Adaptive Radial Basis Function Neural Network Research Articles

State tracking control of nonlinear systems using neural adaptive dynamic sliding mode

This paper describes control issues of a general-class, single-input, unknown, nonlinear, non-affine system using dynamic sliding-mode control (DSMC). Chattering can be removed in DSMC with an integrator as a low-pass filter, placed before the input control signal of the plant. As a result, the augmented system (which contains the integrator) in DSMC has one more dimension than the actual system. Then the plant model must be completely known. To overcome this problem and to identify the plant model, an adaptive radial basis-function neural network has been employed and a robust procedure developed to train the parameters of a neural network based on Lyapunov theory. A smooth controller has been developed and some numerical simulations have been performed to verify the validity of the proposed approach. Two nonlinear systems were used for simulation: a Duffing–Holmes chaotic system and a switch reluctance motor. The advantage of the presented approach is that the system model can be considered unknown and can be in non-affine form.

Adaptive neural network force tracking impedance control for uncertain robotic manipulator based on nonlinear velocity observer

In this paper, an adaptive neural network force tracking impedance control scheme based on a nonlinear observer is proposed to control robotic system with uncertainties and external disturbances. It is supposed that the joint positions and interaction force of the robotic system can be measured, while the joint velocities are unknown and unmeasured. Then, a nonlinear velocity observer is designed to estimate the joint velocities of the manipulator, and the stability of the observer is analyzed using the Lyapunov stability theory. Based on the estimated joint velocities, an adaptive radial basis function neural network (RBFNN) impedance controller is developed to track the desired contact force of the end-effector and the desired trajectories of the manipulator, where the adaptive RBFNN is used to compensate the system uncertainties so that the accuracy of the joint positions and force tracking can be then improved. Based on the Lyapunov stability theorem, it is proved that the proposed adaptive RBFNN impedance control system is stable and the signals in closed-loop system are all bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.

Backstepping Sliding Mode Control for Radar Seeker Servo System Considering Guidance and Control System.

This paper investigates the design of a missile seeker servo system combined with a guidance and control system. Firstly, a complete model containing a missile seeker servo system, missile guidance system, and missile control system (SGCS) was creatively proposed. Secondly, a designed high-order tracking differentiator (HTD) was used to estimate states of systems in real time, which guarantees the feasibility of the designed algorithm. To guarantee tracking precision and robustness, backstepping sliding-mode control was adopted. Aiming at the main problem of projectile motion disturbance, an adaptive radial basis function neural network (RBFNN) was proposed to compensate for disturbance. Adaptive RBFNN especially achieves online adjustment of residual error, which promotes estimation precision and eliminates the “chattering phenomenon”. The boundedness of all signals, including estimation error of high-order tracking differentiator, was especially proved via the Lyapunov stability theory, which is more rigorous. Finally, in considered scenarios, line of sight angle (LOSA)-tracking simulations were carried out to verify the tracking performance, and a Monte Carlo miss-distance simulation is presented to validate the effectiveness of the proposed method.

Global approximation based adaptive RBF neural network control for supercavitating vehicles

A global approximation based adaptive radial basis function (RBF) neural network control strategy is proposed for the trajectory tracking control of supercavitating vehicles (SV). A nominal model is built firstly with the unknown disturbance. Next, the control scheme is established consisting of a computed torque controller (CTC) for the practical vehicle and an RBF neural network controller to estimate model error between the practical vehicle and the nominal model. The network weights are adapted by employing a Lyapunov-based design. Then it is shown by the Lyapunov theory that the trajectory tracking errors asymptotically converge to a small neighborhood of zero. The control performance of the proposed controller is illustrated by simulation.

Adaptive NN Tracking Control for Nonlinear Fractional Order Systems With Uncertainty and Input Saturation

In this paper, an adaptive neural network (NN) backstepping control method is designed for a class of uncertain fractional order nonlinear systems with external disturbance and input saturation, in which the fractional Lyapunov stability theory is used to construct the controller. The complicated unknown fractional order nonlinear function is approximated by a radial basis function (RBF) NN in each step, and the virtual control law and parameters update law are presented based on the backstepping algorithm procedures. At the final step, an adaptive RBF NN controller is constructed, in which no knowledge of system uncertainty and the upper bound of the disturbance is required. Then, a theorem is presented to address that the asymptotical convergence of the tracking error can be guaranteed. The effectiveness of the proposed scheme is illustrated by two simulation examples.

Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems

This paper presents a constructive design of a continuous finite-time controller for a class of mechanical systems known as underactuated systems that satisfy the symmetry properties. An adaptive radial basis function neural network (RBFNN) finite-time control scheme is proposed to stabilize the underactuated system at a given equilibrium, regardless of the various uncertainties and disturbances that the system contains. First, a coordinate transformation is introduced to decouple the control input so that an n-th order underactuated system can be represented into a special cascade form. Next, an adaptive robust finite-time controller is derived from adding a power integrator technique and the RBFNN to approximate the nonlinear unknown dynamics in the new space, whose bounds are supposedly unknown. The stability and finite-time convergence of the closed-loop system are established by using Lyapunov theory. To show the effectiveness of the proposed method, simulations are carried out on the rotary inverted pendulum, a typical example of an underactuated mechanical system.

Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm. (On-Line Harmonics Estimation Application)

In this paper, an adaptive Radial Basis Function Neural Networks (RBFNN) algorithm is used to estimate the fundamental and harmonic components of nonlinear load current. The performance of the adaptive RBFNN is evaluated based on the difference between the original signal and the constructed signal (the summation between fundamental and harmonic components). Also, an extensive investigation is carried out to propose a systematic and optimal selection of the Adaptive RBFNN parameters. These parameters will ensure fast and stable convergence and minimum estimation error. The results show an improving for fundamental and harmonics estimation comparing to the conventional RBFNN. Also, the results show how to control the computational steps and how they are related to the estimation error. The methodology used in this paper facilitates the development and design of signal processing and control systems.Article History: Received Dec 15, 2016; Received in revised form Feb 2nd 2017; Accepted 13rd 2017; Available onlineHow to Cite This Article: Almaita, E.K and Shawawreh J.Al (2017) Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm (On-Line Harmonics Estimation Application). International Journal of Renewable Energy Develeopment, 6(1), 9-17.http://dx.doi.org/10.14710/ijred.6.1.9-17

A Dynamic Model and Control Method for a Two-Axis Inertially Stabilized Platform

To realize high-performance control for a two-axis inertially stabilized platform (ISP), a nonlinear dynamic model based on the geographic coordinate and a compound control method based on the back-stepping sliding mode control and adaptive radial basis function neural network (RBFNN) are proposed. Compared with the traditional dynamic model based on the inertial coordinate, the nonlinear dynamic model based on the geographic coordinate constructs the direct relationship among the control inputs and criteria of the ISP. Moreover, the back-stepping sliding mode control method is proposed to handle the system nonlinearity, parameter variations, and disturbances. Furthermore, the adaptive RBFNN is constructed and optimized to estimate the upper bound of the residual error on line to reduce the chatting phenomenon. The asymptotic stability of the proposed control method has been proven by the Lyapunov stability theory. The effectiveness of the proposed method is validated by a series of simulations and flight tests.

Discrete-time optimal adaptive RBFNN control for robot manipulators with uncertain dynamics

In this paper, a novel optimal adaptive radial basis function neural network (RBFNN) control has been investigated for a class of multiple-input-multiple-output (MIMO) nonlinear robot manipulators with uncertain dynamics in discrete time. To facilitate digital implementations of the robot controller, a robot model in discrete time has been employed. A high order uncertain robot model is able to be transformed to a predictor form, and a feedback control system has been then developed without noncausal problem in discrete time. The controller has been designed by an adaptive neural network (NN) based on the feedback system. The adaptive RBFNN robot control system has been investigated by a critic RBFNN and an actor RBFNN to approximate a desired control and a strategic utility function, respectively. The rigorous Lyapunov analysis is used to establish uniformly ultimate boundedness (UUB) of closed-loop signals, and the high-quality dynamic performance against uncertainties and disturbances is obtained by appropriately selecting the controller parameters. Simulation studies validate that the proposed control scheme has performed better than other available methods currently, for robot manipulators.

Attitude tracking control for spacecraft with robust adaptive RBFNN augmenting sliding mode control

This paper investigates the attitude tracking problem for a rigid spacecraft subject to uncertain inertial parameters and external disturbances. A robust adaptive radial basis function neural network (RBFNN) augmenting sliding mode control strategy is developed. The classical sliding mode control serves as the main control framework, which is augmented by a robust adaptive RBFNN to approximate uncertain dynamics consisting of the inertial parameters and external disturbances. The robust adaptive RBFNN approximation combines a conventional RBFNN and a robust adaption, where the conventional RBFNN dominates in the neural active region, the robust adaptive control takes effect in the robust active region, and a smooth switching function is utilized to achieve a smooth transition between two regions. With this adaptive structure, the full-envelop attitude tracking can be realized. This systematic methodology is demonstrated to be able to accomplish the ultimately convergent attitude tracking of the spacecraft. Simulations verify and highlight the theoretical results.

Adaptive robust control of a class of non-affine variable-speed variable-pitch wind turbines with unmodeled dynamics

In this paper, a novel synthesis of Nussbaum-type functions, and an adaptive radial-basis function neural network is proposed to design controllers for variable-speed, variable-pitch wind turbines. Dynamic equations of the wind turbine are highly nonlinear, uncertain, and affected by unknown disturbance sources. Furthermore, the dynamic equations are non-affine with respect to the pitch angle, which is a control input. To address these problems, a Nussbaum-type function, along with a dynamic control law are adopted to resolve the non-affine nature of the equations. Moreover, an adaptive radial-basis function neural network is designed to approximate non-parametric uncertainties. Further, the closed-loop system is made robust to unknown disturbance sources, where no prior knowledge of disturbance bound is assumed in advance. Finally, the Lyapunov stability analysis is conducted to show the stability of the entire closed-loop system. In order to verify analytical results, a simulation is presented and the results are compared to both a PI and an existing adaptive controllers.

A composite control method based on the adaptive RBFNN feedback control and the ESO for two-axis inertially stabilized platforms

Due to the nonlinearity and time variation of a two-axis inertially stabilized platform (ISP) system, the conventional feedback control cannot be utilized directly. To realize the control performance with fast dynamic response and high stabilization precision, the dynamic model of the ISP system is expected to match the ideal model which satisfies the desired control performance. Therefore, a composite control method based on the adaptive radial basis function neural network (RBFNN) feedback control and the extended state observer (ESO), is proposed for ISP. The adaptive RBFNN is proposed to generate the feedback control parameters online. Based on the state error information in the working process, the adaptive RBFNN can be constructed and optimized directly. Therefore, no priori training data is needed for the construction of the RBFNN. Furthermore, a linear second-order ESO is constructed to compensate for the composite disturbance. The asymptotic stability of the proposed control method has been proven by the Lyapunov stability theory. The applicability of the proposed method is validated by a series of simulations and flight tests.

Modeling and robust backstepping sliding mode control with Adaptive RBFNN for a novel coaxial eight-rotor UAV

This paper focuses on the robust attitude control of a novel coaxial eight-rotor unmanned aerial vehicles (UAV) which has higher drive capability as well as greater robustness against disturbances than quad-rotor UAV. The dynamical and kinematical model for the coaxial eight-rotor UAV is developed, which has never been proposed before. A robust backstepping sliding mode controller (BSMC) with adaptive radial basis function neural network (RBFNN) is proposed to control the attitude of the eightrotor UAV in the presence of model uncertainties and external disturbances. The combinative method of backstepping control and sliding mode control has improved robustness and simplified design procedure benefiting from the advantages of both controllers. The adaptive RBFNN as the uncertainty observer can effectively estimate the lumped uncertainties without the knowledge of their bounds for the eight-rotor UAV. Additionally, the adaptive learning algorithm, which can learn the parameters of RBFNN online and compensate the approximation error, is derived using Lyapunov stability theorem. And then the uniformly ultimate stability of the eight-rotor system is proved. Finally, simulation results demonstrate the validity of the proposed robust control method adopted in the novel coaxial eight-rotor UAV in the case of model uncertainties and external disturbances.

The Adaptive Radial Basis Function Neural Network for Small Rotary-Wing Unmanned Aircraft

This paper proposes an online learning adaptive radial basis function neural network (RBFNN) to deal with measurement errors and environment disturbances to improve control performance. Since the weight matrix of the adaptive neural network can be updated online by the state error information, the adaptive neural network can be constructed directly without prior training. Moreover, with the parameter optimization rule, the residual approximation error can be reduced by the maximum absolute position error, average position error, and mean square position error in sampling windows. The applicability of the proposed method is validated by a series of simulations and flight tests. The adaptive RBFNN control method can realize hovering, straight flight, and autonomous landing control under wind disturbances.

Robust neural network control of MEMS gyroscope using adaptive sliding mode compensator

SUMMARYA new robust neural sliding mode (RNSM) tracking control scheme using radial basis function (RBF) neural network (NN) is presented for MEMS z-axis gyroscope to achieve robustness and asymptotic tracking error convergence. An adaptive RBF NN controller is developed to approximate and compensate the large uncertain system dynamics, and a robust compensator is designed to eliminate the impact of NN modeling error and external disturbances for guaranteeing the asymptotic stability property. Moreover, another RBF NN is employed to learn the upper bound of NN modeling error and external disturbances, so the prior knowledge of the upper bound of system uncertainties is not required. All the adaptive laws in the RNSM control system are derived in the same Lyapunov framework, which can guarantee the stability of the closed loop system. Comparative numerical simulations for an MEMS gyroscope are investigated to verify the effectiveness of the proposed RNSM tracking control scheme.

Price Forecasting for Cell Phone Market Using Adaptive Sliding Window and Adaptive RBF NN

In order to get the excellent accuracy for price forecast in the cell phone market, a novel improved Sliding Window (SW) model based on adaptive windows width and a novel improved Radial Basis Function (RBF) Neural Network (NN) model based on adaptive spread are proposed and the Disturbance Factors Model (DFM) is used in this paper. All of the three kinds of price forecasting models are utilized to verify the accuracy. The cell phone price is extracted from different websites and used as the model verification data. And the experimental results of the forecasting average accuracy based on the DFM obtain 94.61 percent. The experimental results of the forecasting average accuracy based on the ARBF NN model obtain 97.88 percent. The experimental results of the forecasting average accuracy based on the Adaptive SW Model (ASWM) obtain 99.64 percent. Although the results based on the DFM are not very good, it is still a satisfactory result. Since it is at least not a very serious result which proves that it is worth to do further researches in the field of the cell phone market based on the DFM. The results based on the ASWM and the ARBF NN models are satisfied. The improved methods enhance the forecast accuracy compared to the original model. In the field of the price forecast on the cell phone market, the improved methods have a good performance which is valuable and useful not only for businesses, but also for consumers.

Adaptive RBFNN Formation Control of Multi-mobile Robots with Actuator Dynamics

We study the problem of formation control and trajectory tracking for multiple nonholonomic mobile robots with actuator and formation dynamics. An adaptive neural-network (NN) control strategy that integrated kinematic controller with input voltages controller of actuator was proposed. A control law was designed by backstepping technique based on separation-bearing formation control structure of leader-follower. The radial basis function neural network (RBFNN) was adopted to achieve on-line estimation for the dynamics nonlinear uncertain part for follower and leader robots. The adaptive robust controller was adopted to compensate modeling errors of NN. This strategy not only overcomed all kinds of uncertainties of mobile robots, but also ensured the desired trajectory tracking of robot formation in the case of maintaining formation. The stability and convergence of the control system were proved by using the Lyapunov theory. The simulation results showed the effectiveness of this proposed method. DOI: http://dx.doi.org/10.11591/telkomnika.v11i4.2334

Adaptive Chaotic Prediction Algorithm of RBF Neural Network Filtering Model Based on Phase Space Reconstruction

With the analysis of the technology of phase space reconstruction, a modeling and forecasting technique based on the Radial Basis Function (RBF) neural network for chaotic time series is presented in this paper. The predictive model of chaotic time series is established with the adaptive RBF neural networks and the steps of the chaotic learning algorithm with adaptive RBF neural networks are expressed. The network system can enhance the stabilization and associative memory of chaotic dynamics and generalization ability of predictive model even by imperfect and variation inputs during the learning and prediction process by selecting the suitable nonlinear feedback term. The dynamics of network become chaotic one in the weight space. Simulation experiments of chaotic time series produced by Lorenz equation are proceeded by a RBF neural network .The experimental and simulating results indicated that the forecast method of the adaptive RBF neutral network compared with the forecast method of back propagation (BP) neutral network based on the chaotic learning algorithm has faster learning capacity and higher accuracy of forecast．The method provides a new way for the chaotic time series prediction.

Adaptive RBF Neural Network Control for Three-Phase Active Power Filter

Abstract An adaptive radial basis function (RBF) neural network control system for three-phase active power filter (APF) is proposed to eliminate harmonics. Compensation current is generated to track command current so as to eliminate the harmonic current of non-linear load and improve the quality of the power system. The asymptotical stability of the APF system can be guaranteed with the proposed adaptive neural network strategy. The parameters of the neural network can be adaptively updated to achieve the desired tracking task. The simulation results demonstrate good performance, for example showing small current tracking error, reduced total harmonic distortion (THD), improved accuracy and strong robustness in the presence of parameters variation and nonlinear load. It is shown that the adaptive RBF neural network control system for three-phase APF gives better control than hysteresis control.

Robust adaptive neural sliding mode control of MEMS triaxial gyroscope with angular velocity estimation

In this paper, a robust adaptive sliding mode control strategy of micro electro-mechanical system (MEMS) triaxial gyroscope using radial basis function (RBF) neural network is presented for the system identification of MEMS gyroscope. A key property of this scheme is that the prior knowledge of the upper bound of the system uncertainties is not required. An adaptive RBF neural network controller is used to learn the unknown upper bound of model uncertainties and external disturbances. The adaptive RBF neural network is incorporated into the adaptive sliding mode control in the Lyapunov sense, and the stability of the proposed adaptive neural sliding mode control can be established. The dynamics and angular velocities of gyroscope can be identified in real time. Numerical simulations are investigated to verify the effectiveness of the proposed adaptive neural sliding mode control scheme, showing that the designed control system has better robust performance in its insensitivity to system nonlinearities; moreover, system parameters including angular velocity can be consistently estimated and tracking errors converge to zero asymptotically.