This paper presents an approach for the forecast of daily stock price. Stock prices are not constant over time and are becoming increasingly uncertain in modern financial markets, so that their forecasting is more important and challenging. A new structure, called a cerebellar model extreme learning machine (CMELM), is proposed, which includes a cerebellar model neural network used as a main predictor and an extreme learning machine used for parameter learning. In order to attain better accuracy, a wavelet is used to decompose the original stock price time series. This framework is tested using the data from the Taiwanese stock market, and the experimental results show that it outperforms the benchmarks that are established in this study. Because it is extremely fast and sufficiently accurate, the proposed method has great potential for practical applications.

Nonlinear systems, such as robotic systems, play an increasingly important role in our modern daily life and have become more dominant in many industries; however, robotic control still faces various challenges due to diverse and unstructured work environments. This article proposes a double-loop recurrent neural network (DLRNN) with the support of a Type-2 fuzzy system and a self-organizing mechanism for improved performance in nonlinear dynamic robot control. The proposed network has a double-loop recurrent structure, which enables better dynamic mapping. In addition, the network combines a Type-2 fuzzy system with a double-loop recurrent structure to improve the ability to deal with uncertain environments. To achieve an efficient system response, a self-organizing mechanism is proposed to adaptively adjust the number of layers in a DLRNN. This work integrates the proposed network into a conventional sliding mode control (SMC) system to theoretically and empirically prove its stability. The proposed system is applied to a three-joint robot manipulator, leading to a comparative study that considers several existing control approaches. The experimental results confirm the superiority of the proposed system and its effectiveness and robustness in response to various external system disturbances.

A Cerebellar Model Articulation Controller (CMAC) is designed for the synchronization control of chaotic system used for the encryption and decryption of communication systems. Chaotic systems are important nonlinear systems that display complex and unpredictable behavior. Since the architecture of CMAC is small and it can learn fast, so it is suitable for high speed signal processing. The audio and image to be transmitted can be mixed into chaotic systems for encryption transmission, thereby preventing the massage being known by others; and finally use the synchronization of chaotic system to decrypt the correct information at the receiving end. The synchronization of chaotic system can be controlled by using a CMAC. By adjusting the controller parameters, CMAC can achieve fast and stable control for decrypting the original signals.

The writing sequence of numerals or letters often affects aesthetic aspects of the writing outcomes. As such, it remains a challenge for robotic calligraphy systems to perform, mimicking human writers' implicit intention. This article presents a new robot calligraphy system that is able to learn writing sequences with limited sequential information, producing writing results compatible to human writers with good diversity. In particular, the system innovatively applies a gated recurrent unit (GRU) network to generate robotic writing actions with the support of a prelabeled trajectory sequence vector. Also, a new evaluation method is proposed that considers the shape, trajectory sequence, and structural information of the writing outcome, thereby helping ensure the writing quality. A swarm optimization algorithm is exploited to create an optimal set of parameters of the proposed system. The proposed approach is evaluated using Arabic numerals, and the experimental results demonstrate the competitive writing performance of the system against state-of-the-art approaches regarding multiple criteria (including FID, MAE, PSNR, SSIM, and PerLoss), as well as diversity performance concerning variance and entropy. Importantly, the proposed GRU-based robotic motion planning system, supported with swarm optimization can learn from a small dataset, while producing calligraphy writing with diverse and aesthetically pleasing outcomes.

Metalearning has been widely applied for implementing few-shot learning and fast model adaptation. Particularly, existing metalearning methods have been exploited to learn the control mechanism for gradient descent processes, in an effort to facilitate gradient-based learning in gaining high speed and generalization ability. This article presents a novel method that controls the gradient descent process of the model parameters in a neural network, by limiting the model parameters within a low-dimensional latent space. The main challenge for implementing this idea is that a decoder with many parameters may be required. To tackle this problem, the article provides an alternative design of the decoder with a structure that shares certain weights, thereby reducing the number of required parameters. In addition, this work combines ensemble learning with the proposed approach to improve the overall learning performance. Systematic experimental studies demonstrate that the proposed approach offers results superior to the state of the art in performing the Omniglot classification and miniImageNet classification tasks.

This study proposes an efficient intelligent control structure for uncertain nonlinear systems. The controller is implemented by a sliding mode control framework including a modified broad leaning network (BLS) with a double-loop recurrent structure. In addition, the proposed BLS involves a self-organizing mechanism to increase or decrease the size of the BLS. The technique for order of preference by similarity to ideal solution (TOPSIS) method is used to build the self-organizing mechanism. Moreover, two dynamic thresholds of TOPSIS are automatically determined according to the stability of the controller. One dynamic threshold is used to consider whether to retain or remove existing network neurons in the BLS; and the other is used to generate new neurons, so as to meet the requirements of different control states and save computing resources. To improve the network's dynamic characteristics, a double-loop recurrent structure is further introduced into the self-organizing BLS. The Lyapunov stability function is used to ensure the stability of the control system. The proposed controller is applied to the simulation control of a nonlinear chaotic system and a three-link robot manipulator. The experimental results show that the proposed controller can achieve better control performance against other network-based controllers. The source code of this work is placed at https://github.com/wzhuang-xmu/SODLRBLS

In this article, a new idea of chaos synchronization and chaos-based secure communication is developed. First, the chaotic master system is used as a transmitter in chaos-based secure communication, then a drive signal is constructed, and the information message is encrypted into the drive signal to form a transmitted signal for secure communication. Second, in the receiver, a recurrent Takagi-Sugeno-Kang (TSK) fuzzy brain emotional learning cerebellar model articulation controller (RTFBECAC) is developed to control the slave system to follow the master system in the transmitter. Third, after descripting the chaotic signal, the embedded information message can be recovered. Besides, the stability problem is analyzed in detail based on the stability theory. Finally, two simulation examples, including audio signal and image, are introduced to illustrate the effectiveness and the advantages of the proposed method.

Inertial measurement units (IMUs) have been widely used to provide accurate location and movement measurement solutions, along with the advances of modern manufacturing technologies. The scale factors of accelerometers and gyroscopes are linear when the range of the sensors are reasonably small, but the factor becomes nonlinear when the range gets much bigger. Based on this observation, this article presents a calibration method for low-cost IMU by effectively deriving the nonlinear scale factors of the sensors. Two motion patterns of the sensor on a rigid object are moved to collect data for calibration: One motion pattern is to upcast and rotate the rigid object, and another pattern is to place the rigid object on a stable base in different attitudes. The rotation motion produces centripetal and Coriolis force, which increases the measurement range of accelerometers. Four cost functions with different weight factors and two sets of data are utilized to optimize the IMU parameters. The weight factor comes from derived formula with input values which are the variance of the noise of the sampled data. The proposed approach was validated and evaluated on both synthetic and real-world data sets, and the experimental results demonstrated the superiority of the proposed approach in improving the accuracy of IMU for long-range use. In particular, the errors of acceleration and angular velocity led by our algorithm are significantly smaller than those resulted from the existing approaches using the same testing data sets, demonstrating a remarkable improvement of 64.12% and 47.90%, respectively.

This article aims to propose a more efficient control algorithm for uncertain nonlinear systems. An intelligent self-organizing double function-link fuzzy brain emotional control system is proposed which comprises a self-organizing double function-link fuzzy brain emotional controller (SDFLFBEC) and a compensation controller. The proposed SDFLFBEC consists of four substructures and a fuzzy inference system. The substructures are the prefrontal cortex, the amygdala, a double function-link network (FLN) and a self-organizing structure. The prefrontal cortex and the amygdala networks work as a mathematical form that presumes the judgment and emotion of a brain. Specifically, a new double FLN is designed to support the above networks for updating their weights. Next, a self-organizing structure can automatically add or prune the layers to achieve efficient network structure. In addition, the fuzzy inference rules are presented to explain the inference processes of the amygdala and orbitofrontal networks. From the above factors, the proposed SDFLFBEC can effectively reduce the tracking error and achieve favorable control performance. The parameters of the control system are adjusted online using the derived adaptation laws that are taken from a Lyapunov function so that the stability of the system is ensured. Simulation studies of a biped robot and the experimental results of a magnetic levitation system are employed to validate the effectiveness and superiority of the proposed SDFLFBEC.

It has been a challenging task for a robotic arm to accurately reach and grasp objects, which has drawn much research attention. This article proposes a robotic hand-eye coordination system by simulating the human behavior pattern to achieve a fast and robust reaching ability. This is achieved by two neural-network-based controllers, including a rough reaching movement controller implemented by a pretrained radial basis function for rough reaching movements, and a correction movement controller built from a specifically designed brain emotional nesting network (BENN) for smooth correction movements. In particular, the proposed BENN is designed with high nonlinear mapping ability, with its adaptive laws derived from the Lyapunov stability theorem; from this, the robust tracking performance and accordingly the stability of the proposed control system are guaranteed by the utilization of the H∞control approach. The proposed BENN is validated and evaluated by a chaos synchronization simulation, and the overall control system by object grasping tasks through a physical robotic arm in a real-world environment. The experimental results demonstrate the superiority of the proposed control system in reference to those with single neural networks.

This research produces a mixed Gaussian membership function (GMF) fuzzy cerebellar model articulation controller (CMAC) for a three-link robot. A mixed GMF is created using the current and the previous GMFs on each layer of CMAC to detect errors efficiently, so a mixed GMF fuzzy CMAC (MGMFFC) is able to train parameters efficiently and constructs the MGMFFC structure automatically. A Lyapunov cost function and the gradient descent techniques are utilized to get the adaptive with guaranteed system's stable. Simulation studies for a three-link robot show that the MGMFFC attains favorable tracking performance.

This paper develops a novel maximum power point tracking (MPPT) control strategy for nonlinear photovoltaic (PV) systems. The MPPT control problem of the considered PV systems is first formulated in the framework of fuzzy descriptor systems. Then, based on the new formulation, a fuzzy sliding mode control (FSMC) law is constructed to drive the state trajectories into a desired sliding surface within the finite-time T* with T* <; T. Moreover, sufficient conditions are derived to ensure the reachable set boundings of the closed-loop PV control systems in the finite-time intervals [0,T*] and [T*,T]. A simulation example is given to show the effectiveness of the proposed design method.

This paper proposes a self-organizing control system for uncertain nonlinear systems. The proposed neural network is composed of a conventional brain emotional learning network (BEL) and a cerebellar model articulation controller network (CMAC). The input value of the network is feed to a BEL channel and a CMAC channel. The output of the network is generated by the comprehensive action of the two channels. The structure of the network is dynamic, using a self-organizing algorithm allows increasing or decreasing weight layers. The parameters of the proposed network are on-line tuned by the brain emotional learning rules; the updating rules of CMAC and the robust controller are derived from the Lyapunov function; in addition, stability analysis theory is used to guaranty the proposed controller's convergence. A simulated mobile robot is applied to prove the effectiveness of the proposed control system. By comparing with the performance of other neural-network-based control systems, the proposed network produces better performance.

This research poses a double function-link fuzzy brain emotional controller (DFLFBC) to synchronize a 4D hyper-chaotic system. The DFLFBC contains three main structures and a set of fuzzy inference rules. Three main structures are comprised of a double function-link network, an amygdala, and a prefrontal cortex. The double function-link is employed for adjusting the output weights for the prefrontal cortex and amygdala branches. The online learning laws for the proposed approach to online adjust the parameters are derived from the gradient descent algorithm. Synchronization studies of a 4D hyper-chaotic system are implemented to check the capability and performance of the DFLFBC.

Dynamic control, including robotic control, faces both the theoretical challenge of obtaining accurate system models and the practical difficulty of defining uncertain system bounds. To facilitate such challenges, this paper proposes a control system consisting of a novel type of fuzzy neural network and a robust compensator controller. The new fuzzy neural network is implemented by integrating a number of key components embedded in a Type-2 fuzzy cerebellar model articulation controller (CMAC) and a brain emotional learning controller (BELC) network, thereby mimicking an ideal sliding mode controller. The system inputs are fed into the neural network through a Type-2 fuzzy inference system (T2FIS), with the results subsequently piped into sensory and emotional channels which jointly produce the final outputs of the network. That is, the proposed network estimates the nonlinear equations representing the ideal sliding mode controllers using a powerful compensator controller with the support of T2FIS and BELC, guaranteeing robust tracking of the dynamics of the controlled systems. The adaptive dynamic tuning laws of the network are developed by exploiting the popular brain emotional learning rule and the Lyapunov function. The proposed system was applied to a robot manipulator and a mobile robot, demonstrating its efficacy and potential; and a comparative study with alternatives indicates a significant improvement by the proposed system in performing the intelligent dynamic control.

Auto vectorization techniques have been adopted by compilers to exploit data-level parallelism in parallel processing for decades. However, since processor architectures have kept enhancing with new features to improve vector/SIMD performance, legacy application binaries failed to fully exploit new vector/SIMD capabilities in modern architectures. For example, legacy ARMv7 binaries cannot benefit from ARMv8 SIMD double precision capability, and legacy x86 binaries cannot enjoy the power of AVX-512 extensions.

This paper proposes a new efficient identification system for nonlinear systems. The proposed wavelet dual function-link fuzzy brain emotional learning system (WDFLFBELS) is used as an identifier to identify the system and to track the trajectory of nonlinear systems. The WDFLFBELS consists of three sub-structures and a fuzzy inference system. The sub-structures include a prefrontal cortex, an amygdala, and a new dual function-link network, then it can efficiently reduce the identification and tracking errors, and obtain good performance. The gradient descent technique is used to find the adaptive laws to online tune the parameters of the system effectively. Simulation studies for identifying a time-varying system and tracking a chaotic trajectory are performed to validate the effectiveness and superiority of the proposed method.

This paper presents a modified function-link fuzzy cerebellar model articulation controller for the synchronization of nonlinear chaotic systems including uncertainties, external disturbance, and different initial conditions. This study overlaps the previous state and the current state of Gaussian basis functions on each layer in the cerebellar model articulation controller to make a hybrid of two states. It can adjust the appropriate error values to let the network can efficiently learn parameters, enhance the computational performance and forecast the next state of the inputs. The gradient descent method is used to online adjust the controller parameters, and a Lyapunov stability function is applied to warrant the system's stability. Simulation studies for the synchronization of the gyroscope and Lorenz chaotic systems manifest that favorable synchronization performance can be attained.

In this paper, a novel fuzzy neural network structure for uncertain nonlinear systems is proposed. This network is called wavelet Takagi-Sugeno-Kang (TSK) fuzzy cerebellar model neural network, which includes the framework of a cerebellar model neural network (CMNN) and the wavelet-function-based TSK fuzzy inference model. In order to effectively solve the uncertainty problem of nonlinear systems, a new structure is proposed where the wavelet function is used in the consequent parts of TSK-type fuzzy CMNN instead of the linear combination of the input variables in the traditional TSK fuzzy systems. This structure combines the advantages of the wavelet function, the CMNN and the TSK fuzzy inference system; thus, it is a more effective model for the uncertain nonlinear systems. In order to provide fast training, parameter update laws of the proposed model are derived based on the gradient descent method in which the learning-rates are online adapted. Furthermore the Lyapunov function is used to analyze the convergence of the considered systems. Finally, four different types of applications are applied to demonstrate the effectiveness of the proposed model. The simulation comparisons with other neural network models have verified the effectiveness of the new model.

Conventional Chinese calligraphy robots often suffer from the limited sizes of predefined font databases, which prevent the robots from writing new characters. This paper presents a robotic handwriting system to address such limitations, which extracts Chinese characters from textbooks and uses a robot's manipulator to write the characters in a different style. The key technologies of the proposed approach include the following: 1) automatically decomposing Chinese characters into strokes using Harris corner detection technology and 2) matching the decomposed strokes to robotic writing trajectories learned from human gestures. Briefly, the system first decomposes a given Chinese character into a set of strokes and obtains the stroke trajectory writing ability by following the gestures performed by a human demonstrator. Then, it applies a stroke classification method that recognizes the decomposed strokes as robotic writing trajectories. Finally, the robot arm is driven to follow the trajectories and thus write the Chinese character. Seven common Chinese characters have been used in an experiment for system validation and evaluation. The experimental results demonstrate the power of the proposed system, given that the robot successfully wrote all the testing characters in the given Chinese calligraphic style.

Conventional approaches of robotic writing of Chinese character strokes often suffer from limited font generation methods, and thus the writing results often lack of diversity. This has seriously restricted the high quality writing ability of robots. This paper proposes a generative adversarial nets-based calligraphic robotic framework, which enables a robot to learn writing fundamental Chinese strokes with rich diversity and good originality. In particular, the framework considers the learning process of robotic writing as an adversarial procedure which is implemented by three interactive modules including a stroke generation module, a stroke discriminative module and a training module. Noting that the stroke generative module included in the conventional generative adversarial nets cannot solve the non-differentiable problem, the policy gradient commonly used in reinforcement learning is thus adapted in this work to train the generative module by regarding the outputs from the discriminative module as rewards. Experimental results demonstrate that the proposed framework allows a calligraphic robot to successfully write fundamental Chinese strokes with good quality in various styles. The experiment also suggests the proposed approach can achieve human-level stroke writing quality without the requirement of a performance evaluation system. This approach therefore significantly boosts the robotic autonomous creation ability.

This paper aims to design a classifier using the K-means clustering algorithm and the interval type-2 fuzzy neural network (IT2FNN). Firstly, the K-means clustering algorithm will classify the training data into k groups, according to its characteristics. After that, the IT2FNN will train the k classifiers' structure with these data. The testing data will be also determined that they will belong to which classifier. With this parallel structure, the performance of the proposed classifier is competitive with some state-of-the-art techniques. The parameter adaptive laws of the network are derived by using the steepest descent gradient approach. The convergence and stability of the proposed algorithm is guaranteed using the Lyapunov function. The system performance is evaluated by the breast cancer datasets of the University of California at Irvine (UCI). Comparison with other classifiers is also conducted. The experimental results have shown the effectiveness of the proposed method.

This paper addresses event-triggered data transmission in a class of large-scale networked nonlinear systems with transmission delays and nonlinear interconnections. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi-Sugeno model, and exchanges its information through a digital channel. We propose an event-triggering mechanism, which determines when the premise variables and system states should be transmitted to the controller. Our goal is to design a decentralized event-triggered state-feedback fuzzy controller, such that the resulting closed-loop fuzzy control system is asymptotically stable while the measured information is transmitted to the controller as little as possible. By using the input delay and perturbed system approaches, the closed-loop sampled-data fuzzy system with event-triggered control is first reformulated into a continuous-time system with time-varying delay and extra disturbance. Then, based on the new model, we introduce a Lyapunov-Krasovskii functional with virtue of Wirtinger's inequality, where not all of the Lyapunov matrices are required to be positive definite. The codesign result is derived to obtain simultaneously the controller gains, sampled period, network delay, and event-triggered parameter in terms of a set of linear matrix inequalities. Finally, two simulation examples are provided to validate the advantage of the proposed method.

This paper develops a fuzzy adaptive control system consisting of a new type of fuzzy neural network and a robust controller for uncertain nonlinear systems. The new designed neural network contains the key mechanisms of a typical fuzzy CMAC network and a brain emotional learning controller network. First, the input values of the new network are delivered to a receptive field structure that is inspired from the fuzzy CMAC. Then, the values are divided into a sensory and an emotional channels; and the two channels interact with each other to generate the final outputs of the proposed network. The parameters of the proposed network are on-line tuned by the brain emotional learning rules; in addition, stability analysis theory is used to guaranty the proposed controller's convergence. In the experimentation, a “Duffing-Holmes” chaotic system and a simulated mobile robot are applied to verify the effectiveness and feasibility of the proposed control system. By comparing with the performances of other neural network based control systems, we believe our proposed network is capable of producing better control performances of complex uncertain nonlinear systems control.

In recent years, multiobjective immune algorithms (MOIAs) have shown promising performance in solving multiobjective optimization problems (MOPs). However, basic MOIAs only use a single hypermutation operation to evolve individuals, which may induce some difficulties in tackling complicated MOPs. In this paper, we propose a novel hybrid evolutionary framework for MOIAs, in which the cloned individuals are divided into several subpopulations and then evolved using different evolutionary strategies. An example of this hybrid framework is implemented, in which simulated binary crossover and differential evolution with polynomial mutation are adopted. A fine-grained selection mechanism and a novel elitism sharing strategy are also adopted for performance enhancement. Various comparative experiments are conducted on 28 test MOPs and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.

This paper aims to propose an efficient network and applies it as an adaptive filter for the signal processing problems. An adaptive filter is proposed using a novel interval type-2 fuzzy cerebellar model articulation controller (T2FCMAC). The T2FCMAC realizes an interval type-2 fuzzy logic system based on the structure of the CMAC. Due to the better ability of handling uncertainties, type-2 fuzzy sets can solve some complicated problems with outstanding effectiveness than type-1 fuzzy sets. In addition, the Lyapunov function is utilized to derive the conditions of the adaptive learning rates, so that the convergence of the filtering error can be guaranteed. In order to demonstrate the performance of the proposed adaptive T2FCMAC filter, it is tested in signal processing applications, including a nonlinear channel equalization system, a time-varying channel equalization system, and an adaptive noise cancellation system. The advantages of the proposed filter over the other adaptive filters are verified through simulations.

This paper develops a control system with the recurrent wavelet Elman neural network (RWENN) that improves the capabilities of a commercial aircraft to land automatically (autoland) when it is subjected to severe wind disturbances and faults. The proposed RWENN controller is used for the autolanding control, as its real-time learning ability is better than a conventional neural network. The parameters of the RWENN are: 1) translations and dilations of the hidden layer's wavelet functions and 2) the weights between the hidden and output layers. These parameters are learned online using the gradient descent method. The adaptive laws of learning rates are derived from the Lyapunov theorem; hence, system stability can be guaranteed. Moreover, optimal learning rates provide the fastest convergence of parameters. Simulation results show that the RWENN-based control scheme can achieve better performance than other control schemes for the autolanding system in the presence of severe disturbances and faults.

This paper aims to propose a more efficient control algorithm for chaos time-series prediction and synchronization. A novel type-2 fuzzy cerebellar model articulation controller (T2FCMAC) is proposed. In some special cases, this T2FCMAC can be reduced to an interval type-2 fuzzy neural network, a fuzzy neural network, and a fuzzy cerebellar model articulation controller (CMAC). So, this T2FCMAC is a more generalized network with better learning ability, thus, it is used for the chaos time-series prediction and synchronization. Moreover, this T2FCMAC realizes the un-normalized interval type-2 fuzzy logic system based on the structure of the CMAC. It can provide better capabilities for handling uncertainty and more design degree of freedom than traditional type-1 fuzzy CMAC. Unlike most of the interval type-2 fuzzy system, the type-reduction of T2FCMAC is bypassed due to the property of un-normalized interval type-2 fuzzy logic system. This causes T2FCMAC to have lower computational complexity and is more practical. For chaos time-series prediction and synchronization applications, the training architectures with corresponding convergence analyses and optimal learning rates based on Lyapunov stability approach are introduced. Finally, two illustrated examples are presented to demonstrate the performance of the proposed T2FCMAC.

Since the mortality rate of breast cancer in women is gradually increasing, a well-designed computer-aided diagnosis (CAD) system can assist doctors in early diagnosis of the breast cancer. In this paper, a breast nodule CAD system is developed, and this system aims for a high-performance classifier for characterizing breast nodules as either benign or malignant on an ultrasonic image. A fuzzy cerebellar model neural network (FCMNN) CAD system is developed. Since the FCMNN contains the layers with overlapped membership functions, it possesses more generalization ability than a conventional fuzzy neural network. Moreover, a FCMNN can be viewed as a generation of a fuzzy neural network; if each layer of FCMNN is reduced to contain only one different neuron, then the FCMNN can be reduced to a fuzzy neural network. Thus, it is used to develop a CAD system; this is a novel research on a breast nodule ultrasound image CAD system using an FCMNN. The testing of 65 practical ultrasound images demonstrates that the proposed FCMNN CAD system can distinguish benign or malignant breast nodules with relatively high accuracy (more than 90%), and the intensive experimental results where the resulting classifier outperforms other classifiers, such as a support vector machine and a neural network by using the N -folds cross-validation method are shown. The experimental results are even higher than doctor's diagnosis; therefore, the proposed diagnostic system can serve as an assistant system to help doctors correctly diagnose breast nodules.

This study aims to propose a more efficient control algorithm to achieve precision trajectory tracking control for a two-axis linear piezoelectric ceramic motor (LPCM). Since the inherent nonlinear nature and cross-coupling effect of a two-axis LPCM, its accurate model is difficult to obtain; thus, an intelligent adaptive wavelet fuzzy cerebellar model articulation controller backstepping (AWFCB) control system is designed to achieve high precision trajectory tracking control for a two-axis LPCM drive system. A novel wavelet fuzzy cerebellar model articulation controller (CMAC) is proposed in this paper; in some special cases, it can be reduced to a fuzzy system, a fuzzy neural network, a wavelet fuzzy neural network, or a conventional CMAC. The developed wavelet fuzzy CMAC incorporates the wavelet decomposition property and a fuzzy CMAC fast learning ability; thus, it is used for the LPCM control. In the AWFCB control system, a wavelet fuzzy CMAC is used to imitate an ideal backstepping controller, and a smooth compensator is designed to eliminate the residual of the approximation error between the wavelet fuzzy CMAC and the ideal backstepping controller. In order to guarantee the convergence of the tracking error, analytical methods using the Lyapunov function are utilized to derive the adaptation laws to tune the parameters of the control system online. Thus, the stability of the two-axis LPCM control system can be guaranteed. Finally, the experimental results show the precision of the trajectory tracking using AWFCB control. Compared with PID control and adaptive fuzzy sliding-mode control, the AWFCB control can achieve tracking error reduction of about 80%~99% and 48%~97%, respectively.

An antilock braking system (ABS) is designed to maximize wheel traction by preventing the wheels from locking during braking, while also maintaining an adequate ability to steer the vehicle. However, the performance of ABS is often degraded under harsh road conditions. In this paper, a self-organizing function-link fuzzy cerebellar model articulation controller (SOFFC) is proposed and is used as the uncertainty observer of the ABS. The self-organizing approach automatically generates and prunes the fuzzy rules for the SOFFC, without the need for preliminary knowledge. The learning algorithms not only extract the fuzzy rules for the SOFFC, but adjust the parameters of the SOFFC as well. A hybrid control system, composing a computational controller and a hyperbolic tangent compensator (HTC), is then proposed for the ABS. The computational controller, which contains an SOFFC uncertainty observer, forms the principal controller, and the HTC is used to compensate for the estimation uncertainty, in order to achieve ultimately bounded stability in the system. Finally, simulations are performed that demonstrate the effectiveness of the proposed hybrid control system in an ABS under various road conditions.

An adaptive wavelet fuzzy cerebellar model articulation control system is developed for the trajectory tracking control of voice coil motors (VCMs). This control system comprises a wavelet fuzzy cerebellar model articulation controller (WFCMAC) and a fuzzy compensator. The novel WFCMAC incorporates the wavelet decomposition property with a fuzzy CMAC fast learning ability; and it is used to imitate an ideal controller. The fuzzy compensator is developed to attenuate the effect of the approximation error caused by the WFCMAC approximator. The on-line learning algorithm of the controller's parameters is derived based on the Lyapunov function, thus the stability of the system can be guaranteed. Finally, the developed control system is applied to the trajectory tracking control of a VCM.

This paper presents an intelligent adaptive steering control using linear quadratic regulation (LQR) approach and fuzzy cerebella model articulation control (CMAC) method for an electrical unicycle. The fuzzy CMAC is employed to on-line learn unknown frictions between the wheel and the terrain surfaces. The LQR approach is used to design a state feedback controller, in order to simultaneously achieve self-balancing and velocity control for the unicycle with different riders. The performance and merit of the proposed method are well exemplified by conducting simulations on a laboratory-built electric unicycle.

Recurrent wavelet neural network (RWNN) has the advantages such as fast learning property, good generalization capability and information storing ability. With these advantages, this paper proposes an RWNN-based adaptive control (RBAC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The RBAC system is composed of a neural controller and a bounding compensator. The neural controller uses an RWNN to online mimic an ideal controller, and the bounding compensator can provide smooth and chattering-free stability compensation. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. Finally, the proposed RBAC system is applied to the MIMO uncertain nonlinear systems such as a mass-spring-damper mechanical system and a two-link robotic manipulator system. Simulation results verify that the proposed RBAC system can achieve favorable tracking performance with desired robustness without any chattering phenomenon in the control effort.

A Takagi-Suegeno-Kang (TSK) fuzzy cerebellar-model-articulation-controller-based robust adaptive backstepping (TFCRAB) control system is proposed for the uncertain nonlinear systems. This TFCRAB control system is composed of a novel TSK fuzzy cerebellar model articulation controller (TFC) and a robust compensator. The proposed TFC is a generalization of a TSK fuzzy system, a fuzzy neural network, and a conventional cerebellar-model-articulation-controller. It is used as the principal tracking controller to mimic an ideal backstepping controller (IBC). The parameters of TFC are tuned online by the derived adaptation laws based on the Lyapunov stability theorem. The robust compensator is designed to dispel the approximation error between the TFC and the IBC so that the asymptotic stability of the closed-loop system can be guaranteed. Finally, the proposed control system is applied to control a Duffing-Holmes chaotic system and a voice coil motor. From the simulation and experimental results, it is verified that the proposed TFCRAB control scheme can achieve favorable tracking performance and that even the system models of the controlled systems are unknown.

This paper proposes a novel randomly adapting particle swarm optimization (RAPSO) approach which uses a weighed particle in a swarm to solve multi-dimensional optimization problems. In the proposed method, the strategy of the RAPSO acquires the benefit from a weighed particle to achieve optimal position in explorative and exploitative search. The weighed particle provides a better direction of search and avoids trapping in local solution during the optimization process. The simulation results show the effectiveness of the RAPSO, which outperforms the traditional PSO method, cooperative random learning particle swarm optimization (CRPSO), genetic algorithm (GA) and differential evolution (DE) on the 6 benchmark functions.

This study proposes a synchronization control of chaotic systems by using an adaptive recurrent wavelet cerebellar model articulation controller (RWCMAC). The proposed adaptive RWCMAC system contains a RWCMAC and a fuzzy compensation controller. Due to favorable capability of wavelet, the wavelet function is used as a base function of CMAC. Based on Lyapunov stability theory, the parameters of RWCMAC are on-line tuned; and the fuzzy compensation controller is designed to eliminate approximation error between ideal controller and RWCMAC. The developed control system is applied to control an unified chaotic system. The simulation results demonstrate the effectiveness of the proposed control scheme.

This study proposes an adaptive wavelet cerebellar -model-articulation-controller (AWCMAC) for multi-input multi-output nonlinear systems. In this proposed scheme, wavelet cerebellar-model articulation-controller (WCMAC) is the main controller utilized to mimic an ideal controller and the parameters of WCMAC are on-line adjusted by the derived tuning algorithm. Moreover the robust controller is designed to dispel the residual of the approximation error for achieving H∞robust performance. PSO algorithm is used to tune the learning-rates to achieve fast learning speed of AWCMAC. The simulation results of a three-link robotic arm demonstrate the effectiveness of the proposed control scheme.

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.

A novel adaptive filter is proposed using a recurrent cerebellar-model-articulation-controller (CMAC). The proposed locally recurrent globally feedforward recurrent CMAC (RCMAC) has favorable properties of small size, good generalization, rapid learning, and dynamic response, thus it is more suitable for high-speed signal processing. To provide fast training, an efficient parameter learning algorithm based on the normalized gradient descent method is presented, in which the learning rates are on-line adapted. Then the Lyapunov function is utilized to derive the conditions of the adaptive learning rates, so the stability of the filtering error can be guaranteed. To demonstrate the performance of the proposed adaptive RCMAC filter, it is applied to a nonlinear channel equalization system and an adaptive noise cancelation system. The advantages of the proposed filter over other adaptive filters are verified through simulations.

Cerebellar model articulation controller (CMAC) has been already validated that it can approximate a nonlinear function over a domain of interest to any desired accuracy. This paper proposes an adaptive CMAC (PIACMAC) system with a PI-type learning algorithm. The PIACMAC system is composed of a CMAC and a compensation controller. CMAC is used to mimic an ideal controller and the compensation controller is designed to dispel the approximation error between CMAC and ideal controller. The Lyapunov stability theorems is utilized to derive the parameter learning algorithm, so that the uniformly ultimately bounded of PIACMAC system can be guaranteed. Then, the PIACMAC system is applied to a Duffing-Holmes chaotic system. Simulation results verify that the proposed PIACMAC system with a PI-type learning algorithm can achieve better control performance than other control methods.

This paper presents a self-organizing control system based on cerebellar model articulation controller (CMAC) for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. The proposed control system merges a CMAC and sliding-mode control (SMC), so the input space dimension of CMAC can be simplified. The structure of CMAC will be self-organized; that is, the layers of CMAC will grow or prune systematically and their receptive functions can be automatically adjusted. The control system consists of a self-organizing CMAC (SOCM) and a robust controller. SOCM containing a CMAC uncertainty observer is used as the principal controller and the robust controller is designed to dispel the effect of approximation error. The gradient-descent method is used to online tune the parameters of CMAC and the Lyapunov function is applied to guarantee the stability of the system. A simulation study of inverted double pendulums system and an experimental result of linear ultrasonic motor motion control show that favorable tracking performance can be achieved by using the proposed control system.

This paper proposes an adaptive wavelet neuro control (AWNC) system, which is composed of a neural controller and a tangent controller. The neural controller utilizes a wavelet neural network to mimic an ideal controller and the tangent controller is designed to compensate for the approximation error between the ideal controller and the neural controller with using a hyperbolic tangent function. The main advantage of the proposed AWNC is that the weights are tuned on-line, and the uniformly ultimately bounded stability of the system can be guaranteed in the Lyapunov sense. Finally, to show the effectiveness of the proposed AWNC, it is applied to control a chaotic dynamic system. Simulation results verify that the proposed AWNC system can achieve favorable tracking performance. Since the developed AWNC system has no chattering phenomena in the control efforts, it is suitable for practical applications.

Antilock braking system (ABS) controls the slip of each wheel of a vehicle to prevent it from locking such that a high friction is achieved and steerability is maintained. It is designed to maximize wheel traction by preventing the wheels from locking during braking, while also maintaining adequate vehicle steerability; however, the performance is often degraded under harsh road conditions. In this study, a neurocontroller system, which is composed of a computation controller and a compensation controller, is developed for ABS. The computation controller containing a radial basis function neural network uncertainty observer is the principal controller; and the compensation controller is a compensator for the difference between the system uncertainty and the estimated uncertainty. The Lyapunov stability theory is utilized to derive the parameter tuning algorithm, so that the uniformly ultimately bound stability of the closed-loop system can be achieved. Simulations are performed to demonstrate the effectiveness of the proposed neurocontroller system under various road conditions.

This paper develops an intelligent robust control algorithm for a class of uncertain nonlinear multivariable systems. The proposed control algorithm consists of an adaptive recurrent cerebellar-model-articulation-controller (RCMAC) and a robust controller. Based on the H∞control approach, the robust controller is designed to suppress the residual of approximation error between ideal controller and adaptive RCMAC. Finally, the simulations of the proposed adaptive RCMAC-based intelligent robust control for a Chan's chaotic circuit are demonstrated. Simulation results confirm that the proposed control algorithm can achieve favorable tracking performance.

A fuzzy cerebellar model articulation control system is presented for multi-input multi-output (MIMO) nonlinear systems. The proposed control system contains of a fuzzy CMAC (FCMAC) and a robust controller. FCMAC is a main tracking controller utilized to approximate an ideal controller and the parameters of FCMAC are on-line tuned by the derived adaptive laws from the Lyapunov function. The robust controller is designed to suppress the influence of approximate error between the ideal controller and adaptive FCMAC, so that the robust tracking performance of the system can be guaranteed. Finally, two MIMO uncertain nonlinear systems, a Chua's chaotic circuit and a two-inverted pendulum system, are performed to illustrate the effectiveness of the proposed control scheme.

A hybrid control system, integrating principal and compensation controllers, is developed for multiple-input-multiple-output (MIMO) uncertain nonlinear systems. This hybrid control system is based on sliding-mode technique and uses a recurrent cerebellar model articulation controller (RCMAC) as an uncertainty observer. The principal controller containing an RCMAC uncertainty observer is the main controller, and the compensation controller is a compensator for the approximation error of the system uncertainty. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. The Taylor linearization technique is employed to increase the learning ability of RCMAC and the adaptive laws of the control system are derived based on Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. Finally, the proposed design method is applied to control a biped robot. Simulation results demonstrate the effectiveness of the proposed control scheme for the MIMO uncertain nonlinear system.

A design technique of a recurrent cerebellar model articulation controller (RCMAC)-based fault-tolerant control (FTC) system is investigated to rectify the nonlinear faults of a biped robot. The proposed RCMAC-based FTC (RCFTC) scheme contains two components: 1) an online fault estimation module based on an RCMAC is used to provide approximation information for any nonnominal behavior due to the system failure and modeling error of the biped robot; and 2) a controller module consisting of a computed torque controller and a robust FTC is utilized to achieve FTC. In the controller module, the computed torque controller reveals a basic stabilizing controller to stabilize the system, and the robust FTC is utilized to compensate for the effects of the system failure so as to achieve fault accommodation. The adaptive laws of the RCFTC system are rigorously established based on the Lyapunov function, so that the stability of the system can be guaranteed. Finally, two simulation cases of a biped robot are presented to illustrate the effectiveness of the proposed design method. Simulation results show that the RCFTC system can effectively recover the control performance for the system in the presence of the nonlinear faults and modeling uncertainties.

This study proposes a cerebellar model articulation controller (CMAC)-based supervisory control system to resolve the tracking control problem of chaotic chua's circuits. This CMAC-based supervisory control (CMBSC) system is composed of a CMAC and an H∞supervisor. The CMAC is a main tracking controller that is investigated to mimic an ideal control law and the H∞supervisor is a supervisory controller that is developed to attenuate the effect of the approximation error between the CMAC and the ideal control law to a prescribed level. Moreover, the gradient descent method, Lyapunov stability theory and H∞control technique are utilized to derive the on-line parameters tuning algorithm so that the system stability and the robust tracking performance can be achieved. Finally, the proposed CMBSC system is applied to control a chaotic Chua's circuit. Simulation results show that the proposed control scheme is feasible and effective for the nonlinear chaotic systems.

The switching power supplies can convert one level of electrical voltage into another level by switching action. This paper proposes an adaptive neural control system for the switching power supplies. In the ANC control system, a neural controller is the main controller used to mimic an ideal controller and a compensated controller is designed to recover the residual of the approximation error. In this study, an on-line adaptive law with a variable optimal learning-rate is derived based on the Lyapunov stability theorem, so that not only the stability of the system can be guaranteed but also the convergence of controller parameters can be speeded up. Experimental results show that the proposed ANC controller can achieve favorable regulation performance for the switching power supply even under input voltage and load resistance variations.

In this paper, a design technique of cerebellar model articulation controller (CMAC)-based fault-tolerant control (FTC) system is investigated to deal with the nonlinear faults of the biped robot. The proposed CMAC-based FTC (CFTC) scheme contains two main components: (1) the online fault estimation module based on a CMAC is used to provide the approximation information for any non-nominal behavior due to the faults of the biped robot; and (2) the controller module consists of a computed torque controller and a robust fault-tolerant controller. In the controller module, the computed torque controller reveals a basic stabilizing controller to stabilize the system and the robust fault-tolerant controller is utilized to compensate for the effects of the system failure so as to achieve the fault accommodation. The adaptive laws of CMAC are rigorously established based on the Lyapunov function so that the stability of the CFTC system can be guaranteed. Finally, simulation results show that the CFTC can apparently recover the control performance for the biped robot in the existence of the nonlinear faults.

This paper proposes a robust intelligent backstepping control (RIBC) scheme for the car-following control of a platoon of automated vehicles using a recurrent cerebellar model articulation controller (RCMAC) via the Hinfincontrol technique, so that the robust tracking performance can be achieved. In the RIBC system, an adaptive RCMAC is used to mimic an ideal backstepping control law and a robust controller is designed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The adaptation laws of the RIBC system are derived on the basis of the Lyapunov stability analysis and Hinfincontrol theory so that the stability of the system can be guaranteed. Finally, the simulation results denominate that the proposed RIBC system can achieve favorable tracking performance for a safe car-following control.

This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of second-order nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal controller, and the robust controller is designed to achieve L2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat's lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wing-rock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L2 robust control techniques.

This paper proposes an adaptive fuzzy sliding-mode controller with proportional-integral learning algorithm (PI-AFSMC) for the unknown nonlinear systems. All the controller parameters are on-line tuned by the derived learning algorithms in the Lyapunov stability theorem, thus the stability of the system can be guaranteed. Finally, the proposed PI-AFSMC is applied to control a linear piezoelectric ceramic motor. Experimental results demonstrate the effectiveness of the proposed PI-AFSMC can achieve favorable tracking performances with unknown the controlled system dynamics

This paper proposes a wavelet-neural-network-based backstepping control (WNNBC) for the chaotic systems. The WNNBC is comprised of a neural backstepping controller and an adaptive robust controller. The neural backstepping controller containing a wavelet neural network identifier is the principal controller, and the adaptive robust controller is designed to achieve L/sub 2/ tracking performance with desired attenuation level. Finally, simulation results verify that the proposed WNNBC can achieve favorable tracking performance.

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.

The computed torque or inverse dynamics control techniques are based on a good understanding of the system dynamics and even its environment. For the real-time applications, the system dynamics is always difficult to obtain. To tackle this drawback, the goal of this paper is to develop a model-free control method which is referred to as the robust neuro-fuzzy sliding-mode control (RNFSMC) system. The proposed RNFSMC system is comprised of a fuzzy controller and a robust controller. The fuzzy controller is utilized to approximate an ideal controller by the developed tuning algorithms, and the robust controller is designed to achieve H/sup /spl infin// tracking performance index. To investigate the effectiveness of the proposed RNFSMC system, it is applied to control a Chua's chaotic circuit system. Finally, simulation results demonstrate that the effect of the fuzzy approximation error on the tracking error can be attenuated efficiently by the proposed method without any knowledge of the controlled systems.

This paper develops a design method of recurrent fuzzy neural network (RFNN) control system for multi-input multi-output (MIMO) dynamic systems. This control system consist a feedback controller and a RFNN controller. The feedback controller reveals basic stabilizing controller to stabilize the system and the RFNN controller presents a robust controller to deal with unknown part of system dynamics. The adaptive laws of RFNN are derived based on the Lyapunov stability function so that the stability of the system can be guaranteed. Finally, the proposed control system is applied to an F-16 flight control system. Simulation results demonstrate that the developed control system can achieve favorable robust control performances even with some failures of the flight control system.

This paper presents a learning approach using cerebellar-model-articulation-controller (CMAC) to accommodate faults for nonlinear dynamic systems. A CMAC with Gaussian-type receptive-field basis function is proposed to estimate the unknown fault. Then, a robust fault accommodation scheme is derived based on Lyapunov stability theorem. Finally, the proposed fault accommodation system is applied to a jet engine compression system. Simulation results show that this method can effectively achieve the fault accommodation.

In this study, an adaptive recurrent cerebellar model articulation controller (ARCMAC) is designed for feedback control system with unknown dynamics. The proposed ARCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) in efficient learning mechanism, guaranteed system stability and dynamic response. Temporal relations are embedded in ARCMAC by adding feedback connections in the association memory space so that the ARCMAC captures the dynamic response. The dynamic gradient descent method is adopted to adjust ARCMAC parameters on-line. Moreover, the variable optimal learning-rates are derived to achieve most rapid convergence of tracking error. Finally, the effectiveness of the proposed control system is verified by experimental results of linear piezoelectric ceramic motor (LPCM) position control system. Experimental results show that accurate tracking response and superior dynamic performance can be obtained because of the powerful on-line learning capability of the proposed ARCMAC.

Wing rock is a highly nonlinear phenomenon in which an aircraft undergoes limit cycle roll oscillations at high angles of attack. In this paper, a supervisory recurrent fuzzy neural network control (SRFNNC) system is developed to control the wing rock system. This SRFNNC system is comprised of a recurrent fuzzy neural network (RFNN) controller and a supervisory controller. The RFNN controller is investigated to mimic an ideal controller and the supervisory controller is designed to compensate for the approximation error between the RFNN controller and the ideal controller. The RFNN is inherently a recurrent multilayered neural network for realizing fuzzy inference using dynamic fuzzy rules. Moreover, an on-line parameter training methodology, using the gradient descent method and the Lyapunov stability theorem, is proposed to increase the learning capability. Finally, a comparison between the sliding-mode control, the fuzzy sliding control and the proposed SRFNNC of a wing rock system is presented to illustrate the effectiveness of the SRFNNC system. Simulation results demonstrate that the proposed design method can achieve favorable control performance for the wing rock system without the knowledge of system dynamic functions.

This paper presents an adaptive hybrid control system using a diagonal recurrent cerebellar-model-articulation-computer (DRCMAC) network to control a linear piezoelectric ceramic motor (LPCM) driven by a two-inductance two-capacitance (LLCC) resonant inverter. Since the dynamic characteristics and motor parameters of the LPCM are highly nonlinear and time varying, an adaptive hybrid control system is therefore designed based on a hypothetical dynamic model to achieve high-precision position control. The architecture of DRCMAC network is a modified model of a cerebellar-model-articulation-computer (CMAC) network to attain a small number of receptive-fields. The novel idea of this study is that it employs the concept of diagonal recurrent neural network (DRNN) in order to capture the system dynamics and convert the static CMAC into a dynamic one. This adaptive hybrid control system is composed of two parts. One is a DRCMAC network controller that is used to mimic a conventional computed torque control law due to unknown system dynamics, and the other is a compensated controller with bound estimation algorithm that is utilized to recover the residual approximation error for guaranteeing the stable characteristic. The effectiveness of the proposed driving circuit and control system is verified with hardware experiments under the occurrence of uncertainties. In addition, the advantages of the proposed control scheme are indicated in comparison with a traditional integral-proportional (IP) position control system.

An adaptive cerebellar-model-articulation-controller (CMAC)-based supervisory control system is developed for uncertain nonlinear systems. This adaptive CMAC-based supervisory control system consists of an adaptive CMAC and a supervisory controller. In the adaptive CMAC, a CMAC is used to mimic an ideal control law and a compensated controller is designed to recover the residual of the approximation error. The supervisory controller is appended to the adaptive CMAC to force the system states within a predefined constraint set. In this design, if the adaptive CMAC can maintain the system states within the constraint set, the supervisory controller will be idle. Otherwise, the supervisory controller starts working to pull the states back to the constraint set. In addition, the adaptive laws of the control system are derived in the sense of Lyapunov function, so that the stability of the system can be guaranteed. Furthermore, to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Finally, the proposed control system is applied to control a robotic manipulator, a chaotic circuit and a linear piezoelectric ceramic motor (LPCM). Simulation and experimental results demonstrate the effectiveness of the proposed control scheme for uncertain nonlinear systems.

In this paper, a hybrid adaptive fuzzy control (HAFC) system is developed for a wing rock motion system. The design of HAFC system contains three parts: one is an indirect controller, the other is a direct controller and the last is a robust controller. A weighting factor /spl alpha/, which can be adjusted by a tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from the indirect and direct controllers. The robust controller is designed to achieve favorable control performance with a desired robustness. Simulation results demonstrate that the HAFC system can achieve favorable desired tracking performances for unknown the wing rock motion dynamics.

The antilock braking systems are designed to maximize wheel traction by preventing the wheels from locking during braking, while also maintaining adequate vehicle steerability; however, the performance is often degraded under harsh road conditions. In this paper, a hybrid control system with a recurrent neural network (RNN) observer is developed for antilock braking systems. This hybrid control system is comprised of an ideal controller and a compensation controller. The ideal controller, containing an RNN uncertainty observer, is the principal controller; and the compensation controller is a compensator for the difference between the system uncertainty and the estimated uncertainty. Since for dynamic response the RNN has capabilities superior to the feedforward NN, it is utilized for the uncertainty observer. The Taylor linearization technique is employed to increase the learning ability of the RNN. In addition, the on-line parameter adaptation laws are derived based on a Lyapunov function, so the stability of the system can be guaranteed. Simulations are performed to demonstrate the effectiveness of the proposed NN hybrid control system for antilock braking control under various road conditions.

A decoupled fuzzy sliding-mode control for an aeroelastic system is derived. This aeroelastic dynamic system describes the nonlinear plunge and pitch motions of a wing section, using a single trailing-edge flap as the control input. The decoupled fuzzy sliding-mode control design method is proposed to simultaneously control both the plunge and pitch motions of the aeroelastic system. By the decoupled sliding surface, the plunge and pitch motions can be driven to zeros simultaneously with single control input. The proposed decoupled fuzzy sliding-mode control comprises two fuzzy inference systems. The slope of the decoupled sliding surface is tuned by a fuzzy inference system to govern the simultaneous control of the plunge and pitch motions with small convergence time. Then the behavior of the plunge and pitch motions is regulated by a fuzzy sliding-mode control system to achieve favorable control performance. A comparison between the adaptive control, fuzzy sliding-mode control and the proposed decoupled fuzzy sliding-mode control for an aeroelastic system is developed. The simulation results verify that the proposed decoupled fuzzy sliding-mode control can achieve favorable control responses for both the plunge and pitch motions.

A hierarchical fuzzy sliding-mode control is proposed to achieve asymptotic stability and favorable decoupling performance. In this approach, the nonlinear system is decoupled into several subsystems and the state response of each subsystem can be designed to be governed by a corresponding sliding surface. Then the whole system is controlled by a hierarchical sliding-mode controller. The proposed design method is applied to investigate the decoupling control of an inverted pendulum. Simulation is performed and a comparison between the proposed hierarchical fuzzy sliding-mode control and a conventional fuzzy sliding-mode decoupling control is made to demonstrate the effectiveness of the proposed design method.

An adaptive fuzzy sliding-mode control (AFSMC) system with an integral-operation switching surface is adopted to control the rotor position of an induction servomotor drive. The AFSMC system comprises the fuzzy control design and the hitting control design. In the fuzzy control design, a fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the fuzzy controller. The tuning algorithms are derived in the sense of the Lyapunov stability theorem, thus the stability of the control system can be guaranteed. Moreover, to relax the requirement for the approximation error bound, an error estimation mechanism is investigated to observe the approximation error bound in real-time. Experimental results verify that the proposed control systems can achieve favorable tracking performance and that they are robust with regard to parameter variations and external load disturbance.

Tree codes find wide use in a variety of problems such as source encoding, sequential decoding, pattern recognition, and related fields. Efficient algorithms exist to explore the code trees and are well documented in the literature. All of these algorithms search code trees in an incremental manner, releasing a path map symbol at a time. A recent work has investigated the effect of releasing multiple symbols on the performance of the(M, L)algorithm used with speech. Here we investigate the effect of multiple symbol release rules on the performance of the stack algorithm in the context of speech encoding. We show that significant computational reduction can result with the use of such rules. We use an efficient data structure, the AVL tree data structure, to store code tree paths.