Control of magnetic bearing systems via the Chebyshevpolynomial-based unified model (CPBUM) neural network

A Chebyshev polynomial-based unified model (CPBUM) neural network is introduced and applied to control a magnetic bearing systems. First, we show that the CPBUM neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural network. It turns out that the CPBUM neural network is more suitable in the design of controller than the conventional feedforward/recurrent neural network. Second, we propose the inverse system method, based on the CPBUM neural networks, to control a magnetic bearing system. The proposed controller has two structures; namely, off-line and on-line learning structures. We derive a new learning algorithm for each proposed structure. The experimental results show that the proposed neural network architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.     

Identification of a golf swing robot using soft computing approach

Golf swing robots have been recently developed in an attempt to simulate the ultra high-speed swing motions of golfers. Accurate identification of a golf swing robot is an important and challenging research topic, which has been regarded as a fundamental basis in the motion analysis and control of the robots. But there have been few studies conducted on the golf swing robot identification, and comparative analyses using different kinds of soft computing methodologies have not been found in the literature. This paper investigates the identification of a golf swing robot based on four kinds of soft computing methods, including feedforward neural networks (FFNN), dynamic recurrent neural networks (DRNN), fuzzy neural networks (FNN) and dynamic recurrent fuzzy neural networks (DRFNN). The performance comparison is evaluated based on three sets of swing trajectory data with different boundary conditions. The sensitivity of the results to the changes in system structure and learning rate is also investigated. The results suggest that both FNN and DRFNN can be used as a soft computing method to identify a golf robot more accurately than FFNN and DRNN, which can be used in the motion control of the robot.     

非线性系统的回归网络辨识

针对未知非线性系统的辨识问题,本文提出了一种新型的回归网络模型,证明了该网络模型在一定条件下能够逼近非线性系统的输入输出关系,提出了训练网络前向连接和反向连接权值的动态反向传播算法,伪真结果验证该方法的有效性。     

Modeling and sensitivity analysis of neural networks

This paper investigates the use of neural networks for the identification of linear time invariant dynamical systems. Two classes of networks, namely the multilayer feedforward network and the recurrent network with linear neurons, are studied. A notation based on Kronecker product and vector-valued function of matrix is introduced for neural models. It permits to write a feedforward network as a one step ahead predictor used in parameter estimation. A special attention is devoted to system theory interpretation of neural models. Sensitivity analysis can be formulated using derivatives based on the above-mentioned notation.     

Neural network synthesis for thermal processes

Neural networks are relatively new and highly attractive tools for modelling complex systems. The main feature of neural networks is their inherent plasticity which enables them to fit virtually any nonlinear function provided they have a sufficient number of parameters. Neural networks are a general class of nonlinear systems. Neural models can be used advantageously to model the dynamic behaviour of physical processes. In this paper, feedforward neural networks are used for modelling of dynamic thermal processes. The synthesis of neural networks is directly associated with the minimization of an objective function normally defined as the square of the difference between the output of the process being modelled and the output predicted by the network. Learning schemes are used for the evaluation of the connection weights of the feedforward neural network. In this paper, the dynamic modelling of several thermal processes using feedforward neural networks is presented. In one example, the identified neural model of the inverse of the plant is used as a controller.     

Model predictive control of an industrial packed bed reactor using neural networks

This paper discusses an industrial application of a multivariable nonlinear feedforward/feedback model predictive control where the model is given by a dynamic neural network. A multi-pass packed bed reactor temperature profile is modelled via recurrent neural networks using the backpropagation through time training algorithm. This model is then used in conjunction with an optimizer to build a nonlinear model predictive controller. Results show that, compared with conventional control schemes, the neural network model based controller can achieve tighter temperature control for disturbance rejection     

基于反馈神经网络的动态化工过程建模

针对非线性动态化工过程建模存在的问题,提出了一种新的反馈神经网络结构,并将状态反馈、时间序列延尺以及集中节点的概念结合起来,用于提高反馈神经网络的性能,同时又使得网络结构不至于太复杂,在用此网络结构建模的时间,成功地将BP算法用一网络模型的训练。文中将这种反馈神经网络结构分别对一个单输入单输出（SISO）的非线笥动态系统和一个多输入单输出（SIMO）的连续全混釜（CSTR）模型进行建模,并将所得模型与基于表态BP神经神经所得的模型在模型输出精度和抗干扰性等方面进行了比较,证明了该反馈神经在动态过程建模中能够比静态BP模型更好地反映出动态过程的输入输出关系,并具有一定的抗干扰能力。     

Neurocontrol of nonlinear dynamical systems with Kalman filtertrained recurrent networks

Although the potential of the powerful mapping and representational capabilities of recurrent network architectures is generally recognized by the neural network research community, recurrent neural networks have not been widely used for the control of nonlinear dynamical systems, possibly due to the relative ineffectiveness of simple gradient descent training algorithms. Developments in the use of parameter-based extended Kalman filter algorithms for training recurrent networks may provide a mechanism by which these architectures will prove to be of practical value. This paper presents a decoupled extended Kalman filter (DEKF) algorithm for training of recurrent networks with special emphasis on application to control problems. We demonstrate in simulation the application of the DEKF algorithm to a series of example control problems ranging from the well-known cart-pole and bioreactor benchmark problems to an automotive subsystem, engine idle speed control. These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise.     

Neural network controller with flexible structure based on feedback-error-learning approach

In practice, the back-propagation algorithm often runs very slowly, and the question naturally arises as to whether there are necessarily intrinsic computation and difficulties with training neural networks, or better training algorithms might exist. Two important issues will be investigated in this framework. One establishes a flexible structure, to construct very simple neural network for multi-input/output systems. The other issue is how to obtain the learning algorthm to achieve good performance in the training phase. In this paper, the feedforward neural network with flexible bipolar sigmoid functions (FBSFs) are investigated to learn the inverse model of the system. The FBSF has changeable shape by changing the values of its parameter according to the desired trajectory or the teaching signal. The proposed neural network is trained to learn the inverse dynamic model by using back-propagation learning algorithms. In these learning algorithms, not only the connection weights but also the sigmoid function parameters (SFPs) are adjustable. The feedback-error-learning is used as a learning method for the feedforward controller. In this case, the output of a feedback controller is fed to the neural network model. The suggested method is applied to a two-link robotic manipulator control system which is configured as a direct controller for the system to demonstrate the capability of our scheme. Also, the advantages of the proposed structure over other traditional neural network structures are discussed.     

The Chebyshev-polynomials-based unified model neural networks forfunction approximation

In this paper, we propose the approximate transformable technique, which includes the direct transformation and indirect transformation, to obtain a Chebyshev-Polynomials-Based (CPB) unified model neural networks for feedforward/recurrent neural networks via Chebyshev polynomials approximation. Based on this approximate transformable technique, we have derived the relationship between the single-layer neural networks and multilayer perceptron neural networks. It is shown that the CPB unified model neural networks can be represented as a functional link networks that are based on Chebyshev polynomials, and those networks use the recursive least square method with forgetting factor as learning algorithm. It turns out that the CPB unified model neural networks not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural networks. Furthermore, we have also derived the condition such that the unified model generating by Chebyshev polynomials is optimal in the sense of error least square approximation in the single variable ease. Computer simulations show that the proposed method does have the capability of universal approximator in some functional approximation with considerable reduction in learning time.     

循环神经网络前馈补偿的压电驱动器跟踪控制

压电驱动器固有的迟滞特性,以及其他动态特性严重地影响其跟踪性能.循环神经网络能够准确拟合非线性系统,并且具有记忆存储能力,本文设计了一种循环神经网络对压电驱动器的迟滞特性进行建模,进而得到能够准确模拟输出位移和输入电压之间关系的逆模型,并据此对压电驱动器进行前馈补偿.此外,考虑到建模误差以及其他扰动对驱动器跟踪精度的影...     

Solving the problem of negative synaptic weights in cortical models

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.     

Indirect control of a class of nonlinear dynamic systems

Identification and control designs are considered using neural networks for a class of nonlinear partially known dynamic systems. Real-time implementation of two designs, a neural identifier and a proposed neural controller, using an experimental system, comparisons with two other neural networks as well as conventional schemes, and an implementation architecture are reported. The proposed control design facilitates incorporation of available knowledge about the structure of the system. The study also illustrates the inherent capability of neural networks to handle nonlinearities and perform control effectively for a real world system, based on minimal system information.     

Prediction and identification using wavelet-based recurrent fuzzy neural networks

This paper presents a wavelet-based recurrent fuzzy neural network (WRFNN) for prediction and identification of nonlinear dynamic systems. The proposed WRFNN model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This paper adopts the nonorthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer of the feedforward wavelet-based fuzzy neural networks (WFNN). An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Finally, computer simulations have demonstrated that the proposed WRFNN model requires fewer adjustable parameters and obtains a smaller rms error than other methods.     

基于回归神经网络的非线性时变系统辨识

为克服基于前馈神经网络的非线性系统辨识算法存在需预先估计系统输入输出滞后阶数的缺陷，提出一种基于回归神经网络的非线性时变系统的辨识算法，针对现有的回归网络学习算法大多采用梯度算法，收敛速度缓慢问题，提出一种具有快速收敛性的扩展卡尔曼滤波学习算法，大大提高了学习收敛速度，并推导了一种基于单个神经元的局部化算法，减少了计算量，仿真实例证明，所提出的算法是有效的。     

前馈神经网络的新学习算法研究及其应用

为了提高多层前馈神经网络的权的学习效率。通过引入变尺度法,提出一种新的学习算法。理论上新算法不仅具有变尺度优化方法的一切优点,而且也能起到Kick—Out学习算法中动量项及修正项的相同作用,同时又克服了动量系数及修正项系数难以适当选择的困难。仿真试验证明了新学习算法用于非线性动态系统建模时的有效性。     

Learning long-term dependencies in NARX recurrent neural networks

It has previously been shown that gradient-descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long-term dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. We show that the long-term dependencies problem is lessened for a class of architectures called nonlinear autoregressive models with exogenous (NARX) recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning can be more effective in NARX networks than in recurrent neural network architectures that have "hidden states" on problems including grammatical inference and nonlinear system identification. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are consistent with this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventional recurrent neural networks. We show that although NARX networks do not circumvent the problem of long-term dependencies, they can greatly improve performance on long-term dependency problems. We also describe in detail some of the assumptions regarding what it means to latch information robustly and suggest possible ways to loosen these assumptions.     

A data-based framework for fault detection and diagnostics of non-linear systems with partial state measurement

A novel framework based on the use of dynamic neural networks for data-based process monitoring, fault detection and diagnostics of non-linear systems with partial state measurement is presented in this paper. The proposed framework considers the presence of three kinds of states in a generic system model: states that can easily be measured in real time and in-situ, states that are difficult to measure online but can be measured offline to generate training data, and states that cannot be measured at all. The motivation for such a categorization of state variables comes from a wide class of problems in the manufacturing and chemical industries, wherein certain states are not measurable without expensive equipments or offline analysis while some other states may not be accessible at all. The framework makes use of a recurrent neural network for modeling the hidden dynamics of the system from available measurements and uses this model along with a non-linear observer to augment the information provided by the measured variables. The performance of the proposed method is verified on a synthetic problem as well as a benchmark simulation problem.     

Training trajectories by continuous recurrent multilayer networks

This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagin's maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.