The Role and Place of Artificial Neural Network Architectures Structural Redundancy in the Input Data Prototypes and Generalization Development

Neural Networks (NN) are the functional unit of Deep Learning and are known to mimic the behavior of the human brain to solve complex data-driven problems. Whenever we train our own neural networks, we need to take care of something called the generalization of the neural network. The performance of Artificial Neural Networks (ANN) mostly depends upon its generalization capability. In this paper, we propose an innovative approach to enhance the generalization capability of artificial neural networks (ANN) using structural redundancy. A novel perspective on handling input data prototypes and their impact on the development of generalization, which could improve to ANN architectures accuracy and reliability is described.

Adaptive H~∞ Control of Nonlinear Systems with Neural Networks

The discussion is devoted to the adaptive H ∞ control method based on RBF neural networks for uncertain nonlinear systems in this paper. The controller consists of an equivalent controller and an H ∞ controller. The RBF neural networks are used to approximate the nonlinear functions and the approximation errors of the neural networks are used in the adaptive law to improve the performance of the systems. The H ∞ controller is designed for attenuating the influence of external disturbance and neural network approximation errors. The controller can not only guarantee stability of the nonlinear systems, but also attenuate the effect of the external disturbance and neural networks approximation errors to reach performance indexes. Finally, an example validates the effectiveness of this method.

An Adaptive RBF Neural Network Control Method for a Class of Nonlinear Systems

This paper focuses on designing an adaptive radial basis function neural network(RBFNN) control method for a class of nonlinear systems with unknown parameters and bounded disturbances. The problems raised by the unknown functions and external disturbances in the nonlinear system are overcome by RBFNN, combined with the single parameter direct adaptive control method. The novel adaptive control method is designed to reduce the amount of computations effectively.The uniform ultimate boundedness of the closed-loop system is guaranteed by the proposed controller. A coupled motor drives(CMD) system, which satisfies the structure of nonlinear system,is taken for simulation to confirm the effectiveness of the method.Simulations show that the developed adaptive controller has favorable performance on tracking desired signal and verify the stability of the closed-loop system.

Evaluation on Stability of Stope Structure Based on Nonlinear Dynamics of Coupling Artificial Neural Network

The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.

Adaptive Neural Network Dynamic Surface Control for Perturbed Nonlinear Time-delay Systems

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of ＂explosion of complexity＂ in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of ＂curse of dimensionality＂ and ＂explosion of complexity＂ are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.

Adaptive RBF neural network control of robot with actuator nonlinearities

In this paper, an adaptive neural network control scheme for robot manipulators with actuator nonlinearities is presented. The control scheme consists of an adaptive neural network controller and an actuator nonlinearities compensator. Since the actuator nonlinearities are usually included in the robot driving motor, a compensator using radial basis function (RBF) network is proposed to estimate the actuator nonlinearities and eliminate their effects. Subsequently, an adaptive neural network controller that neither requires the evaluation of inverse dynamical model nor the time-consuming training process is given. In addition, GL matrix and its product operator are introduced to help prove the stability of the closed control system. Considering the adaptive neural network controller and the RBF network compensator as the whole control scheme, the closed-loop system is proved to be uniformly ultimately bounded (UUB). The whole scheme provides a general procedure to control the robot manipulators with actuator nonlinearities. Simulation results verify the effectiveness of the designed scheme and the theoretical discussion.

Model algorithm control using neural networks for input delayed nonlinear control system

The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to ＂learn＂the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.

Nonlinear Dynamics and Stability of Neural Networks with Delay-Time

In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks(NNs)tracking controller is proposed for a class of single-input/singleoutput(SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter.Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature.In controller design of the proposed approach, a state observer,based on the strictly positive real(SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.

Adaptive Output-feedback Regulation for Nonlinear Delayed Systems Using Neural Network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.

A Fuzzy-Neural Network Control of Nonlinear Dynamic Systems

In this paper, an adaptive dynamic control scheme based on a fuzzy neural network is presented, that presents utilizes both feed-forward and feedback controller elements. The former of the two elements comprises a neural network with both identification and control role, and the latter is a fuzzy neural algorithm, which is introduced to provide additional control enhancement. The feedforward controller provides only coarse control, whereas the feedback controller can generate on-line conditional proposition rule automatically to improve the overall control action. These properties make the design very versatile and applicable to a range of industrial applications.

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.

Adaptive output-feedback control for MIMO nonlinear systems with time-varying delays using neural networks

An adaptive neural network output-feedback regulation approach is proposed for a class of multi-input-multi-output nonlinear time-varying delayed systems.Both the designed observer and controller are free from time delays.Different from the existing results,this paper need not the assumption that the upper bounding functions of time-delay terms are known,and only a neural network is employed to compensate for all the upper bounding functions of time-delay terms,so the designed controller procedure is more simplified.In addition,the resulting closed-loop system is proved to be semi-globally ultimately uniformly bounded,and the output regulation error converges to a small residual set around the origin.Two simulation examples are provided to verify the effectiveness of control scheme.

Dynamic Neural Network Based Nonlinear Control of a Distillation Column

Taking advantage of the knowledge of top and bottom compositions of a distillation column, a dynamic neural network (DNN) is designed to identify the input-output relationship of the column. The weight-training algorithm is derived from a Lyapunov function. Based on this empirical model, a nonlinear H∞ controller is synthesized. The effectiveness of the control strategy is demonstrated using simulation results.

The adaptive control using BP neural networks for a nonlinear servo-motor

The servo-motor possesses a strongly nonlinear property due to the effect of the stimulating input voltage, load-torque and environmental operating conditions. So it is rather difficult to derive a traditional mathematical model which is capable of expressing both its dynamics and steady-state characteristics. A neural network-based adaptive control strategy is proposed in this paper. In this method, two neural networks have been adopted for system identification （NNI） and control （NNC）, respectively. Then, the commonly-used specialized learning has been modified, by taking the NNI output as the approximation output of the servo-motor during the weights training to get sensitivity information. Moreover, the rule for choosing the learning rate is given on the basis of the analysis of Lyapunov stability. Finally, an example of applying the proposed control strategy on a servo-motor is presented to show its effectiveness.

A New Class of Nonlinear Error Control Codes Based on Neural Networks

By mcans of stable attractors of discret Hopfield neural network (DHNN) , anew class of nonlinear error control codes is sugsested and some relativetheorems are presented. A kind of single error control codes is also given forillustrating this new approach.

Neural network based adaptive sliding mode control of uncertain nonlinear systems

The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.

Nonlinear Decoupling PID Control Using Neural Networks and Multiple Models

For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential （PID） controller is proposed, which consists of a traditional PID controller, a decoupling compensator and a feedforward compensator for the unmodeled dynamics. The parameters of such controller is selected based on the generalized minimum variance control law. The unmodeled dynamics is estimated and compensated by neural networks, a switching mechanism is introduced to improve tracking performance, then a nonlinear decoupling PID control algorithm is proposed. All signals in such switching system are globally bounded and the tracking error is convergent. Simulations show effectiveness of the algorithm.

Algorithm of neural-network about solving nonlinear least squares adjustment by parameters

Study on solving nonlinear least squares adjustment by parameters is one of the most important and new subjects in modern surveying and mapping field . Many researchers have done a lot of work and gained some solving methods. These methods mainly include iterative algorithms and direct algorithms mainly. The former searches some methods of rapid convergence based on which surveying adjustment is a kind of problem of nonlinear programming. Among them the iterative algorithms of the most in common use are the Gauss-Newton method, damped least quares, quasi-Newton method and some mutations etc. Although these methods improved the quantity of the observation results to a certain degree, and increased the accuracy of the adjustment results, what we want is whether the initial values of unknown parameters are close to their real values. Of course, the model of the latter has better degree in linearity, that is to say, they nearly have the meaning of deeper theories researches. This paper puts forward a kind of method of solving the problems of nonlinear least squares adjustment by parameters based on neural network theory, and studies its stability and convergency. The results of calculating of living example indicate the method acts well for solving parameters problems by nonlinear least squares adjustment without giving exact approximation of parameters.

Adaptive L_2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L 2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set. Moreover, the generalized matching conditions are also relaxed in the proposed L 2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.