Indirect adaptive self-organizing RBF neural controller design with a dynamical training approach

This study proposes an indirect adaptive self-organizing RBF neural control (IASRNC) system which is composed of a feedback controller, a neural identifier and a smooth compensator. The neural identifier which contains a self-organizing RBF (SORBF) network with structure and parameter learning is designed to online estimate a system dynamics using the gradient descent method. The SORBF network can add new hidden neurons and prune insignificant hidden neurons online. The smooth compensator is designed to dispel the effect of minimum approximation error introduced by the neural identifier in the Lyapunov stability theorem. In general, how to determine the learning rate of parameter adaptation laws usually requires some trial-and-error tuning procedures. This paper proposes a dynamical learning rate approach based on a discrete-type Lyapunov function to speed up the convergence of tracking error. Finally, the proposed IASRNC system is applied to control two chaotic systems. Simulation results verify that the proposed IASRNC scheme can achieve a favorable tracking performance.     

Design of an adaptive self-organizing fuzzy neural network controller for uncertain nonlinear chaotic systems

Though the control performances of the fuzzy neural network controller are acceptable in many previous published papers, the applications are only parameter learning in which the parameters of fuzzy rules are adjusted but the number of fuzzy rules should be determined by some trials. In this paper, a Takagi–Sugeno-Kang (TSK)-type self-organizing fuzzy neural network (TSK-SOFNN) is studied. The learning algorithm of the proposed TSK-SOFNN not only automatically generates and prunes the fuzzy rules of TSK-SOFNN but also adjusts the parameters of existing fuzzy rules in TSK-SOFNN. Then, an adaptive self-organizing fuzzy neural network controller (ASOFNNC) system composed of a neural controller and a smooth compensator is proposed. The neural controller using the TSK-SOFNN is designed to approximate an ideal controller, and the smooth compensator is designed to dispel the approximation error between the ideal controller and the neural controller. Moreover, a proportional-integral (PI) type parameter tuning mechanism is derived based on the Lyapunov stability theory, thus not only the system stability can be achieved but also the convergence of tracking error can be speeded up. Finally, the proposed ASOFNNC system is applied to a chaotic system. The simulation results verify the system stabilization, favorable tracking performance, and no chattering phenomena can be achieved using the proposed ASOFNNC system.     

A fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks

In this paper, we present a fast and accurate online self-organizing scheme for parsimonious fuzzy neural networks (FAOS-PFNN), where a novel structure learning algorithm incorporating a pruning strategy into new growth criteria is developed. The proposed growing procedure without pruning not only speeds up the online learning process but also facilitates a more parsimonious fuzzy neural network while achieving comparable performance and accuracy by virtue of the growing and pruning strategy. The FAOS-PFNN starts with no hidden neurons and parsimoniously generates new hidden units according to the proposed growth criteria as learning proceeds. In the parameter learning phase, all the free parameters of hidden units, regardless of whether they are newly created or originally existing, are updated by the extended Kalman filter (EKF) method. The effectiveness and superiority of the FAOS-PFNN paradigm is compared with other popular approaches like resource allocation network (RAN), RAN via the extended Kalman filter (RANEKF), minimal resource allocation network (MRAN), adaptive-network-based fuzzy inference system (ANFIS), orthogonal least squares (OLS), RBF-AFS, dynamic fuzzy neural networks (DFNN), generalized DFNN (GDFNN), generalized GAP-RBF (GGAP-RBF), online sequential extreme learning machine (OS-ELM) and self-organizing fuzzy neural network (SOFNN) on various benchmark problems in the areas of function approximation, nonlinear dynamic system identification, chaotic time-series prediction and real-world regression problems. Simulation results demonstrate that the proposed FAOS-PFNN algorithm can achieve faster learning speed and more compact network structure with comparably high accuracy of approximation and generalization.     

Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system

In this paper, a fuzzy-identification-based adaptive backstepping control (FABC) scheme is proposed. The FABC system is composed of a backstepping controller and a robust controller. The backstepping controller, which uses a self-organizing fuzzy system (SFS) with the structure and parameter learning phases to on-line estimate the controlled system dynamics, is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the SFS. The developed SFS automatically generates and prunes the fuzzy rules by the proposed structure adaptation algorithm and the parameters of the fuzzy rules and membership functions tunes on-line in the Lyapunov sense. Thus, the overall closed-loop FABC system can guarantee that the tracking error and parameter estimation error are uniformly ultimately bounded; and the tracking error converges to a desired small neighborhood around zero. Finally, the proposed FABC system is applied to a chaotic dynamic system to show its effectiveness. The simulation results verify that the proposed FABC system can achieve favorable tracking performance even with unknown controlled system dynamics.     

Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems

This paper presents a novel quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems via H^∞ approach. In the proposed algorithm, a self-constructing neural fuzzy network (SCNFN) is developed with both structure and parameter learning phases, so that the number of fuzzy rules and network parameters can be adaptively determined. Based on the SCNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an optimal NFN-based controller is designed to overcome the effects of unstructured uncertainty and approximation error by integrating the NFN identifier, linear optimal control and H^∞ approach as a whole. The adaptive tuning laws of network parameters are derived in the sense of quadratic stability technique and Lyapunov synthesis approach to ensure the network convergence and H^∞ synchronization performance. The merits of the proposed control scheme are not only that the conservative estimation of NFN approximation error bound is avoided but also that a suitable-sized neural structure is found to sufficiently approximate the system uncertainties. Simulation results are provided to verify the effectiveness and robustness of the proposed control method.     

Faster Self-Organizing Fuzzy Neural Network Training and a Hyperparameter Analysis for a Brain–Computer Interface

This paper introduces a number of modifications to the learning algorithm of the self-organizing fuzzy neural network (SOFNN) to improve computational efficiency. It is shown that the modified SOFNN favorably compares to other evolving fuzzy systems in terms of accuracy and structural complexity. An analysis of the SOFNN's effectiveness when applied in an electroencephalogram (EEG)-based brain-computer interface (BCI) involving the neural-time-series-prediction-preprocessing (NTSPP) framework is also presented, where a sensitivity analysis (SA) of the SOFNN hyperparameters was performed using EEG data recorded from three subjects during left/right-motor-imagery-based BCI experiments. The aim of this one-time SA was to eliminate the need to choose subject- and signal-specific hyperparameters for the SOFNN and thus apply the SOFNN in the NTSPP framework as a parameterless self-organizing framework for EEG preprocessing. The results indicate that a general set of NTSPP parameters chosen via the SA provide the best results when tested in a BCI system. Therefore, with this general set of SOFNN parameters and its self-organizing structure, in conjunction with parameterless feature extraction and linear discriminant classification, a fully parameterless BCI that lends itself well to autonomous adaptation is realizable.     

Online adaptive fuzzy neural identification and control of a class of MIMO nonlinear systems

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for identification and control of a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems. The proposed controller has the following salient features: 1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically; 2) online learning ability of uncertain MIMO nonlinear systems; 3) fast learning speed; 4) fast convergence of tracking errors; 5) adaptive control, where structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; 6) robust control, where global stability of the system is established using the Lyapunov approach. Simulation studies on an inverted pendulum and a two-link robot manipulator show that the performance of the proposed controller is superior.     

基于自组织模糊神经网络溶解氧控制方法研究

针对污水处理过程中溶解氧浓度难以控制的问题,提出了一种基于自组织模糊神经网络（self-organizing fuzzy neural network, SOFNN）的溶解氧（dissolved oxygen, DO）控制方法。首先,采用激活强度和神经元重要性两个评判标准,来判断神经元对网络的贡献及活跃程度。然后,对不活跃的神经元进行删减,以此来对神经网络结构进行自适应的调整,从而满足实际控制要求,提高控制精度。其次,采用梯度下降算法对SOFNN神经网络的各个参数进行实时调整,以保证网络的精度。最后,将该自组织方法用在Mackey-Glass时间序列预测中,结果表明所提出的自组织模糊神经网络具有较好的预测效果;同时将所提出的SOFNN方法在BSM1仿真平台上进行实验验证。结果表明,所提出的自组织模糊神经网络控制方法能够对溶解氧浓度进行较好地控制,具有一定的自适应能力。     

不确定分数阶多涡卷混沌系统自适应重复学习同步控制

研究了不确定分数阶多涡卷混沌系统的自适应重复学习同步控制问题.通过利用滞环函数,设计了一类参数可调的分数阶多涡卷混沌系统.针对这类分数阶多涡卷混沌系统,在考虑非参数化不确定性、周期时变参数化不确定性、常参数化不确定性和外部扰动情况下,提出了一种重复学习同步控制方案.利用自适应神经网络技术补偿了系统中的函数型不确定性,通过自适应重复学习控制技术处理了周期时变参数化不确定性,并利用自适应鲁棒学习项处理了神经网络逼近误差和干扰的影响,实现了主系统和从系统的完全同步.综合利用分数阶频率分布模型和类Lyapunov复合能量函数方法证明了同步误差的学习收敛性.数值仿真验证了所提方法的有效性.     

一种多电机同步传动模糊神经网络控制器的设计

设计了具有知识表达和自学习能力的模糊神经网络同步控制器．建立了模糊控制规则，进而提出了多电机同步控制的模糊神经网络学习算法．对四轴同步控制系统进行仿真实验．结果表明模糊神经网络同步控制器能有效实现多电机同步控制，收敛速度较快．鲁棒性较好。     

A Type-2 Self-Organizing Neural Fuzzy System and Its FPGA Implementation

This paper proposes a type-2 self-organizing neural fuzzy system (T2SONFS) and its hardware implementation. The antecedent parts in each T2SONFS fuzzy rule are interval type-2 fuzzy sets, and the consequent part is of Mamdani type. Using interval type-2 fuzzy sets in T2SONFS enables it to be more robust than type-1 fuzzy systems. T2SONFS learning consists of structure and parameter identification. For structure identification, an online clustering algorithm is proposed to generate rules automatically and flexibly distribute them in the input space. For parameter identification, a rule-ordered Kalman filter algorithm is proposed to tune the consequent-part parameters. The learned T2SONFS is hardware implemented, and implementation techniques are proposed to simplify the complex computation process of a type-2 fuzzy system. The T2SONFS is applied to nonlinear system identification and truck backing control problems with clean and noisy training data. Comparisons between type-1 and type-2 neural fuzzy systems verify the learning ability and robustness of the T2SONFS. The learned T2SONFS is hardware implemented in a field-programmable gate array chip to verify functionality of the designed circuits.      

基于UKF的增长型模糊神经网络设计

为了实现模糊神经网络结构和参数的同时调整,提出一种基于无迹卡尔曼滤波(UKF)的增长型模糊神经网络(UKF-GFNN).首先,利用UKF对模糊神经网络的参数进行调整;然后,设计一种基于隐含层神经元输出强度的模糊规则增长机制,实现模糊神经网络的结构增长;最后,将所提出的增长型模糊神经网络应用于非线性系统建模.实验结果显示,基于UKF的增长型模糊神经网络能够实现结构和参数的自校正,并且具有较高的建模精度.     

Adaptive dynamic CMAC neural control of nonlinear chaotic systems with L2 tracking performance

The advantage of using cerebellar model articulation control (CMAC) network has been well documented in many applications. However, the structure of a CMAC network which will influence the learning performance is difficult to select. This paper proposes a dynamic structure CMAC network (DSCN) which the network structure can grow or prune systematically and their parameters can be adjusted automatically. Then, an adaptive dynamic CMAC neural control (ADCNC) system which is composed of a computation controller and a robust compensator is proposed via second-order sliding-mode approach. The computation controller containing a DSCN identifier is the principal controller and the robust compensator is designed to achieve L₂ tracking performance with a desired attenuation level. Moreover, a proportional–integral (PI)-type adaptation learning algorithm is derived to speed up the convergence of the tracking error in the sense of Lyapunov function and Barbalat’s lemma, thus the system stability can be guaranteed. Finally, the proposed ADCNC system is applied to control a chaotic system. The simulation results are demonstrated that the proposed ADCNC scheme can achieve a favorable control performance even under the variations of system parameters and initial point.     

Adaptive neural complementary sliding-mode control via functional-linked wavelet neural network

Chaos control can be applied in the vast areas of physics and engineering systems, but the parameters of chaotic system are inevitably perturbed by external inartificial factors and cannot be exactly known. This paper proposes an adaptive neural complementary sliding-mode control (ANCSC) system, which is composed of a neural controller and a robust compensator, for a chaotic system. The neural controller uses a functional-linked wavelet neural network (FWNN) to approximate an ideal complementary sliding-mode controller. Since the output weights of FWNN are equipped with a functional-linked type form, the FWNN offers good learning accuracy. The robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Without requiring preliminary offline learning, the parameter learning algorithm can online tune the controller parameters of the proposed ANCSC system to ensure system stable. Finally, it shows by the simulation results that favorable control performance can be achieved for a chaotic system by the proposed ANCSC scheme.     

基于自适应重复学习的不确定多涡卷混沌系统同步控制

基于滞环函数提出一种参数可调的多涡卷混沌系统构造方法. 针对复杂不确定性系统, 综合利用自适应神经网络和重复学习控制方法设计一种自适应重复学习同步控制器; 利用自适应重复学习控制方法对周期时变参数化不确定性进行处理; 对函数型不确定性利用神经网络逼近技术进行补偿; 设计鲁棒学习项对神经网络逼近误差和扰动上界进行估计; 通过构造类Lyapunov 复合能量函数证明了同步误差学习的收敛性. 仿真结果验证了所提出方法的有效性.

     

一种用于非线性控制的神经网络模糊自组织控制器

本文提出一种神经网络自组织控制器，并应用于非线性跟踪控制中，为了加快模糊控制器的在线学习，文中给出了一种变的最速梯度下降学习算法，仿真结果表明，该控制是有效的。     

Design for Self-Organizing Fuzzy Neural Networks Based on Genetic Algorithms

A novel hybrid learning algorithm based on a genetic algorithm to design a growing fuzzy neural network, named self-organizing fuzzy neural network based on genetic algorithms (SOFNNGA), to implement Takagi-Sugeno (TS) type fuzzy models is proposed in this paper. A new adding method based on geometric growing criterion and the epsiv-completeness of fuzzy rules is first used to generate the initial structure. Then a hybrid algorithm based on genetic algorithms, backpropagation, and recursive least squares estimation is used to adjust all parameters including the number of fuzzy rules. This has two steps: First, the linear parameter matrix is adjusted, and second, the centers and widths of all membership functions are modified. The GA is introduced to identify the least important neurons, i.e., the least important fuzzy rules. Simulations are presented to illustrate the performance of the proposed algorithm     

不确定Lorenz系统的参数识别与异结构同步

设计了一种参数识别器和同步控制器,研究了不确定混沌系统的参数识别与异结构同步问题．根据稳定性原理,确定了参数识别器和同步控制器的结构,以不确定Lorenz混沌系统和Rossler混沌系统为例,验证了其有效性．仿真模拟结果表明,在参数识别器和同步控制器的共同作用下,异结构不确定Lorenz混沌系统和Rossler混沌系统可以达到完全同步,并且不确定Lorenz混沌系统的参数全部可以得到识别．     

基于快速算法的模糊神经网络自适应控制

针对过程控制中被控对象常具有非线性、不确定性及参数时变等复杂因素，而难以建立精确的数学模型的情况，提出了一种基于快速学习算法的模糊神经网络自适应预测控制方案。该方案用神经网络作辨识器，模糊神经网络作控制器来实现非线性系统的自适应预测控制。为了克服传统的梯度下降法收敛速度慢、容易陷入局部极小值的缺点，该方案采用递推最小二乘法训练模糊神经网络。仿真结果表明，该方案可以实现模糊控制和神经网络的优势互补，对不确定非线性系统具有很好的控制效果。     

An ART-based fuzzy adaptive learning control network

This paper addresses the structure and an associated online learning algorithm of a feedforward multilayer neural net for realizing the basic elements and functions of a fuzzy controller. The proposed fuzzy adaptive learning control network (FALCON) can be contrasted with traditional fuzzy control systems in network structure and learning ability. An online structure/parameter learning algorithm, FALCON-ART, is proposed for constructing FALCON dynamically. It combines backpropagation for parameter learning and fuzzy ART for structure learning. FALCON-ART partitions the input state space and output control space using irregular fuzzy hyperboxes according to the data distribution. In many existing fuzzy or neural fuzzy control systems, the input and output spaces are always partitioned into “grids”. As the number of variables increases, the number of partitioned grids grows combinatorially. To avoid this problem in some complex systems, FALCON-ART partitions the I/O spaces flexibly based on data distribution. It can create and train FALCON in a highly autonomous way. In its initial form, there is no membership function, fuzzy partition, and fuzzy logic rule. They are created and begin to grow as the first training pattern arrives. Thus, the users need not give it any a priori knowledge or initial information. FALCON-ART can online partition the I/O spaces, tune membership functions, find proper fuzzy logic rules, and annihilate redundant rules dynamically upon receiving online data