASMC). In NFASMC, the uncertain part of the dynamics is estimated using an adaptive radial basis function neural network. Gyro sensor output errors are estimated in real-time, using ICD based error estimation scheme and used in the control law along with the sensor’s corrupted outputs. In ICD-FASMC, the uncertain dynamics and angular rates of UAV are estimated using the ICD such that the requirement of the gyro sensor outputs for control design is bypassed. The switching gain of the designed controllers is made adaptive using fuzzy logic to mitigate the chattering effect. The stability of the proposed controllers is proved using the Lyapunov approach. The proposed schemes are implemented using a nonlinear simulation of a fixed-wing UAV. Simulation results are presented to show the effectiveness of the proposed techniques.

Neural adaptive with impedance learning control for uncertain cooperative multiple robot manipulators

In this paper, an adaptive radial basis function neural network (RBFNN) control scheme is studied for the desired tracking of multiple robot manipulators with carrying a common object in joint-space. First, a non-zero time-varying parameter is introduced into the RBFNN, as well as a novel universal approximation of RBFNN with this non-zero parameter is introduced. Second, a switching control scheme based on this approximation property is designed. When the states of uncertainties terms leave the universal approximation domains, the suggested adaptive laws established by a sliding surface would pull them back, then the uncertain nonlinear functions are approximated by the RBFNNs in the domains. With this new structure of control technique, the limitation of a finite universal approximation can be broken. Third, the cooperative multiple manipulators can track the desired trajectory determined through impedance learning, which is used to modulate the control input in order to optimize the environment robot interaction. Finally, simulation results are shown to demonstrate the effectiveness in terms of expected tracking performance and position tracking errors constraints.

An Adaptive Inverse Model Control Method of Vehicle Yaw Stability with Active Front Steering Based on Adaptive RBF Neural Networks

In order to enhance vehicle yaw stability, this paper proposes a novel adaptive inverse model control (AIMC) method for active front steering (AFS) design based on adaptive radial basis function (RBF) neural networks. To approximate the uncertain nonlinearity and modeling errors in vehicle dynamics, an adaptive RBF neural network (ARBFNN) controller is firstly designed. For smaller tracking errors and better robustness, a RBF networks-based AIMC system is further established. Apart from the ARBFNN control law, another two RBF neural networks are utilized, which work as model identifier and inverse model controller, respectively. After being trained offline, both of them are updated by using online learning algorithms. For faster learning and stability, adaptive learning rates are developed. Consequently, the inverse model controller is able to generate required steering wheel angle. Finally, the comparative studies are carried out and the simulation results illustrate the robustness and effectiveness of proposed control strategy.

A Study on the Design of Error-Based Adaptive Robust RBF Neural Network Back-Stepping Controller for 2-DOF Snake Robot’s Head

In this paper, we will propose the controller of a 2-DOF head in a snake robot for effective image data reading when the snake robot is driving, and present an error-based adaptive robust radial base function neural network back-stepping controller. The snake robot head system is a nonlinear system, and there are unmeasurable disturbances that occur while driving. To solve this problem, we use back-stepping controller and radial basis function neural network to compensate for unmeasurable disturbances to improve the steady state. In order to further compensate for the network approximation error that occurs during training or large signal changes, we use adaptive coefficients and error functions to approximate the network approximation error and design adaptive robust terms. Compared to the previous controller, the proposed controller can actively compensate for large signal changes and has the advantage of not generating residual input in a steady state. The proposed controller is based on Lyapunov function candidate to design an adaptive law and prove the system stability. The stability of the control system is proven through Lyapunov analysis and bounded. The proposed controller compared and verified the controller performance for two inputs through simulation and presented the efficiency of the controller.

Adaptive Neural Network-Based Fixed-Time Control for Trajectory Tracking of Robotic Systems

This brief investigates the problem of fixed-time trajectory tracking control of uncertain robotic systems. Firstly, an adaptive radial basis function neural network is designed to estimate the model uncertainties and viscous frictions in robotic systems. Secondly, a segmented terminal sliding mode control (TSMC) variable is adopted to alleviate the singularity problem. To improve the tracking performance, a new second-order fixed-time reaching law is designed. Then, in order to make the tracking errors converge to a small neighborhood of the origin in a fixed-time independent of the initial state, a novel fixed-time non-singular TSMC based on the adaptive neural network is proposed. Finally, the experimental results demonstrate the effectiveness and advantage of the proposed control method.

Adaptive Neural Network-Based Prescribed-Time Observer for Battery State-of-Charge Estimation

Convergence speed is an important indicator to evaluate the performance of state-of-charge (SOC) estimators. To improve the convergence speed, this article proposes an adaptive radial basis function neural network-based prescribed-time observer to estimate the battery SOC. First, an adaptive RBF NN is employed to approximate the nonlinear part of the battery equivalent circuit model, and the online learning process of network weight can adapt the variations in battery parameters. Then, a prescribed-time SOC observer is developed to ensure the state and weight estimation errors converge within the convergence time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> , which can be prescribed by users and is irrelevant on initial values. Thus, the network weight no longer needs to update when time exceeds <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> , and the computational burden can be effectively saved. Furthermore, a switched-gain scheme with a naturally switched time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is employed to simultaneously guarantee the convergence speed and estimation accuracy. An adaptive robust term is designed to compensate the approximation error and possible variations of the network weight in the steady state. Finally, the theoretical stability is proved by the Lyapunov theory, and the practical effectiveness is evaluated by experiments and simulations.