Adaptive supervisory WCMAC neural network controller (SWC) for nonlinear systems

This paper proposes a wavelet-based cerebellar model arithmetic controller neural network (called WCMAC) and develops an adaptive supervisory WCMAC control (SWC) scheme for nonlinear uncertain systems. The WCMAC is modified from the traditional CMAC for obtaining high approximation accuracy and convergent rate using the advantages of wavelet functions and fuzzy TSK-model. For nonlinear uncertain systems, a PD-type WCMAC controller with filter is constructed to approximate an ideal control signal. The corresponding adaptive supervisory controller is used to recover the residual of approximation error. Finally, the adaptive SWC scheme is applied to chaotic system identification and control including Mackey–Glass time-series prediction, control of inverted pendulum system, and control of Chua circuit system. These demonstrate the effectiveness of our adaptive SWC approach for nonlinear uncertain systems.     

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.     

一种自适应CMAC在交流励磁水轮发电系统中仿真研究

在分析常规CMAC结构的基础上,针对一类非线性、参数时变和不确定的控制系统,提出了一种自适应CMAC神经网络的控制器．该控制器以系统动态误差和给定信号量作为CMAC的激励信号,并与自适应线性神经元网络相结合构成系统的复合控制．为了验证其有效性,将其应用到交流励磁水轮发电机系统的多变量非线性控制中,并与常规的PID控制效果进行了比较．仿真结果表明,该控制器具有较强鲁棒性和自适应能力,控制品质优良。     

SYNCHRONIZATION OF CHAOTIC GYRO SYSTEMS USING RECURRENT WAVELET CMAC

This study addresses synchronization of two chaotic gyros by using an adaptive recurrent wavelet cerebellar model articulation controller (RWCMAC). The proposed adaptive RWCMAC system contains an RWCMAC and a robust controller. Based on Lyapunov stability theory, the parameters of RWCMAC are on-line tuned and the robust controller is designed for achieving H ^∞ robust performance. Finally, the proposed adaptive RWCMAC system is applied to synchronize two chaotic gyros. Numerical simulation results demonstrate the effectiveness of the proposed control scheme.     

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.     

基于PID控制的遗传神经网络在焦炉温度控制中的应用研究

以某焦化厂焦炉温度控制系统的开发为背景，提出了一种基于遗传算法的CMAC(小脑模型关联控制器)与PID复合控制方法来优化焦炉对象的温度控制．用遗传算法优化PID控制器的初始参数，然后再结合CMAC网络进行控制．针对焦炉生产过程的简化模型，在Matlab中对这种控制方法进行了仿真．仿真研究表明该方法应用于焦炉控制是可行的．     

Wavelet CMAC for MIMO uncertain nonlinear systems using a modified social ski-driver algorithm

This study uses a Mexican hat wavelet membership function for a cerebellar model articulation controller (CMAC) to develop a more efficient adaptive controller for multiple input multiple output (MIMO) uncertain nonlinear systems. The main controller is called the adaptive Mexican hat wavelet CMAC (MWCMAC), and an auxiliary controller is used to remove the residual error. For the MWCMAC, the online learning laws are derived from the gradient descent method. In addition, the learning rate values are very important and have a great impact on the performance of the control system; however, they are difficult to choose accurately. Therefore, a modified social ski driver (SSD) algorithm is proposed to find optimal learning rates for the control parameters. Finally, a magnetic ball levitation system and a nine-link biped robot are used to illustrate the effectiveness of the proposed SSD-based MWCMAC control system. The comparisons with other existing control algorithms have shown the superiority of the proposed control system.     

Intelligent backstepping control for wheeled inverted pendulum

The adaptive output recurrent cerebellar model articulation control (AORCMAC) is an adaptive system with simple computation, good generalization capability and fast learning property. The proposed AORCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) in efficient learning mechanism and dynamic response. In this study, an intelligent backstepping tracking control system is proposed for wheeled inverted pendulums (WIPs) with unknown system dynamics and external disturbance. In this control system, an ABORCMAC is used to copy an ideal backstepping control (IBC), and a compensated controller is designed to compensate for difference between the IBC law and AORCMAC. Moreover, all adaptation laws of the proposed system are derived based on the Lyapunov stability analysis, the Taylor linearization technique, so that the stability of the closed-loop system can be guaranteed.     

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.     

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.     

Design of intelligent power controller for DC–DC converters using CMAC neural network

DC–DC converters are the devices which can convert a certain electrical voltage to another level of electrical voltage. They are very popularly used because of the high efficiency and small size. This paper proposes an intelligent power controller for the DC–DC converters via cerebella model articulation controller (CMAC) neural network approach. The proposed intelligent power controller is composed of a CMAC neural controller and a robust controller. The CMAC neural controller uses a CMAC neural network to online mimic an ideal controller, and the robust controller is designed to achieve L ₂ tracking performance with desired attenuation level. Finally, a comparison among a PI control, adaptive neural control and the proposed intelligent power control is made. The experimental results are provided to demonstrate the proposed intelligent power controller can cope with the input voltage and load resistance variations to ensure the stability while providing fast transient response and simple computation.     

Missile guidance law design using adaptive cerebellar model articulation controller

An adaptive cerebellar model articulation controller (CMAC) is proposed for command to line-of-sight (CLOS) missile guidance law design. In this design, the three-dimensional (3-D) CLOS guidance problem is formulated as a tracking problem of a time-varying nonlinear system. The adaptive CMAC control system is comprised of a CMAC and a compensation controller. The CMAC control is used to imitate a feedback linearization control law and the compensation controller is utilized to compensate the difference between the feedback linearization control law and the CMAC control. The online adaptive law is derived based on the Lyapunov stability theorem to learn the weights of receptive-field basis functions in CMAC control. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Then the adaptive CMAC control system is designed to achieve satisfactory tracking performance. Simulation results for different engagement scenarios illustrate the validity of the proposed adaptive CMAC-based guidance law.     

Specificity enhancement in classification of breast MRI lesion based on multi-classifier

In the conventional CMAC-based adaptive controller design, a switching compensator is designed to guarantee system stability in the Lyapunov stability sense but the undesirable chattering phenomenon occurs. This paper proposes a CMAC-based smooth adaptive neural control (CSANC) system that is composed of a neural controller and a saturation compensator. The neural controller uses a CMAC neural network to online mimic an ideal controller and the saturation compensator is designed to dispel the approximation error between the ideal controller and neural controller without any chattering phenomena. The parameter adaptive algorithms of the CSANC system are derived in the sense of Lyapunov stability, so the system stability can be guaranteed. Finally, the proposed CSANC system is applied to a Chua’s chaotic circuit and a DC motor driver. Simulation and experimental results show the CSANC system can achieve a favorable tracking performance. It should be emphasized that the development of the proposed CSANC system doesn’t need the knowledge of the system dynamics.     

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。     

Hierarchically clustered adaptive quantization CMAC and its learning convergence.

The cerebellar model articulation controller (CMAC) neural network (NN) is a well-established computational model of the human cerebellum. Nevertheless, there are two major drawbacks associated with the uniform quantization scheme of the CMAC network. They are the following: (1) a constant output resolution associated with the entire input space and (2) the generalization-accuracy dilemma. Moreover, the size of the CMAC network is an exponential function of the number of inputs. Depending on the characteristics of the training data, only a small percentage of the entire set of CMAC memory cells is utilized. Therefore, the efficient utilization of the CMAC memory is a crucial issue. One approach is to quantize the input space nonuniformly. For existing nonuniformly quantized CMAC systems, there is a tradeoff between memory efficiency and computational complexity. Inspired by the underlying organizational mechanism of the human brain, this paper presents a novel CMAC architecture named hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC). HCAQ-CMAC employs hierarchical clustering for the nonuniform quantization of the input space to identify significant input segments and subsequently allocating more memory cells to these regions. The stability of the HCAQ-CMAC network is theoretically guaranteed by the proof of its learning convergence. The performance of the proposed network is subsequently benchmarked against the original CMAC network, as well as two other existing CMAC variants on two real-life applications, namely, automated control of car maneuver and modeling of the human blood glucose dynamics. The experimental results have demonstrated that the HCAQ-CMAC network offers an efficient memory allocation scheme and improves the generalization and accuracy of the network output to achieve better or comparable performances with smaller memory usages. Index Terms-Cerebellar model articulation controller (CMAC), hierarchical clustering, hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC), learning convergence, nonuniform quantization.     

The Kernel Recursive Least Squares CMAC with Vector Eligibility

The cerebellar model articulation controller (CMAC) neural network is an associative memory that is biologically inspired by the cerebellum, which is found in the brains of animals. In recent works, the kernel recursive least squares CMAC (KRLS–CMAC) was proposed as a superior alternative to the standard CMAC as it converges faster and does not require tuning of a learning rate parameter. One improvement to the standard CMAC that has been discussed in the literature is eligibility, and vector eligibility. With vector eligibility the CMAC is able to control online motion control problems that it could not previously, stabilize the system much faster, and converge to a more intelligent solution. This paper integrates vector eligibility with the KRLS–CMAC and shows how the combination is advantageous through two simulated control experiments.     

智能假腿的CMAC控制与实例仿真

针对智能假腿系统模型的非线性与参数的不确定性等系统特性,提出了一种基于小脑模型神经网络控制器(CMAC)的假腿实时智能控制方法。该方法首先根据一种自制的假肢膝关节自适应结构,建立了智能假腿摆动相动力学数学模型,以描述智能假腿膝关节阻尼器控制参数与摆动运动参数之间的直接耦合关系。以此动力学模型为控制对象,设计了一种基于PD-CMAC的假腿系统智能控制器,并进行了实例仿真。仿真结果表明,假腿膝关节可以很快(约在0.5s时间内)跟踪好目标曲线,具有良好的实时性与精度;此外,膝关节阻尼器针阀开口位置与相应的假腿膝关节的角速度变化具有明显的负相关性;可以通过对假腿阻尼器针阀开口位置的调节,达到假腿跟踪健康腿摆动步态的目的。     

Hénon混沌同步的自适应逆控制

基于自适应逆控制原理,在噪声存在的情况下,提出了一种实现混沌同步的自适应逆控制方法.为此首先简要介绍了控制方法结构,然后利用神经网络算法对被控对象模型进行辨识和训练发送端的控制器.仿真证明该方法能够很好的消除干扰,使得被噪声污染的混沌同步系统能够保持良好的同步.此外自适应逆控制是开环控制,具有很好的实施性.     

非线性系统的再励学习控制研究

研究了一种带有的CMAC神经网络的再励学习（RL）控制方法,以解决具有高度非线性的系统控制问题。研究的重点在于算法的简化以及具有连续输出的函数学习上。控制策略由两部分构成;再励学习控制器和固定增益常规控制器。前者用于学习系统的非线性,后者用于稳定系统。仿真结果表明,所提出的控制策略不仅是有效的,而且具有很高的控制精度。     

Adaptive linear finite-element method for modelling nonlinear dynamic systems

This paper proposes a method of identifying nonlinear dynamic models with observation data (or a training data set) which exhibits a simple structure, adaptive input-space partition and fast convergence. The method employs the multiscale approximation concepts which have been introduced in numerical analysis motivated by wavelet analysis concepts. The partition or equivalently scaled basis functions are determined and selected adaptively in a sequenced and ordered manner. This method may be also considered as a single-layer neural network but with adaptive neural neurons. The number of multiscale basis functions required depends on the degree of nonlinearity of the system being modelled. The method is compared with the cerebellar model with interpolation (CEINT) and the cerebellar model articulation control (CMAC) methods and has been shown to achieve comparative modelling accuracies but with a reduced memory space and a concomitantly reduced training set.