A genetic algorithm based robust learning credit assignment cerebellar model articulation controller

In this paper, a novel approach of genetic algorithm based robust learning credit assignment cerebellar model articulation controller (GCA-CMAC) is proposed. The cerebellar model articulation controller (CMAC) is a neurological model, which has an attractive property of learning speed. However, the distributions of errors into the addressed hypercubes of CMAC are not proportional to their credibility and may cause unacceptable learning performance. The credit assignment CMAC (CA-CMAC) can solve this problem by using the creditability of hypercubes that the calculated errors are assigned proportional to the inverse of learning times. Afterward, the obtained learning times can be optimized by genetic algorithm (GA) to increase its accuracy. In this paper, the proposed algorithm is to combine credit assignment ideas and GA to provide accurate learning for CMAC. Moreover, we embed the robust learning approach into the GCA-CMAC and dynamically adjust the learning constant for training data with noise or outliers. From simulation results, it shows that the proposed algorithm outperforms other CMACs.     

CMAC 算法收敛性分析及泛化能力研究

利用矩阵理论和线性方程组迭代收敛的一般性原理,在不附加特殊条件折情况下,证明了CMAC算法在批量和增量两种学习方式下的收敛定理,对在关联矩阵正定条件下得出的结论进行推广和改进。在此基础上提出了一种学习率自寻优的CMAC改进算法,并提出一种简单可行的评价CMAC网络整体泛化性能的指标,通过计算仿真验证了收敛定量的正确性和改进算法的优越性,并研究得出了CMAC网络各个参数对其泛化性能影响的相关结论。     

Standalone CMAC Control System With Online Learning Ability

A cerebellar model articulation controller (CMAC) control system, which contains only one single-input controller implemented by a differentiable CMAC, is proposed in this paper. In the proposed scheme, the CMAC controller is solely used to control the plant, and no conventional controller is needed. Without a preliminary offline learning, the single-input CMAC controller can provide the control effort to the plant at each online learning step. To train the differentiable CMAC online, the gradient descent algorithm is employed to derive the learning rules. The sensitivity of the plant, with respect to the input, is approximated by a simple formula so that the learning rules can be applied to unknown plants. Moreover, based on a discrete-type Lyapunov function, conditions on the learning rates guaranteeing the convergence of the output error are derived in this paper. Finally, simulations on controlling three different plants are given to demonstrate the effectiveness of the proposed controller.      

具有微分输出的神经网络New-CMAC及其学习收敛性

基于传统的CMAC神经网络和局部加权回归技术,提出了与传统CMAC(cerebellar model articulation computer)有着同样存储空间量的改进的新CMAC网络New-CMAC,它具有传统的输出和具有其微分信息的输出,因而更适合于自动控制.接着,又提出了其新的学习算法,并研究了其学习收敛性.     

一种新型模糊神经网络函数逼近器

论文提出了一种新型模糊小脑模型神经网络(NFCMAC),它采用模糊隶属度函数作为接收域函数,能够获得较常规CMAC连续性强且有解析微分的复杂函数近似,具有计算量少,学习效率高等优点。同时研究了NFCMAC接受域函数的映射方法、隶属度函数及其参数的选取规律和学习算法。仿真结果表明NFCMAC具有良好的泛化能力和逼近精度,具有较高的收敛速度。     

Learning Convergence of CMAC Algorithm

CMAC convergence properties both in batch and in incremental learning are analyzed. The previous conclusions about the CMAC convergence, which are deduced under the condition that the articulation matrix is positive definite, are improved into the new less limited and more general conclusions in which no additive conditions are needed. An improved CMAC algorithm with self-optimizing learning rate is proposed from the new conclusions. Simulation results show the correctness of the new conclusions and the advantages of the improved algorithm.     

提高小脑模型神经网络精度的算法及仿真应用

CMAC(cerebella model articulation controller)神经网络的局部结构使得学习非线性函数更快.然而,在许多应用领域,CMAC的学习精度不能满足应用要求.该文提出了一种改进CMAC学习精度的联想插补算法,同时给出了一个仿真实验.其结果表明,使用此算法,改进的CMAC的学习精度比改进前提高了10倍,学习收敛也更快.     

Integration of CMAC technique and weighted regression for efficientlearning and output differentiability

Cerebellar model articulation controllers (CMAC) have attractive properties of learning convergence and speed. Many studies have used CMAC in learning control and demonstrated successful results. However, due to the fact that CMAC is a table lookup technique, a model implemented by a CMAC does not provide a derivative of its output. This is an inconvenience when using CMAC in learning structures that require such derivatives. This paper presents a new scheme that integrates the CMAC addressing technique with weighted regression to resolve this problem. Derivatives exist everywhere except on the boundaries of quantized regions. Compared with the conventional CMAC, the new scheme requires the same amount of memory and has similar learning speed, but provides output differentiability and more precise output. Compared with the typical weighted regression technique, the new scheme offers an efficient way to organize and utilize collected information.     

新的基于mass-assignment的模糊CMAC神经网络及其学习收敛性

基于J.F.Baldwin等人提出的mass-assignment理论,提出了新的基于mass-assignment的模糊CMAC神经网络,接着研究了其学习规则.理论研究结果揭示出,此新模糊CMAC是一个全局逼近器,并且具有学习收敛性.故此新模糊CMAC有非常重要的应用潜力.     

Credit assigned CMAC and its application to online learning robust controllers

In this paper, a novel learning scheme is proposed to speed up the learning process in cerebellar model articulation controllers (CMAC). In the conventional CMAC learning scheme, the correct numbers of errors are equally distributed into all addressed hypercubes, regardless of the credibility of the hypercubes. The proposed learning approach uses the inverse of learned times of the addressed hypercubes as the credibility (confidence) of the learned values, resulting in learning speed becoming very fast. To further demonstrate online learning capability of the proposed credit assigned CMAC learning scheme, this paper also presents a learning robust controller that can actually learn online. Based on robust controllers presented in the literature, the proposed online learning robust controller uses previous control input, current output acceleration, and current desired output as the state to define the nominal effective moment of the system from the CMAC table. An initial trial mechanism for the early learning stage is also proposed. With our proposed credit-assigned CMAC, the robust learning controller can accurately trace various trajectories online.     

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.     

Learning convergence of CMAC technique

CMAC is one useful learning technique that was developed two decades ago but yet lacks adequate theoretical foundation. Most past studies focused on development of algorithms, improvement of the CMAC structure, and applications. Given a learning problem, very little about the CMAC learning behavior such as the convergence characteristics, effects of hash mapping, effects of memory size, the error bound, etc. can be analyzed or predicted. In this paper, we describe the CMAC technique with mathematical formulation and use the formulation to study the CMAC convergence properties. Both information retrieval and learning rules are described by algebraic equations in matrix form. Convergence characteristics and learning behaviors for the CMAC with and without hash mapping are investigated with the use of these equations and eigenvalues of some derived matrices. The formulation and results provide a foundation for further investigation of this technique.     

Adaptive CMAC neural control of chaotic systems with a PI-type learning algorithm

The cerebellar model articulation controller (CMAC) has the advantages such as fast learning property, good generalization capability and information storing ability. Based on these advantages, this paper proposes an adaptive CMAC neural control (ACNC) system with a PI-type learning algorithm and applies it to control the chaotic systems. The ACNC system is composed of an adaptive CMAC and a compensation controller. Adaptive CMAC is used to mimic an ideal controller and the compensation controller is designed to dispel the approximation error between adaptive CMAC and ideal controller. Based on the Lyapunov stability theorems, the designed ACNC feedback control system is guaranteed to be uniformly ultimately bounded. Finally, the ACNC system is applied to control two chaotic systems, a Genesio chaotic system and a Duffing–Holmes chaotic system. Simulation results verify that the proposed ACNC system with a PI-type learning algorithm can achieve better control performance than other control methods.     

ART-type CMAC network classifier

In this paper, the learning process of ART 2 (adaptive resonant theory) network is applied to construct the structure of cerebellar model articulation controller (CMAC) to form an ART-type CMAC network. The proposed updating rule is in an unsupervised manner as the ART 2 network or the self-organizing map (SOM), and could equally distribute the learning information into the association memory locations as the CMAC network. If the winner fails a vigilance test, a new state is created; otherwise, the memory contents corresponding to the winner are updated according to the learning information. Like SOM, the proposed network also has a neighborhood region, but the neighborhood region is implicit in the network structure and need not be defined in advance. This paper also analyzes the convergence properties of the ART-type CMAC network. The proposed network is applied to solve data classification problems for illustration. Experiment results demonstrate the effectiveness and feasibility of the ART-type CMAC network in solving five benchmark datasets selected from the UCI repository.     

A self-organizing CMAC network with gray credit assignment.

This paper attempts to incorporate the structure of the cerebellar-model-articulation-controller (CMAC) network into the Kohonen layer of the self-organizing map (SOM) to construct a self-organizing CMAC (SOCMAC) network. The proposed SOCMAC network can perform the function of an SOM and can distribute the learning error into the memory contents of all addressed hypercubes as a CMAC. The learning of the SOCMAC is in an unsupervised manner. The neighborhood region of the SOCMAC is implicit in the structure of a two-dimensional CMAC network and needs not be defined in advance. Based on gray relational analysis, a credit-assignment technique for SOCMAC learning is introduced to hasten the overall learning process. This paper also analyzes the convergence properties of the SOCMAC. It is shown that under the proposed updating rule, both the memory contents and the state outputs of the SOCMAC converge almost surely. The SOCMAC is applied to solve both data-clustering and data-classification problems, and simulation results show that the proposed network achieves better performance than other known SOMs.     

一种CMAC网络模型及其在机器人控制中的应用

小脑模型关节控制器（CMAC）具有学习算法简单、在线学习速度快的优点,非常适于机器人等复杂系统的自适应控制,本文阐述了CMAC的原理,证明了其收敛性,提出了一种适合于机器人轨迹跟踪控制的CMAC,并给出了仿真实验结果。     

基于信度分配的并行集成CMAC及其在建模中的应用

Albus CMAC(cerebella model articulation controller) 神经网络是一种模拟人类小脑学习结构的小脑模型关节控制器, 它具有很强的记忆与输出泛化能力, 但对于在线学习来说, Albus CMAC仍难满足快速性的要求. 本文在常规CMAC神经网络的基础上, 针对其在学习精度与存储容量之间的矛盾, 引入信度分配概念, 提出了一种基于信度分配的并行集成CMAC. 它将大规模网络切割为多个子网络分别训练后再组合, 大大地提高了计算效率. 通过对复杂非线性函数建模的仿真研究表明, 该方案提高了系统建模的泛化能力和算法的收敛速度. 文章最后讨论了学习常数和泛化参数对该神经网络在线学习效果的影响.     

基于平衡学习的CMAC 神经网络非线性辨识算法

为提高小脑模型关节控制器(CMAC)神经网络在线学习的快速性和准确性，提出一种平衡学习的概念，并设计一种改进的CMAC学习算法．在常规的CMAC中，误差的校正值被平均地分配给所有激活存储单元，而不管这些存储单元的可信度；在改进的CMAC中，利用激活单元先前学习次数作为可信度，其误差校正值与激活单元先前学习次数的负k次方成比例．仿真结果表明，当k为一适当数值时，改进CMAC具有较快的学习速度和较高的精度，特别是在神经网络的初始学习阶段．     

基于平衡学习的CMAC神经网络非线性滑模容错控制

以一改进的信度分配CMAC(cerebellar model articulation controllers)神经网络为在线故障诊断的手段,将变结构滑模摔制技术引入容错控制器设计之中,提出一种动态非线性系统主动容错控制方法.在常规CMAC学习算法中,误差被平均地分配给所有被激活的存储单元,不管各存储单元存储数据(权值)的可信程度.改进的CMAC中,利用激活单元先前学习次数作为可信度,其误差校正值与激活单元先前学习次数的-p次方成比例,从而提高神经网络的在线学习速度和精度;在此基础上利用滑模控制算法进行容错控制律的在线重构,实现动态非线性系统在线故障诊断与容错控制的集成.分析了系统的稳定性,仿真结果表明改进故障学习算法及容错控制的有效性.     

Adaptive fault-tolerant control of non-linear systems: an improved CMAC-based fault learning approach

The conventional cerebellar model articulation controllers (CMAC) learning scheme equally distributes the correcting errors into all addressed hypercubes, regardless of the credibility of those hypercubes. This paper presents the adaptive fault-tolerant control scheme of non-linear systems using a fuzzy credit assignment CMAC neural network online fault learning approach. The credit assignment concept is introduced into fuzzy CMAC weight adjusting to use the learned times of addressed hypercubes as the credibility of CMAC. The correcting errors are proportional to the inversion of learned times of addressed hypercubes. With this fault learning model, the learning speed of fault can be improved. After the unknown fault is estimated, online, by using the fuzzy credit assignment CMAC, the effective control law reconfiguration strategy based on the sliding mode control technique is used to compensate for the effect of the fault. The proposed fault-tolerant controller adjusts its control signal by adding a corrective sliding mode control signal to confine the system performance within a boundary layer. The numerical simulations demonstrate the effectiveness of the proposed CMAC algorithm and fault-tolerant controller.