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.     

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.     

A robust learning algorithm based on support vector regression and robust fuzzy cerebellar model articulation controller

For real-world applications, the obtained data are always subject to noise or outliers. The learning mechanism of cerebellar model articulation controller (CMAC), a neurological model, is to imitate the cerebellum of human being. CMAC has an attractive property of learning speed in which a small subset addressed by the input space determines output instantaneously. For fuzzy cerebellar model articulation controller (FCMAC), the concept of fuzzy is incorporated into CMAC to improve the accuracy problem. However, the distributions of errors into the addressed hypercubes may cause unacceptable learning performance for input data with noise or outliers. For robust fuzzy cerebellar model articulation controller (RFCMAC), the robust learning of M-estimator can be embedded into FCMAC to degrade noise or outliers. Meanwhile, support vector machine (SVR) is a machine learning theory based algorithm which has been applied successfully to a number of regression problems when noise or outliers exist. Unfortunately, the practical application of SVR is limited to defining a set of parameters for obtaining admirable performance by the user. In this paper, a robust learning algorithm based on support SVR and RFCMAC is proposed. The proposed algorithm has both the advantage of SVR, the ability to avoid corruption effects, and the advantage of RFCMAC, the ability to obtain attractive properties of learning performance and to increase accurate approximation. Additionally, particle swarm optimization (PSO) is applied to obtain the best parameters setting for SVR. From simulation results, it shows that the proposed algorithm outperforms other algorithms.     

应用信度分配的模糊CMAC实现非线性系统的容错控制

The adaptive fault-tolerant control scheme of dynamic nonlinear system based on the credit assigned fuzzy CMAC neural network is presented. The proposed learning approach uses the learned times of addressed hypercubes as the credibility, the amounts of correcting errors are proportional to the inversion of the learned times of addressed hypercubes. With this idea, the learning speed can indeed be improved. Based on the improved CMAC learning approach and using the sliding control technique, the effective control law reconfiguration strategy is presented. Thesystem stability and performance are analyzed under failure scenarios. The numerical simulation demonstrates the effectiveness of the improved CMAC algorithm and the proposed fault-tolerant controller.     

Robust and fast learning for fuzzy cerebellar model articulation controllers.

In this paper, the online learning capability and the robust property for the learning algorithms of cerebellar model articulation controllers (CMAC) are discussed. Both the traditional CMAC and fuzzy CMAC are considered. In the study, we find a way of embeding the idea of M-estimators into the CMAC learning algorithms to provide the robust property against outliers existing in training data. An annealing schedule is also adopted for the learning constant to fulfill robust learning. In the study, we also extend our previous work of adopting the credit assignment idea into CMAC learning to provide fast learning for fuzzy CMAC. From demonstrated examples, it is clearly evident that the proposed algorithm indeed has faster and more robust learning. In our study, we then employ the proposed CMAC for an online learning control scheme used in the literature. In the implementation, we also propose to use a tuning parameter instead of a fixed constant to achieve both online learning and fine-tuning effects. The simulation results indeed show the effectiveness of the proposed approaches.     

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 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.     

一种基于模糊CMAC神经网络的自学习控制器

通过分析模糊控制和基于广义基函数的ＣＭＡＣ神经网络,提出一种模糊ＣＭＡＣ（ＦＣＭＡＣ）神经网络。通过ＦＣＭＡＣ权系数的在线学习,实现修正模糊逻辑。给出一种基于ＦＣＭＡＣ的自学习控制器的结构及合适的学习算法,这种网络每次学习少量参数,算法简单。仿真结果表明所提出的控制器优于传统的ＰＩＤ控制器。     

模糊CMAC及其在机器人轨迹跟踪控制中的应用

小脑模型关节控制器(CMAC)具有结构简单,学习快速的优点,但是它的空间划分方式不能在线进行调整,影响了其自适应能力的提高.本文将模糊理论引入CMAC,提出了一种能够反映人类小脑认知的模糊性和连续性的模糊小脑模型关节控制器(FCMAC).该控制器对CMAC的空间划分方式进行了模糊化处理,可通过BP学习算法对CMAC的空间划分方式进行在线调整,大大提高了CMAC的自适应能力.所提出的FCMAC被应用于机器人的轨迹跟踪控制系统以克服机器人系统中非线性和不确定性因素的影响.仿真实验结果表明,所提FCMAC与传统的CMAC相比性能上有了很大的改善.     

Learning convergence in the cerebellar model articulationcontroller

A new way to look at the learning algorithm in the cerebellar model articulation controller (CMAC) proposed by J.S. Albus (1975) is presented. A proof that the CMAC learning always converges with arbitrary accuracy on any set of training data is obtained. An alternative way to implement CMAC based on the insights obtained in the process is proposed. The scheme is tested with a computer simulation for learning the inverse dynamics of a two-link robot arm.     

基于干扰观测器的一类不确定仿射非线性系统有限时间收敛backstepping控制

针对一类不确定仿射非线性系统的跟踪控制问题,提出一种基于干扰观测器的有限时间收敛backstepping控制方法.为增强小脑模型(CMAC)泛化和学习能力,将非对称高斯函数和模糊理论相结合,给出非对称模糊CMAC结构,设计干扰观测器实现系统未知复合干扰在线准确逼近;基于非对称模糊CMAC干扰观测器,给出有限时间收敛backstepping控制器设计步骤,利用Lyapunov稳定理论证明闭环系统稳定性,其中采用非线性微分器获取虚拟控制量滤波和微分信息以避免backstepping设计中的微分“膨胀问题”,设计辅助系统修正因微分器带来的误差对系统跟踪性能影响,引入基于障碍型函数的自适应滑模鲁棒项抑制复合干扰估计偏差对跟踪误差的影响;将所提方法应用于无人机飞行控制仿真实验,结果表明所提方法的有效性.     

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。     

Synchronization of unified chaotic system via adaptive wavelet cerebellar model articulation controller

This study aims to propose a more efficient control algorithm for the chaotic system synchronization. In this study, a novel wavelet cerebellar model articulation controller (WCMAC) is proposed, which incorporates the wavelet decomposition property with a cerebellar model articulation controller (CMAC). This WCMAC is a generalization network; in some special cases, it can be reduced to a wavelet neural network, a neural network and a conventional CMAC. Then, an adaptive wavelet cerebellar model articulation control system (AWCCS) is proposed to synchronize a unified chaotic system. In this AWCCS, WCMAC is the main controller utilized to mimic a perfect controller and the parameters of WCMAC are online adjusted by the derived adaptive laws; and a compensation controller is designed to dispel the residual of the approximation error for achieving $ H^{\infty } $ robust performance. The derived AWCCS is then applied to the chaotic system synchronization control. Finally, the effectiveness of the proposed control system is demonstrated through simulation results.     

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.     

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.      

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.     

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.     

Design and Implementation of a Hierarchical‐Clustering CMAC PID Controller

In industrial control processes, proportional‐integral‐derivative (PID) control algorithm is widely employed. Therefore, it is meaningful to design advanced PID controllers, especially for nonlinear control objects. One of the advanced PID controllers is a cerebellar model articulation controller (CMAC) PID controller. In this controller, the PID control parameters are calculated and tuned. The CMAC achieves a higher accuracy by increasing the number of labels of each weight table; this requires a larger memory, and the generalization ability of the controller decreases. On the other hand, if the CMAC requires less memory, the generalization ability increases and accuracy decreases. Hence, in this paper, a novel CMAC in which the accuracy is compatible with the generalization ability is proposed in this paper. In the proposed CMAC, the number of labels of each weight table can be decided by using a hierarchical clustering technology. Moreover, the efficiency of the memory allocation is improved. The effectiveness of the proposed method is verified by experiments.     

Integral variable structure control of nonlinear system using a CMAC neural network learning approach.

This work presents a novel integral variable structure control (IVSC) that combines a cerebellar model articulation controller (CMAC) neural network and a soft supervisor controller for use in designing single-input single-output (SISO) nonlinear system. Based on the Lyapunov theorem, the soft supervisor controller is designed to guarantee the global stability of the system. The CMAC neural network is used to perform the equivalent control on IVSC, using a real-time learning algorithm. The proposed IVSC control scheme alleviates the dependency on system parameters and eliminates the chattering of the control signal through an efficient learning scheme. The CMAC-based IVSC (CIVSC) scheme is proven to be globally stable inasmuch all signals involved are bounded and the tracking error converges to zero. A numerical simulation demonstrates the effectiveness and robustness of the proposed controller.