Advanced self-organizing polynomial neural network

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.     

Optimization of self-organizing polynomial neural networks

The main disadvantage of self-organizing polynomial neural networks (SOPNN) automatically structured and trained by the group method of data handling (GMDH) algorithm is a partial optimization of model weights as the GMDH algorithm optimizes only the weights of the topmost (output) node. In order to estimate to what extent the approximation accuracy of the obtained model can be improved the particle swarm optimization (PSO) has been used for the optimization of weights of all node-polynomials. Since the PSO is generally computationally expensive and time consuming a more efficient Levenberg–Marquardt (LM) algorithm is adapted for the optimization of the SOPNN. After it has been optimized by the LM algorithm the SOPNN outperformed the corresponding models based on artificial neural networks (ANN) and support vector method (SVM). The research is based on the meta-modeling of the thermodynamic effects in fluid flow measurements with time-constraints. The outstanding characteristics of the optimized SOPNN models are also demonstrated in learning the recurrence relations of multiple superimposed oscillations (MSO).     

An improved SPSA algorithm for system identification using fuzzy rules for training neural networks

Simultaneous perturbation stochastic approximation (SPSA) belongs to the class of gradient-free optimization methods that extract gradient information from successive objective function evaluation. This paper describes an improved SPSA algorithm, which entails fuzzy adaptive gain sequences, gradient smoothing, and a step rejection procedure to enhance convergence and stability. The proposed fuzzy adaptive simultaneous perturbation approximation (FASPA) algorithm is particularly well suited to problems involving a large number of parameters such as those encountered in nonlinear system identification using neural networks (NNs). Accordingly, a multilayer perceptron (MLP) network with popular training algorithms was used to predicate the system response. We found that an MLP trained by FASPSA had the desired accuracy that was comparable to results obtained by traditional system identification algorithms. Simulation results for typical nonlinear systems demonstrate that the proposed NN architecture trained with FASPSA yields improved system identification as measured by reduced time of convergence and a smaller identification error.     

Adaptive neural network control of nonlinear systems by state andoutput feedback

This paper presents a novel control method for a general class of nonlinear systems using neural networks (NNs). Firstly, under the conditions of the system output and its time derivatives being available for feedback, an adaptive state feedback NN controller is developed. When only the output is measurable, by using a high-gain observer to estimate the derivatives of the system output, an adaptive output feedback NN controller is proposed. The closed-loop system is proven to be semi-globally uniformly ultimately bounded (SGUUB). In addition, if the approximation accuracy of the neural networks is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussions.     

基于神经网络非线性系统辨识和控制的研究

本文提出了由静态的前馈网络和稳定的滤波器构成的非线性系统的辨识模型，在神经网络固有的逼近误差存在的情况下，从理论上讨论了神经网络应用于辨识控制过程中系统的稳定性问题，最后研究了在非线性系统的轨迹跟踪过程中增加滑动控制来偿神经网络的逼近误差，从而提高系统跟踪性能。     

A comparative evaluation of neural networks and hidden Markov models for monitoring turning tool wear

Condition monitoring of machine tool inserts is important for increasing the reliability and quality of machining operations. Various methods have been proposed for effective tool condition monitoring (TCM), and currently it is generally accepted that the indirect sensor-based approach is the best practical solution to reliable TCM. Furthermore, in recent years, neural networks (NNs) have been shown to model successfully, the complex relationships between input feature sets of sensor signals and tool wear data. NNs have several properties that make them ideal for effectively handling noisy and even incomplete data sets. There are several NN paradigms which can be combined to model static and dynamic systems. Another powerful method of modeling noisy dynamic systems is by using hidden Markov models (HMMs), which are commonly employed in modern speech-recognition systems. The use of HMMs for TCM was recently proposed in the literature. Though the results of these studies were quite promising, no comparative results of competing methods such as NNs are currently available. This paper is aimed at presenting a comparative evaluation of the performance of NNs and HMMs for a TCM application. The methods are employed on exactly the same data sets obtained from an industrial turning operation. The advantages and disadvantages of both methods are described, which will assist the condition-monitoring community to choose a modeling method for other applications.     

Wavelet networks for nonlinear system modeling

This study presents a nonlinear systems and function learning by using wavelet network. Wavelet networks are as neural network for training and structural approach. But, training algorithms of wavelet networks is required a smaller number of iterations when the compared with neural networks. Gaussian-based mother wavelet function is used as an activation function. Wavelet networks have three main parameters; dilation, translation, and connection parameters (weights). Initial values of these parameters are randomly selected. They are optimized during training (learning) phase. Because of random selection of all initial values, it may not be suitable for process modeling. Because wavelet functions are rapidly vanishing functions. For this reason heuristic procedure has been used. In this study serial-parallel identification model has been applied to system modeling. This structure does not utilize feedback. Real system outputs have been exercised for prediction of the future system outputs. So that stability and approximation of the network is guaranteed. Gradient methods have been applied for parameters updating with momentum term. Quadratic cost function is used for error minimization. Three example problems have been examined in the simulation. They are static nonlinear functions and discrete dynamic nonlinear system.     

Semiglobal ISpS disturbance attenuation with output tracking via direct adaptive design.

Direct adaptive partial state feedback control is presented to achieve semiglobally input-to-state practically stable (ISpS) disturbance attenuation with output tracking for a class of uncertain time-varying nonlinear systems in which the unmeasured dynamics do not possess a constant disturbance attenuation level (CDAL). Identifying a necessary condition for the existence of a CDAL, direct adaptive neural networks (NNs) control is developed, where the universal approximation property of NNs and the domination design are employed together to overcome the difficulties due to the lack of state information, unknown system nonlinearities, and unknown state-dependent disturbance attenuation gain. The proposed method is coherent in the sense that it is applicable to the case in which a CDAL exists.     

Knowledge-based parameter identification of TSK fuzzy models

Linear/1st order Takagi–Sugeno–Kang (TSK) fuzzy models are widely used to identify static nonlinear systems from a set of input–output pairs. The synergetic integration of TSK fuzzy models with artificial neural networks (ANN) has led to the emergence of hybrid neuro-fuzzy models that can have excellent adaptability and interpretability at the same time. One drawback of these hybrid models is that they tend to have more black-box characteristics of ANN than the transparency of fuzzy systems. If the quality of training data is questionable then it may lead to a fuzzy model with poor interpretability. In an attempt to remediate this problem, we propose a parameter identification technique for TSK models that relies on a-priori available qualitative domain knowledge. The technique is devised for rule-centered TSK models in which the consequent polynomial can be interpreted as the 1st order Taylor series approximation of the underlying nonlinear function that is being modeled. The resulting neuro-fuzzy model is named as a-priori knowledge-based fuzzy model (APKFM). We have shown that besides being reasonably accurate, APKFM has excellent interpretability and extrapolation capability. The effectiveness of APKFM is shown using two examples of static systems. In the first example, a toy nonlinear function is chosen for approximation by an APKFM. In the second example, a real world problem pertaining to the maintenance cost estimation of electricity distribution networks is addressed.     

Squared and absolute errors in optimal approximation of nonlinear systems

Optimal squared error and absolute error-based approximation problems for static polynomial models of nonlinear, discrete-time, systems are studied in detail. These problems have many similarities with other linear-in-the-parameters approximation problems, such as with optimal approximation problems for linear time-invariant models of linear and nonlinear systems. Nonprobabilistic signal analysis is used.Close connections between the studied approximation problems and certain classical topics in approximation theory, such as optimal L₂(−1,1) and L₁(−1,1) approximation, are established by analysing conditions under which sample averages of static nonlinear functions of the input converge to appropriate Riemann integrals of the static functions. These results should play a significant role in the analysis of corresponding system identification and model validation problems. Furthermore, these results demonstrate that optimal modelling based on the absolute error can offer advantages over squared error-based modelling. Especially, modelling problems in which some signals possess heavy tails can benefit from absolute value-based signal and error analysis.     

Composite adaptive locally weighted learning control for multi-constraint nonlinear systems

A composite adaptive locally weighted learning (LWL) control approach is proposed for a class of uncertain nonlinear systems with system constraints, including state constraints and asymmetric control saturation in this paper. The system constraints are tackled by considering the control input as an extended state variable and introducing barrier Lyapunov functions (BLFs) into the backstepping procedure. The system uncertainty is approximated by a composite adaptive LWL neural networks (NNs), in which a prediction error is constructed by using a series-parallel identification model, and NN weights are updated by both the tracking error and the prediction error. The update law with composite error feedback improves uncertainty approximation accuracy and trajectory tracking accuracy. The feasibility and effectiveness of the proposed approach have been demonstrated by formal proof and simulation results.     

Nonlinear control structures based on embedded neural system models

This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

Neural Network-based Adaptive State-feedback Control for High-order Stochastic Nonlinear Systems

This paper focuses on investigating the issue of adaptive state-feedback control based on neural networks(NNs)for a class of high-order stochastic uncertain systems with unknown nonlinearities. By introducing the radial basis function neural network(RBFNN) approximation method, utilizing the backstepping method and choosing an approximate Lyapunov function, we construct an adaptive state-feedback controller which assures the closed-loop system to be mean square semi-global-uniformly ultimately bounded(M-SGUUB). A simulation example is shown to illustrate the effectiveness of the design scheme.     

Decentralized control design for large-scale systems with strong interconnections using neural networks

We propose a decentralized neural network (NN) controller for a class of large-scale nonlinear systems with the strong interconnections. The NNs are used to approximate the unknown subsystems and interconnections. Due to the functional approximation capabilities of NNs, the additional precautions are not required to be made for avoiding the possible control singularity problems. Semiglobal asymptotic stability results are obtained and the tracking error converges to zero. Furthermore, the issue of transient performance of the subsystems is also addressed under an analytical framework.     

Truncated adaptation design for decentralised neural dynamic surface control of interconnected nonlinear systems under input saturation

This paper studies decentralised neural adaptive control of a class of interconnected nonlinear systems, each subsystem is in the presence of input saturation and external disturbance and has independent system order. Using a novel truncated adaptation design, dynamic surface control technique and minimal-learning-parameters algorithm, the proposed method circumvents the problems of ‘explosion of complexity’ and ‘dimension curse’ that exist in the traditional backstepping design. Comparing to the methodology that neural weights are online updated in the controllers, only one scalar needs to be updated in the controllers of each subsystem when dealing with unknown systematic dynamics. Radial basis function neural networks (NNs) are used in the online approximation of unknown systematic dynamics. It is proved using Lyapunov stability theory that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. The tracking errors of each subsystems, the amplitude of NN approximation residuals and external disturbances can be attenuated to arbitrarily small by tuning proper design parameters. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Dynamics identification and control of nonlinear MIMO coupled plant using supervised neural gas and comparison with recurrent neural controller

The dynamics identification and subsequent control of a nonlinear system is not a trivial issue. The application of a neural gas network that is trained with a supervised batch version of the algorithm can produce identification models in a robust way. In this paper, the neural model identifies each local transfer function, demonstrating that the local linear approximation can be done. Moreover, other parameters are analyzed in order to obtain a correct modeling. Furthermore, the algorithm is applied to control a nonlinear multi-input multi-output system composed of tanks. In addition, this plant is a coupled system where the manipulated input variables are influencing all the output variables. The aim of the work is to demonstrate that the supervised neural gas algorithm is able to obtain linear models to be used in a state space design scenario to control nonlinear coupled systems and guarantee a robust control method. The results are compared with the common approach of using a recurrent neural controller trained with a dynamic backpropagation algorithm. Regarding the steady-state errors in disturbance rejection, reference tracking and sensitivity to simple process changes, the proposed approach shows an interesting application to control nonlinear plants.

     

Neural-network-based approximate output regulation of discrete-time nonlinear systems.

The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.     

确定学习与基于数据的建模及控制

确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.