Topology Preservation and Cooperative Learning in Identification of Multiple Model Systems

The self-organizing network (SON)-based multiple model system is a recently proposed method for identifying the dynamics of a general nonlinear system. It has been observed by researchers that cooperative learning among neighboring regions is sometimes important for the success of identification of a nonlinear system under the multiple model system framework. In this paper, we intend to formally evaluate the effects of cooperative learning and topology preservation in identification of multiple model system based on SON. The results of the mathematical analysis supports the heuristic that a good learning strategy for identifying the local model parameters of a SON-based multiple model system is to choose a neighborhood function whose effective region is initially wider and is reduced gradually during learning. An example of nonlinear function approximation is also provided at the end of this paper to demonstrate the results of the mathematical analysis.      

基于进化深度学习的特征提取算法

信息全面与维数灾难的矛盾是大数据时代网络态势感知需要解决的首要难题。特征提取一直是主流的降维方法,但现有算法对高维非线性数据效果不佳;深度学习是一类具有多层非线性映射的学习算法,可以完成复杂函数的逼近,但对隐层相关参数十分敏感。针对上述问题,将进化算法的思想引入深度学习,提出了一种基于进化深度学习的特征提取算法。该算法利用遗传算法及进化策略实现全局搜索及优化的特点,并对深度学习结构及相关参数进行了优化。理论分析及实验结果都证明了该算法的有效性。     

Multiplication-free radial basis function network

For the purpose of adaptive function approximation, a new radial basis function network is proposed which is nonlinear in its parameters. The goal is to reduce significantly the computational effort for a serial processor, by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation. The approximation scheme makes use of a grid-based Gaussian basis function network. Due to the local support of digitally implemented Gaussian functions the function representation is parametric local and therefore well suited for an online implementation on a microcomputer. A gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved.     

An adiabatic neural network for RBF approximation

Numerous studies have addressed nonlinear functional approximation by multilayer perceptrons (MLPs) and RBF networks as a special case of the more general mapping problem. The performance of both these supervised network models intimately depends on the efficiency of their learning process. This paper presents an unsupervised recurrent neural network, based on the recurrent Mean Field Theory (MFT) network model, that finds a least-squares approximation to an arbitrary L₂ function, given a set of Gaussian radially symmetric basis functions (RBFs). Essential is the reformulation of RBF approximation as a problem of constrained optimisation. A new concept of adiabatic network organisation is introduced. Together with an adaptive mechanism of temperature control this allows the network to build a hierarchical multiresolution approximation with preservation of the global optimisation characteristics. A revised problem mapping results in a position invariant local interconnectivity pattern, which makes the network attractive for electronic implementation. The dynamics and performance of the network are illustrated by numerical simulation.     

Reinforcement Learning in Continuous Time and Space: Interference and Not Ill Conditioning Is the Main Problem When Using Distributed Function Approximators

Many interesting problems in reinforcement learning (RL) are continuous and/or high dimensional, and in this instance, RL techniques require the use of function approximators for learning value functions and policies. Often, local linear models have been preferred over distributed nonlinear models for function approximation in RL. We suggest that one reason for the difficulties encountered when using distributed architectures in RL is the problem of negative interference, whereby learning of new data disrupts previously learned mappings. The continuous temporal difference (TD) learning algorithm TD(lambda) was used to learn a value function in a limited-torque pendulum swing-up task using a multilayer perceptron (MLP) network. Three different approaches were examined for learning in the MLP networks; 1) simple gradient descent; 2) vario-eta; and 3) a pseudopattern rehearsal strategy that attempts to reduce the effects of interference. Our results show that MLP networks can be used for value function approximation in this task but require long training times. We also found that vario-eta destabilized learning and resulted in a failure of the learning process to converge. Finally, we showed that the pseudopattern rehearsal strategy drastically improved the speed of learning. The results indicate that interference is a greater problem than ill conditioning for this task.     

基于模糊神经网络的强化学习及其在机器人导航中的应用

研究基于行为的移动机器人控制方法.将模糊神经网络与强化学习理论相结合,构成模糊强化系统.它既可获取模糊规则的结论部分和模糊隶属度函数参数,也可解决连续状态空间和动作空间的强化学习问题.将残差算法用于神经网络的学习,保证了函数逼近的快速性和收敛性.将该系统的学习结果作为反应式自主机器人的行为控制器,有效地解决了复杂环境中的机器人导航问题.     

超闭球CMAC的性能分析及多CMAC结构

如何选择合适网络参数是传统CMAC(Cerebellar Model Articulation Controller)应用中的一个难题.采用泛化均方差(GMSE)和学习均方差(LMSE)来分别评价超闭球CMAC的泛化能力与记忆精度,并引入权调整率的概念,来研究CMAC结构参数与学习性能的关系.研究结果表明,在样本分布和量化级数不变时,泛化均方差和学习均方差是权调整率的非增函数.因此超闭球CMAC在满足存储空间和计算速度的要求下尽量使得权调整率较大.还提出了并行CMAC结构以进一步提高单个超闭球CMAC的非线性逼近能力.仿真结果证明了该方法的有效性.     

A hybrid learning scheme combining EM and MASMOD algorithms forfuzzy local linearization modeling

Fuzzy local linearization (FLL) is a useful divide-and-conquer method for coping with complex problems such as modeling unknown nonlinear systems from data for state estimation and control. Based on a probabilistic interpretation of FLL, the paper proposes a hybrid learning scheme for FLL modeling, which uses a modified adaptive spline modeling (MASMOD) algorithm to construct the antecedent parts (membership functions) in the FLL model, and an expectation-maximization (EM) algorithm to parameterize the consequent parts (local linear models). The hybrid method not only has an approximation ability as good as most neuro-fuzzy network models, but also produces a parsimonious network structure (gain from MASMOD) and provides covariance information about the model error (gain from EM) which is valuable in applications such as state estimation and control. Numerical examples on nonlinear time-series analysis and nonlinear trajectory estimation using FLL models are presented to validate the derived algorithm.     

Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique

This paper investigates the problem of adaptive control for a class of stochastic nonlinear time‐delay systems with unknown dead zone. A neural network‐based adaptive control scheme is developed by using the dynamic surface control (DSC) technique and the minimal learning parameters algorithm. The dynamic surface control technique, which can avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, is first extended to the stochastic nonlinear time‐delay system with unknown dead zone. The unknown nonlinearities are approximated by the function approximation technique using the radial basis function neural network. For the purpose of reducing the numbers of parameters, which are updated online for each subsystem in the process of approximating the unknown functions, the minimal learning parameters algorithm is then introduced. Also, the adverse effects of unknown time‐delay are removed by using the appropriate Lyapunov–Krasovskii functionals. In addition, the proposed control scheme is systematically derived without requiring any information on the boundedness of the dead zone parameters and avoids the possible controller singularity problem in the approximation‐based adaptive control schemes with feedback linearization technique. It is shown that the proposed control approach can guarantee that all the signals of the closed‐loop system are bounded in probability, and the tracking errors can be made arbitrary small by choosing the suitable design parameters. Finally, a simulation example is provided to illustrate the performance of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

Control of a nonlinear liquid level system using a new artificial neural network based reinforcement learning approach

Most industrial processes exhibit inherent nonlinear characteristics. Hence, classical control strategies which use linearized models are not effective in achieving optimal control. In this paper an Artificial Neural Network (ANN) based reinforcement learning (RL) strategy is proposed for controlling a nonlinear interacting liquid level system. This ANN-RL control strategy takes advantage of the generalization, noise immunity and function approximation capabilities of the ANN and optimal decision making capabilities of the RL approach. Two different ANN-RL approaches for solving a generic nonlinear control problem are proposed and their performances are evaluated by applying them to two benchmark nonlinear liquid level control problems. Comparison of the ANN-RL approach is also made to a discretized state space based pure RL control strategy. Performance comparison on the benchmark nonlinear liquid level control problems indicate that the ANN-RL approach results in better control as evidenced by less oscillations, disturbance rejection and overshoot.     

基于径向基神经网络的多步Sarsa控制算法

针对具有连续状态空间的无模型非线性系统,提出一种基于径向基(radial basis function, RBF)神经网络的多步强化学习控制算法.首先,将神经网络引入强化学习系统,利用RBF神经网络的函数逼近功能近似表示状态-动作值函数,解决连续状态空间表达问题;然后,结合资格迹机制形成多步Sarsa算法,通过记录经历过的状态提高系统的学习效率;最后,采用温度参数衰减的方式改进softmax策略,优化动作的选择概率,达到平衡探索和利用关系的目的. MountainCar任务的仿真实验表明:所提出算法经过少量训练能够有效实现无模型情况下的连续非线性系统控制;与单步算法相比,该算法完成任务所用的平均收敛步数更少,效果更稳定,表明非线性值函数近似与多步算法结合在控制任务中同样可以具有良好的性能.     

River flow forecasting through nonlinear local approximation in a fuzzy model

This study investigates the potential of nonlinear local function approximation in a Takagi–Sugeno (TS) fuzzy model for river flow forecasting. Generally, in a TS framework, the local approximation is performed by a linear model, while in this approach, linear function approximation is substituted using a nonlinear function approximation. The primary hypothesis herein is that the process being modeled (rainfall–runoff in this study) is highly nonlinear, and a linear approximation at the local domain might still leave a lot of unexplained variance by the model. In this study, subtractive clustering technique is used for domain partition, and neural network is used for function approximation. The modeling approach has been tested on two case studies: Kolar basin in India and Kentucky basin in USA. The results of fuzzy nonlinear local approximation (FNLLA) model are highly promising. The performance of the FNLLA is compared with that of a pure fuzzy inference system (FIS), and it is observed that both the models perform similar at 1-step-ahead forecasts. However, the FNLLA performs much better than FIS at higher lead times. It is also observed that FNLLA forecasts the river flow with lesser error compared to FIS. In the case of Kolar River, more than 40 % of the total data are forecasted with <2 % error by FNLLA at 1 h ahead, while the corresponding value for FIS is only 20 %. In the case of 3-h-ahead forecasts, these values are 25 % for FNLLA and 15 % for FIS. Performance of FNLLA in the case of Kentucky River basin was also better compared to FIS. It is also found that FNLLA simulates the peak flow better than FIS, which is certainly an improvement over the existing models.     

A rapid learning and dynamic stepwise updating algorithm for flatneural networks and the application to time-series prediction

A fast learning algorithm is proposed to find an optimal weights of the flat neural networks (especially, the functional-link network). Although the flat networks are used for nonlinear function approximation, they can be formulated as linear systems. Thus, the weights of the networks can be solved easily using a linear least-square method. This formulation makes it easier to update the weights instantly for both a new added pattern and a new added enhancement node. A dynamic stepwise updating algorithm is proposed to update the weights of the system on-the-fly. The model is tested on several time-series data including an infrared laser data set, a chaotic time-series, a monthly flour price data set, and a nonlinear system identification problem. The simulation results are compared to existing models in which more complex architectures and more costly training are needed. The results indicate that the proposed model is very attractive to real-time processes.     

A systematic approach to a self-generating fuzzy rule-table forfunction approximation

In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.     

基于PSO算法的WNN大包线增益调参控制律设计

提出了一种基于粒子群优化算法的小波神经网络大包线调参控制律设计方法.该方法用小波函数代替了Sigmoid函数作为激活函数.由于结合了小波变换良好的高频域时间精度、低频域频率精度的性质和神经网络的自学习功能,因而具有较强逼近非线性函数的能力.为了克服局部极小值问题并进一步提高对非线性函数逼近能力,利用粒子群优化算法对小波神经网络进行参数训练,并利用该网络实现了大包线增益调参.飞行仿真结果表明,所设计的小波神经网络增益调参控制器具有优良的控制性能,不仅能够保证平衡状态下的控制效果,而且在未训练的平衡状态下依然具有良好的控制性能,并且在存在20%的建模误差时,最大超调量仅为6 m,仅是使用常规增益调参方法的18%.     

Integrating relevance vector machines and genetic algorithms for optimization of seed-separating process

A hybrid intelligent approach based on relevance vector machines (RVMs) and genetic algorithms (GAs) has been developed for optimal control of parameters of nonlinear manufacturing processes. It concerns the finding of the near-optimal control parameters of the nonlinear discrete manufacturing process with a specific objective. First, the nonlinear process with measurement noise is regressed by the relevance vector learning mechanism based on a kernel-based Bayesian framework. For minimizing the approximate error, uniform design sampling, online incremental learning and cross-validation are used in the learning process of RVMs. Such well-trained models become a specialized process simulation tool, which is valuable in prediction and optimization of nonlinear processes. Next, the near-optimal setpoints of the control system, which maximize the objective function, are sought by GAs from the numerous values of the objective function obtained from the simulation. As a case study, the seed separator system (5XZW-1.5) is used for evaluating the proposed intelligent approach. The control parameters to reach the maximum weighted objective, which combine the system output and evaluation functions, are optimized. The experimental results show the effectiveness of the proposed hybrid approach.     

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.