Neural Network Approximation Errors Research Articles

Adaptive robust backstepping control for a class of uncertain dynamical systems using neural networks

The problem of robust stabilization is considered for a class of nonlinear systems in the presence of structure uncertainties, external disturbances, and unknown time-varying virtual control coefficients. It is supposed that the upper bounds of the external disturbances and the virtual control coefficients are unknown. The unknown structural uncertainties are approximated by using neural networks (NNs). In particular, the prior knowledge about the weights and approximation errors of NNs is not required. The improved adaptation laws with $$\sigma $$ -modification are employed to estimate the unknown parameters, which contain the upper bounds of the external disturbances and the virtual control coefficients, and the norm forms of weights and approximate errors of the NNs. Then, by making use of the updated values of these unknown parameters, a class of backstepping approach-based continuous adaptive robust state feedback controllers is synthesized. It is also shown that the proposed adaptive robust backstepping controller can guarantee the uniform asymptotic stability of such uncertain dynamical systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed controller.

Neural network-based compensation control for trajectory tracking of industrial robots

In this paper, a novel dynamic compensatory strategy based on radial basis function (RBF) neural network robust H∞ controller is put forward for improving trajectory tracking accuracy of robot manipulators on account of modelling errors and external disturbances. The proposed strategy is effective to compensate the computed torque controller relied on precise dynamic model of robot, consisting of a RBF neural network, a variable structure controller and a robust H∞ controller. Furthermore, a velocity feed-forward with proposed method is employed to achieve higher trajectory tracking accuracy of end-effector and avoid the consideration of torque interface. The parameters of uncertain dynamics model are estimated by RBF neural network, while a variable structure controller is employed to make up the approximation errors of neural network. With the help of robust H∞ controller, effect of external disturbances will be attenuated and the robust tracking performance is achieved. Based on Lyapunov stability theorem, it is shown that the proposed controller can guarantee the stability of the control system and the desired performance of robotic system. The simulations and experiments on a multi-robot cutting manipulator indicate that the proposed compensatory strategy for industrial robot manipulator is superior to traditional computed torque control method in consideration of uncertainties.

Adaptive neural finite-time control for a class of switched nonlinear systems

This paper investigates the adaptive finite-time stabilization of a class of switched nonlinear systems with unknown nonlinear terms using neural networks. Under the assumption that all the growth conditions for the unknown nonlinear perturbation functions are partially known, the common finite-time controller and adaptive law are constructed by extending the adding-a-power-integrator technique and using the backstepping methodology. The unknown parts of the growth conditions are modeled by the neural networks and the known parts are exploited for the controller design. The bounds of neural network approximation errors are assumed to be unknown and are estimated online. It is shown that the state of the closed-loop system is finite-time stable and the parameter estimations are bounded under arbitrary switching. A simulation example is provided to show the effectiveness of the proposed method.

Adaptive Dynamic Programming for a Class of Complex-Valued Nonlinear Systems

In this brief, an optimal control scheme based on adaptive dynamic programming (ADP) is developed to solve infinite-horizon optimal control problems of continuous-time complex-valued nonlinear systems. A new performance index function is established on the basis of complex-valued state and control. Using system transformations, the complex-valued system is transformed into a real-valued one, which overcomes Cauchy-Riemann conditions effectively. With the transformed system and the performance index function, a new ADP method is developed to obtain the optimal control law by using neural networks. A compensation controller is developed to compensate the approximation errors of neural networks. Stability properties of the nonlinear system are analyzed and convergence properties of the weights for neural networks are presented. Finally, simulation results demonstrate the performance of the developed optimal control scheme for complex-valued nonlinear systems.

Online adaptive policy learning algorithm for H∞ state feedback control of unknown affine nonlinear discrete-time systems.

The problem of H∞ state feedback control of affine nonlinear discrete-time systems with unknown dynamics is investigated in this paper. An online adaptive policy learning algorithm (APLA) based on adaptive dynamic programming (ADP) is proposed for learning in real-time the solution to the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in the H∞ control problem. In the proposed algorithm, three neural networks (NNs) are utilized to find suitable approximations of the optimal value function and the saddle point feedback control and disturbance policies. Novel weight updating laws are given to tune the critic, actor, and disturbance NNs simultaneously by using data generated in real-time along the system trajectories. Considering NN approximation errors, we provide the stability analysis of the proposed algorithm with Lyapunov approach. Moreover, the need of the system input dynamics for the proposed algorithm is relaxed by using a NN identification scheme. Finally, simulation examples show the effectiveness of the proposed algorithm.

Adaptive Control of Space Robot Manipulators with Task Space Base on Neural Network

As are considered, the body posture is controlled and position cannot control, space manipulator system model is difficult to be set up because of disturbance and model uncertainty. An adaptive control strategy based on neural network is put forward. Neural network on-line modeling technology is used to approximate the system uncertain model, and the strategy avoids solving the inverse Jacobi matrix, neural network approximation error and external bounded disturbance are eliminated by variable structure control controller. Inverse dynamic model of the control strategy does not need to be estimated, also do not need to take the training process, globally asymptotically stable of the closed-loop system is proved based on the lyapunov theory. The simulation results show that the designed controller can achieve high control precision has the important value of engineering application.

Design of Robust Adaptive Neural Switching Controller for Robotic Manipulators with Uncertainty and Disturbances

In this paper, we present the robust adaptive neural switching control problem for the application of robotic manipulators with uncertainty and disturbances. The control scheme relaxes the hypothesis that the bounds of external disturbance and approximation errors of neural networks are known. RBF Neural Networks (Radial Basis Function NNs) are adopted to approximate unknown functions of robotic manipulators and an H ? $\infty $ controller is designed to enhance system robustness and stabilization due to the existence of the compound disturbance which consists of approximation errors of the neural networks and external disturbance. The adaptive updated laws and the admissible switching signals have been derived from switched multiple Lyapunov function method, so that both system tracking stability and error convergence can be guaranteed in the closed-loop system. Experimental results have demonstrated the improved performance of the proposed control scheme over PD (Proportional Differential) control strategy, which have shown good accuracy of position tracking.

Dead Zone Compensation Control of Free-floating Space Robotic Manipulators Based on Neural Network

Model errors and dead-zone problems of free-floating space manipulators are considered. An adaptive compensation control method based on neural network is put forward. Neural network with good approximation ability is used to compensate the model errors. Variable structure controller is designed to eliminate approximation errors of neural network. Two neural networks is designed respectively to estimate and compensate dead zone model of joint actuator. By the dead zone compensation principle, the online adaptive learning law of weights is designed. The stability of control system is proved based on Lyapunov theory. The simulation results verify the effectiveness of the controller.

Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer.

In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.

Neural network-based adaptive position tracking control for bilateral teleoperation under constant time delay

The trajectory tracking problem for the teleoperation systems is addressed in this paper. Two neural network-based controllers are designed for the teleoperation system in free motion. First, with the defined synchronization variables containing the velocity error and the position error between master and slaver, a new adaptive controller using the acceleration signal is designed to guarantee the position and velocity tracking performance between the master and the slave manipulators. Second, with the acceleration signal unavailable, a controller with the new synchronization variables is proposed such that the trajectory tracking error between the master and the slave robots asymptotically converges to zero. By choosing proper Lyapunov functions, the asymptotic tracking performance with these two controllers is proved without the knowledge of the upper bound of the neural network approximation error and the external disturbance. Finally, the simulations are performed to show the effectiveness of the proposed methods.

H2 Fault Tolerant Controller Design for a Class of Nonlinear Systems with a Spacecraft Control Application

This paper presents an H2 robust fault tolerant controller design method for uncertain systems in the presence of unknown failures. The developed H2 controller with optimal index incorporates a neural network learning action and sliding mode control action. A radial basis function (RBF) neural network is utilized to approximate the unknown nonlinear dynamics. An updating rule is designed to estimate actuator failure. The sliding-mode control is used to eliminate the effect of neural network approximation error. Based on Lyapunov function, the sufficient condition for H2 optimal performance is developed in terms of nonlinear quadratic matrix inequality. In order to reduce computing cost, a simplification algorithm is developed, which avoids solving on-line nonlinear matrix inequality. A numerical example on a spacecraft system is presented to demonstrate the effectiveness of the proposed methods.

The Estimate for Approximation Error of Neural Network with Two Weights

The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of R m to R n and any continuous function, which has limit at infinite place, from limitless close subset of R m to R n. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.

ADAPTIVE TRACKING CONTROL OF NONHOLONOMIC SYSTEMS BASED ON FEEDBACK ERROR LEARNING

In this paper, we present an adaptive feedback error learning (AFEL) control scheme that are suitable for a class of nonholonomic wheeled mobile robots with uncertainties. The proposed algorithm employs nonlinear function approximation with automatic growth of the neural network (NN) learning according to the nonlinearities and the working domain of the tracking control system. The unknown function in dynamical system is approximated by training nonlinear NN models, and, imperfect approximation errors of NNs are relaxed by designing parallel robust term. Lyapunov synthesis is proposed for AFEL control design with guaranteed stability. Inspired by composite adaptive control scheme, the proposed adaptive control algorithm employs both closed-loop tracking errors and estimation errors to optimize the parameters by NN online weight tuning algorithms, which guarantee small tracking errors and no loss of stability in robot motion with bounded input signals. We demonstrate superior tracking results using the proposed AFEL control method in various Matlab simulations.

Sliding Mode Control for a Class of Uncertain MIMO Nonlinear Systems with Application to Near-Space Vehicles

We propose a robust sliding mode control (SMC) scheme for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems with the unknown external disturbance, the system uncertainty, and the backlash-like hysteresis. To tackle the continuous system uncertainty, the radial basis function (RBF) neural network is employed to approximate it. And then, combine the unknown external disturbance, and the unknown neural network approximation error with the affection caused by backlash-like hysteresis as a compounded disturbance which is estimated using the developed nonlinear disturbance observer. The robust sliding mode control based on the nonlinear disturbance observer and RBF neural network is presented to track the desired system output in the presence of the unknown system uncertainty, the external disturbance, and the backlash-like hysteresis. Finally, the designed robust sliding mode control strategy is applied to the near-space vehicle (NSV) attitude dynamics, and simulation results are given to illustrate the effectiveness of the proposed sliding mode control approach.

Optimal control for discrete-time affine non-linear systems using general value iteration

In this study, the authors propose a novel adaptive dynamic programming scheme based on general value iteration (VI) to obtain near optimal control for discrete-time affine non-linear systems with continuous state and control spaces. First, the selection of initial value function is different from the traditional VI, and a new method is introduced to demonstrate the convergence property and convergence speed of value function. Then, the control law obtained at each iteration can stabilise the system under some conditions. At last, an error-bound-based condition is derived considering the approximation errors of neural networks, and then the error between the optimal and approximated value functions can also be estimated. To facilitate the implementation of the iterative scheme, three neural networks with Levenberg-Marquardt training algorithm are used to approximate the unknown system, the value function and the control law. Two simulation examples are presented to demonstrate the effectiveness of the proposed scheme.

Stability analysis of robust adaptive hybrid position/force controller for robot manipulators using neural network with uncertainties

The aim of this paper is to design a robust adaptive neural network-based hybrid position/force control scheme for robot manipulators in the presence of model uncertainties and external disturbance. The feedforward neural network employed to learn a highly nonlinear function requires no preliminary learning. The control purposes are to achieve the stability in the sense of Lyapunov for desired interaction force between the end-effector and the environment and to regulate robot tip position in cartesian space. An adaptive compensator is also developed to eliminate the effect of disturbance term of neural network approximation error and external disturbance or unmodeled dynamics etc. A key feature of this compensator is that the prior information of the disturbance bound is not required. Finally, a comparative simulation study with a model-based robust control scheme for a two-link robot manipulator is presented.

Adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence

In this paper, a novel neuro-optimal control scheme is proposed for unknown nonaffine nonlinear discrete-time systems by using adaptive dynamic programming (ADP) method. A neuro identifier is established by employing recurrent neural networks (RNNs) model to reconstruct the unknown system dynamics. The convergence of the identification error is proved by using the Lyapunov theory. Then based on the established RNN model, the ADP method is utilized to design the approximate optimal controller. Two neural networks (NNs) are used to implement the iterative algorithm. The convergence of the action NN error and weight estimation errors is demonstrated while considering the NN approximation errors. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

Nonlinear inversion-based control with adaptive neural network compensation for uncertain MIMO systems

A robust output feedback control scheme for uncertain nonlinear multiple-input and multiple-output (MIMO) systems is proposed, which combines a nonlinear inversion-based controller with a neural network-based robust compensator. The nonlinear inversion-based controller acts as the main controller, and a neural network with an adaptive update law is designed to model the unknown system dynamics, a variable structure controller is employed to eliminate the effect of the neural network approximation errors and to ensure the system stability. Furthermore, an H∞ controller which is a component of the robust compensator is designed to achieve a certain robust tracking performance and to attenuate the effect of external disturbances to a prescribed level. The proposed approach indicates that the nonlinear inversion-based control method is also valid for controlling uncertain nonlinear MIMO systems with uncertainties and disturbances, provided that a compensative controller is designed appropriately. Simulation results demonstrated that the proposed controller performed better in comparison to the nonlinear inversion-based control method and an advanced neural network-based hybrid controller.

Robust Adaptive Neural Sliding Mode Approach for Tracking Control of a MEMS Triaxial Gyroscope

In this paper, a neural network adaptive sliding mode control is proposed for an MEMS triaxial gyroscope with unknown system nonlinearities. An input-output linearization technique is incorporated into the neural adaptive tracking control to cancel the nonlinearities, and the neural network whose parameters are updated from the Lyapunov approach is used to perform the linearization control law. The sliding mode control is utilized to compensate the neural network's approximation errors. The stability of the closed-loop system can be guaranteed with the proposed adaptive neural sliding mode control. Numerical simulations are investigated to verify the effectiveness of the proposed adaptive neural sliding mode control scheme.

Robust Adaptive Neural Sliding Mode Approach for Tracking Control of a MEMS Triaxial Gyroscope

In this paper, a neural network adaptive sliding mode control is proposed for an MEMS triaxial gyroscope with unknown system nonlinearities. An input-output linearization technique is incorporated into the neural adaptive tracking control to cancel the nonlinearities, and the neural network whose parameters are updated from the Lyapunov approach is used to perform the linearization control law. The sliding mode control is utilized to compensate the neural network's approximation errors. The stability of the closed-loop system can be guaranteed with the proposed adaptive neural sliding mode control. Numerical simulations are investigated to verify the effectiveness of the proposed adaptive neural sliding mode control scheme.