An improved ant colony optimization (ACO) algorithm is proposed in this paper for improving the accuracy of path planning. The main idea of this paper is to avoid local minima by continuously tuning a setting parameter and the establishment of novel mechanisms for updating partial pheromone and opposite pheromone. As a result, the global search of the proposed ACO algorithm can be significantly enhanced in terms of calculating optimal path compared to the conventional ACO algorithm. Simulation results of the proposed approach show better performances in terms of the shortest distance, mean distance, and success rate towards optimal paths. To further reduce the computation time, the proposed ACO algorithm for path planning is realized on a FPGA chip to verify its practicalities. Experimental results indicate that the efficiency of the path planning is significantly improved by the hardware design of embedded applications.

Robot localization plays an important role in the field of robot navigation. One of the most commonly used localization algorithms is Monte Carlo Localization algorithm (MCL). Unfortunately, the traditional MCL is not reliable all the time in both pose tracking and global localization. Many modified MCL algorithms have been proposed to improve the efficiency and performance, such as improved Monte Carlo Localization with robust orientation estimation algorithm (IMCLROE) proposed by the authors. However, the IMCLROE requires a lot of storage space and intensive computation, especially in a highly complicated environment. In recent years, cloud computing has been widely used because of ubiquitous network. As an attempt to solve the above problems based on cloud computing, we propose a cloud-based improved Monte Carlo Localization algorithm with robust orientation estimation with a distributed orientation estimation technique in calculating important factor of each particle. With the use of cloud computing, real-time paradox between accuracy and efficiency in a high-resolution grid map can be addressed. Experimental results confirm that the proposed cloud-based architecture can efficiently establish a map database and reduce the computational load for robot localization.

This paper presents mean-based fuzzy controllers for trajectory tracking for a class of multiple-input multiple-output robotic systems with nonaffine-like form and parametric uncertainties, in which direct adaptive controllers with state estimators are developed via a mean-based fuzzy identifier without prior knowledge of the membership functions. By using the proposed adaptive technique, unfavorable influence from the initial design of membership functions can be effectively diminished. Moreover, the computation burden of the adaptive laws can be successfully alleviated because the derivative of the fuzzy systems is not required. A Lyapunov-based stability analysis is utilized to guarantee successful system control and desired tracking performance of the closed-loop system. Finally, two examples are provided to demonstrate the feasibility of the proposed control method.

This paper presents a novel direct adaptive controller design via decomposed fuzzy Petri net to solve the control tracking problem. The controller combines decomposed fuzzy system (DFS) and Petri net to achieve good performance with less computation time. In the DFS structure, fuzzy variables are decomposed into several layers. DFS has been shown to have fast learning capability but with a complicated system structure. In this study, Petri net is employed to form a mechanism in constructing meaningful component fuzzy systems in the DFS so that the number of fuzzy components can be dramatically reduced without significantly degrading the modeling performance. Finally, the effectiveness of the proposed controller scheme is verified by simulation results.

Although traditional ant colony system (ACS) has the ability of fast convergence, it tends to find local optima. To solve this problem, this paper proposes an improved ant colony system algorithm for path planning of mobile robots by considering two main aspects, including continuous tuning of a setting parameter and the establishment of new mechanisms for pheromone updating. As a result, the ability of global searching of the improved ACS can be significantly enhanced in comparison to the traditional ACS algorithms in deriving an optimal path for mobile robots. Simulation results show the proposed approach has a better performance in terms of shortest distance, mean distance, and successful rate of the optimal paths than those obtained by the traditional ACS algorithms.

In this paper, we propose a hybrid adaptive control scheme based on Hopfield-based dynamic neural network (HACHNN) for SISO nonlinear systems. An auxiliary direct adaptive controller is proposed to ensure the stability in the time-interval of when an indirect adaptive controller is failed because of ĝ(x)→0. The weights of the Hopfield-based dynamic neural network are on-line tuned by the adaptive laws derived in the sense of Lyapunov theorem, so that the stability of the closed-loop system can be guaranteed, and all signals in the closed-loop system are bounded. The designed structure of the Hopfield-based dynamic neural network maintains the tracking performance of the control scheme, and it also makes the practical implementation much easier.

The paper proposes a fuzzy control method with a real-time genetic algorithm for an uncertain DC server motor with a Buck converter. The parameters of the fuzzy system are online adjusted by the real-time genetic algorithm in order to generate appropriate control input. For the purpose of on-line evaluating the stability of the closed-loop system, an energy fitness function derived from backstepping technique is involved in the genetic algorithm. According to the experimental results, the genetic fuzzy control scheme performs on-line tracking successfully.

In this paper, we propose an online observer-based Takagi–Sugeno (T–S) fuzzy-output tracking-control technique and an improved generalized projection-update law for a class of general nonaffine nonlinear systems with unknown functions and external disturbances. First, a T–S fuzzy model and a mean-value estimation technique are adopted to approximate a so-called virtual linearized system (VLS) of a real system and avoiding a high-order derivative problem, respectively. Second, a novel design concept combining the T–S fuzzy controller, observer, and tuning algorithm by neural networks is proposed to improve system performance. After that, we also use improved generalized projection-update laws, which prevent parameters drift and confine adjustable parameters to the specified regions, to tune adjustable parameters. As a result, both the stability guarantee based on strictly positive real (SPR) Lyapunov theory and Barbalat's lemma and the better tracking performance are concluded. To illustrate the effectiveness of the proposed T–S fuzzy controller and observer-design methodology, numerical simulation results are given in this paper.

This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.

An on-line tracking controller design based on using T-S fuzzy-neural modeling for a class of general robot manipulators is investigated in this paper. Also, we use projection update laws to tune adjustable parameters for preventing parameters drift. In addition, stability of the closed-loop systems is proven by using strictly-positive-real (SPR) Lyapunov theory. The proposed overall scheme guarantees that all signals involved are bounded and the outputs of the closed-loop system asymptotically track the desired output trajectories. Finally, an example including two cases confirms the effectiveness of the proposed method.

Vehicles are not always driven on smooth roads. If parts of the suspension system fail, it becomes an uncertain system. Thus we need an approximator to remodel this uncertain system to maintain good control. In this paper, we propose a new method to on-line identify the uncertain suspension system and design a T-S fuzzy-neural controller to control it. We first use the mean value theorem to transform the active suspension system into a virtual linearized system. In addition, an on-line adaptive T-S fuzzy-neural modeling approach to the design of robust tracking controllers is developed for the uncertain active suspension system. Finally, this paper gives simulation results of an uncertain suspension system with the on-line adaptive T-S fuzzy-neural controller, and is shown to provide good effectiveness under the conditions that parts of the suspension system fail.

This paper proposes anti-lock braking system to integrate with active suspensions system applied in a quarter vehicles model, and can use a road estimate to get the road condition. This estimate is based on the LuGre friction model with a road condition parameter, and can transmit a reference slip ration to slip ratio controller through a mapping function considering the effect of road characteristics. In the controller design, an observer-based direct adaptive fuzzy-neural controller (DAFC) for an ABS is developed. After, this paper will discuss that active suspension system influence on ABS. Active suspension systems are not ideal, unchanging, and certain, as many control systems assume. If parts of the suspension system fail, it becomes an uncertain system. In such cases, we need an approximator to remodel this uncertain system to maintain good control. We propose a new method to on-line identify the uncertain active suspension system and design a T-S fuzzy-neural controller to control it. Finally, integrating algorithm is constructed to coordinate these two subsystems. Simulation results of the ABS with active suspension system, and is shown to provide good effectiveness under varying conditions.

This paper proposes a radial basis function neural network adaptive backstepping controller (RBFNN_ABC) for multiple-input multiple-output (MIMO) nonlinear systems in block-triangular form. The control scheme incorporates the adaptive neural backstepping design technique with a first-order filter at each step of the backstepping design to avoid the higher-order derivative problem, which is generated by the backstepping design. This problem may create an unpredictable and unfavorable influence on control performance because higher-order derivative term errors are introduced into the neural approximation model. Finally, simulation results demonstrate that the output tracking error between the plant output and the desired reference can be made arbitrarily small.

A serious problem limiting the applicability of the fuzzy neural networks is the “curse of dimensionality”, especially for general continuous functions. A way to deal with this problem is to construct a dynamic hierarchical fuzzy neural network. In this paper, we propose a two-stage genetic algorithm to intelligently construct the dynamic hierarchical fuzzy neural network (IfFNN) based on the merged-FNN for general continuous functions. First, we use a genetic algorithm which is popular for flowshop scheduling problems (GA_FSP) to construct the INN. Then, a reduced-form genetic algorithm (RGA) optimizes the INN constructed by GA _FSP. For a real-world application, the presented method is used to approximate the Taiwanese stock market.

This paper presents a practical nighttime vehicle distance measuring method based on a single CCD image. The method combines an image-based distance measuring system. To solve the nighttime feature extraction problem, the proposed method uses two taillights as the feature. Based on the proportionality of similar triangles, distance between a CCD camera and the taillights of the vehicle ahead can be measured. The method focuses on detecting the taillights and differentiating the targeted vehicle from others on the basis of partial image analysis instead of whole image processing. The system is both fast and simple. The accuracy of the proposed method is demonstrated in this paper through experiences.

This paper proposes on-line modeling via Takagi-Sugeno (T-S) fuzzy models and robust adaptive control for a class of generalized multiple input multiple output (MIMO) nonlinear dynamic systems with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way and is used to be an error compensator for external disturbances and system uncertainly, i.e. the unmodeled dynamics, modeling errors and external disturbances. In second type adaptive laws, fuzzy B-spline membership functions (BMFs) are developed for on-line tuning. In this paper, we can prove that the closed-loop system which is controlled by the proposed controller is stable and the tracking error will converge to zero.

This paper proposes an antilock braking system (ABS), in which unknown road characteristics are resolved by a road estimator. This estimator is based on the LuGre friction model with a road condition parameter, and can transmit a reference slip ratio to a slip ratio controller through a mapping function considering the effect of wheel angular velocity. In the controller design, a direct adaptive fuzzy-neural controller (DAFC) for an ABS is developed. Finally, this paper gives simulation results of an ABS with the road estimator and the DAFC, and shows good effectiveness under varying road conditions.

This paper proposes on-line modeling via Takagi-Sugeno (T-S) fuzzy models and robust adaptive control for a class of unknown nonlinear dynamic systems with external disturbances. The T-S fuzzy model is established to approximate an unknown nonlinear dynamic system in a linearized way. Fuzzy B-spline membership functions (BMFs) which possesses a fixed number of control points are developed for on-line tuning. In this paper, the closed-loop system which is controlled by the proposed controller can be stabilized and the tracking error will converge to zero. An example is simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.

This paper proposes an observer-based adaptive fuzzy-neural controller, structured by a merged fuzzy-neural network (merged-FNN) to reduce the number of adjustable parameters. In this paper, the merged-FNN is proved to take the place of the traditional fuzzy-neural networks under some assumptions. Moreover, the overall adaptive schemes using the proposed merged-FNN guarantees that all signals involved are bounded and the output of the closed-loop system asymptotically tracks the desired output trajectory. From experimental examples, the proposed merged-FNN has far fewer parameters than the traditional FNN, and the computation time is significantly reduced. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.

In this paper, a novel online B-spline membership function (BMF) fuzzy-neural sliding mode controller trained by an adaptive bound reduced-form genetic algorithm (ABRGA) is developed to guarantee robust stability and tracking performance for robot manipulators with uncertainties and external disturbances. The general sliding manifold is used to construct the sliding surface and reduce the chattering of the control signal, which can be nonlinear or time varying. For the purpose of identification, the proposed BMF fuzzy-neural network trained by the ABRGA approximates the regressor of the manipulator. An adaptive bound algorithm is used to aid and speed up the searching speed of the RGA. Simulation results show that the proposed on-line ABRGA-based BMF fuzzy-neural sliding mode controller is effective and yields superior tracking performance for robot manipulators.

This paper presents a method of discrete time nonlinear system identification using a HopfieId neural network (HNN) as a coefficient learning mechanism to obtain optimized coefficients over a set of Gaussian basis functions. A linear combination of Gaussian basis functions is used to replace the nonlinear function of the equivalent discrete time nonlinear system. The outputs of the HNN, which are coefficients over a set of Gaussian basis functions, are discretized to be a discrete Hopfield learning model. Using the outputs of the HNN, one can obtain the optimized coefficients of the linear combination of Gaussian basis functions conditional on properly choosing an activation function scaling factor of the HNN. The main contributions of this paper is that the convergence of learning of the HNN can be guaranteed if the activation function scaling factor is properly chosen. Finally, to demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.

In this paper, an observer-based direct adaptive fuzzy-neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities. A direct adaptive fuzzy-neural controller and a class of generalized nonlinear systems, which are called nonaffine nonlinear systems, are instead of the indirect one and affine nonlinear systems given by Leu et al. By using implicit function theorem and Taylor series expansion, the observer-based control law and the weight update law of the fuzzy-neural controller are derived for the nonaffine nonlinear systems. Based on strictly-positive-real (SPR) Lyapunov theory, the stability of the closed-loop system can be verified. Moreover, the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed-loop system will asymptotically track the desired output trajectory. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper.

In this paper, we investigate a novel robust control approach for a class of uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones. Sliding mode control (SMC) is suggested to design stabilizing controllers for these uncertain nonlinear systems. The controllers guarantee the global reaching condition of the sliding mode in these systems. They can work effectively for systems either with or without sector nonlinearities and deadzones in the inputs. Moreover, the controllers ensure that the system trajectories globally exponentially converge to the sliding mode. Illustrative examples are demonstrated to verify the effectiveness of the proposed sliding mode controller.

Sliding mode controllers for the bilinear systems with time varying uncertainties are developed in this paper. The bilinear coefficient matching condition which is similar to the traditional matching condition for linear system is defined for the homogeneous bilinear systems. It can be seen that the bilinear coefficient matching condition is very limited and is not generally applicable to the nonhomogeneous bilinear system. Thus, the sliding coefficient matching condition is also considered for the bilinear systems with time varying uncertainties. Then, the sufficient conditions are provided for the reaching mode of the time varying uncertain bilinear systems to be guaranteed by the designed sliding mode controllers. Moreover, the stability of the uncertain bilinear systems with the sliding mode controller is discussed. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controllers.

In this paper, we propose a novel design of a GA-based output-feedback direct adaptive fuzzy-neural controller (GODAF controller) for uncertain nonlinear dynamical systems. The weighting factors of the direct adaptive fuzzy-neural controller can successfully be tuned online via a GA approach. Because of the capability of genetic algorithms (GAs) in directed random search for global optimization, one is used to evolutionarily obtain the optimal weighting factors for the fuzzy-neural network. Specifically, we use a reduced-form genetic algorithm (RGA) to adjust the weightings of the fuzzy-neural network. In RGA, a sequential-search -based crossover point (SSCP) method determines a suitable crossover point before a single gene crossover actually takes place so that the speed of searching for an optimal weighting vector of the fuzzy-neural network can be improved. A new fitness function for online tuning the weighting vector of the fuzzy-neural controller is established by the Lyapunov design approach. A supervisory controller is incorporated into the GODAF controller to guarantee the stability of the closed-loop nonlinear system. Examples of nonlinear systems controlled by the GODAF controller are demonstrated to illustrate the effectiveness of the proposed method.

An adaptive fuzzy integral sliding mode controller for mismatched time-varying linear systems is presented in this paper. The proposed fuzzy integral sliding mode controller is designed to have zero steady state system error under step inputs and alleviate the undesired chattering around the sliding surface. The parameters in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy integral sliding mode control system. Thus, the bounds of the uncertainties are not required to be known in advance. The designed fuzzy integral sliding mode control system is shown to be invariant on the sliding surface. Moreover, the reaching mode of the sliding surface is guaranteed and the close-loop system is stable. Simulation results are included to illustrate the effectiveness of the presented fuzzy integral sliding mode controller.

In this paper, an output feedback direct adaptive fuzzy neural controller for an anti-lock braking system (ABS) is developed. It is assumed that only the system output and the wheel slip ratio, is available for measurement. The main control strategy is to force the wheel slip ratio tracking variant optimal slip ratios, which may vary with the environment and assumed to be known during the vehicle-stopping period. By using the strictly-positive-real (SPR) Lyapunov theory, the stability of the closed-loop system can be verified. To demonstrate the effectiveness of the proposed method, simulation results are illustrated.

In this paper, a novel approach to adjust both the control points of B-spline membership functions (BMFs) and the weightings of fuzzy-neural networks using a reduced-form genetic algorithm (RGA) is proposed. Fuzzy-neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, genetic algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional genetic algorithms is not desirable. Such conventional genetic algorithms are inherently incapable of dealing with a vast number (over 100) of adjustable parameters in the fuzzy-neural networks. In this paper, the RGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed, serving as a single gene crossover operation. Chromosomes consisting of both, the control points of BMFs and the weightings of the fuzzy-neural network are coded as an adjustable vector with real number components that are searched by the RGA. Simulation results have shown that faster convergence of the evolution process searching for an optimal fuzzy-neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy-neural network via the RGA are demonstrated to illustrate the effectiveness of the proposed method.

A set of enhanced digital integrators (EDI) with improved accuracy using genetic algorithms are proposed in this paper. By specifying a desired power for the integrator to be sought and the interval for comparison, chromosomes consisting of parameters of the enhanced digital integrator are then searched by the genetic algorithm based on root mean squared (RMS) error between the original integrator and candidates of the enhanced digital integrator. Thus, all the best parameters of an optimal enhanced digital integrator can be evolutionarily obtained. To demonstrate the effectiveness of the proposed approach, the derived enhanced digital integrators are used to obtain the discrete approximation for continuous systems.

An approach to adjust both control points of B-spline membership functions (BMFs) and weightings of fuzzy-neural networks using a simplified genetic algorithm (SGA) is proposed. The SGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed as a single point crossover operation. Chromosomes consisting of both the control points of BMFs and the weightings of fuzzy-neural networks are coded as an adjustable vector with real number components and searched by the SGA. Because of the use of the SGA, faster convergence of the evolution process to search for an optimal fuzzy-neural network can be achieved. Nonlinear functions approximated by using the fuzzy-neural networks via the SGA are demonstrated to illustrate the applicability of the proposed method.

A novel adaptive fuzzy-neural sliding-mode controller with H(infinity) tracking performance for uncertain nonlinear systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. Because of the advantages of fuzzy-neural systems, which can uniformly approximate nonlinear continuous functions to arbitrary accuracy, adaptive fuzzy-neural control theory is then employed to derive the update laws for approximating the uncertain nonlinear functions of the dynamical system. Furthermore, the H(infinity) tracking design technique and the sliding-mode control method are incorporated into the adaptive fuzzy-neural control scheme so that the derived controller is robust with respect to unmodeled dynamics, disturbances and approximate errors. Compared with conventional methods, the proposed approach not only assures closed-loop stability, but also guarantees an H(infinity) tracking performance for the overall system based on a much relaxed assumption without prior knowledge on the upper bound of the lumped uncertainties. Simulation results have demonstrated that the effect of the lumped uncertainties on tracking error is efficiently attenuated, and chattering of the control input is significantly reduced by using the proposed approach.

A framework to automatically generate a reduced-order discrete-time model for the sampled system of a continuous plant preceded by a zero-order hold (ZOH) using an enhanced multi-resolution dynamic genetic algorithm (EMDGA) is proposed in this paper. Chromosomes consisting of the denominator and the numerator parameters of the reduced-order model are coded as a vector with floating-point-type components and searched by the genetic algorithm. Therefore, a stable optimal reduced-order model satisfying the error range specified can be evolutionarily obtained. Because of the use of the multi-resolution dynamic adaptation algorithm and the genetic operators, the convergence rate of the evolution process to search for an optimal reduced-order model can be expedited. Another advantage of this approach is that the reduced discrete-time model evolves based on samples taken directly from the continuous plant, instead of the exact discrete-time model, so that computation time is saved.

In this paper, a robust adaptive fuzzy-neural control scheme for nonlinear dynamical systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbance, and modeling errors. A generalized projection update law, which generalizes the projection algorithm modification and the switching-sigma adaptive law, is used to tune the adjustable parameters for preventing parameter drift and confining states of the system to the specified regions. Moreover, a variable structure control method is incorporated into the control law so that the derived controller is robust with respect to unmodeled dynamics, disturbances, and modeling errors. To demonstrate the effectiveness of the proposed method, several examples are illustrated in this paper.

In this paper, an adaptive fuzzy controller for strict-feedback canonical nonlinear systems is proposed. The completely unknown nonlinearities and disturbances of the systems are considered. Since fuzzy logic systems can uniformly approximate nonlinear continuous functions to arbitrary accuracy, the adaptive fuzzy control theory is employed to derive the control law for the strict-feedback system with unknown nonlinear functions and disturbances. Moreover, H/sub /spl infin// tracking performance is applied to substantially attenuate the effect of the modeling errors and disturbances. Finally, examples are simulated to confirm the applicability of the proposed methods.

A robust adaptive fuzzy-neural controller for a class of unknown nonlinear dynamic systems with external disturbances is proposed. The fuzzy-neural approximator is established to approximate an unknown nonlinear dynamic system in a linearized way. The fuzzy B-spline membership function (BMF) which possesses a fixed number of control points is developed for online tuning. The concept of tuning the adjustable vectors, which include membership functions and weighting factors, is described to derive the update laws of the robust adaptive fuzzy-neural controller. Furthermore, the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated by the error compensator which is also constructed by fuzzy-neural inference. We prove that the closed-loop system which is controlled by the robust adaptive fuzzy-neural controller is stable and the tracking error will converge to zero under mild assumptions. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods.

In this paper, an observer-based adaptive fuzzy-neural controller for a class of unknown nonlinear dynamical systems is developed. The observer-based output feedback control law and update law to tune on-line the weighting factors of the adaptive fuzzy-neural controller are derived. The total states of the nonlinear system are not assumed to be available for measurement. Also, the unknown nonlinearities of the nonlinear dynamical systems are not restricted to the system output only. The overall adaptive scheme guarantees that all signals involved are bounded. Simulation results demonstrate the applicability of the proposed method in order to achieve desired performance.

The adaptive fuzzy-neural controllers tuned online for a class of unknown nonlinear dynamical systems are proposed. To approximate the unknown nonlinear dynamical systems, the fuzzy-neural approximator is established. Furthermore, the control law and update law to tune on-line both the B-spline membership functions and the weighting factors of the adaptive fuzzy-neural controller are derived. Therefore, the control performance of the controller is improved. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.

The paper describes a novel application of the B-spline membership functions (BMF's) and the fuzzy neural network to the function approximation with outliers in training data. According to the robust objective function, we use gradient descent method to derive the new learning rules of the weighting values and BMF's of the fuzzy neural network for robust function approximation. In this paper, the robust learning algorithm is derived. During the learning process, the robust objective function comes into effect and the approximated function will gradually be unaffected by the erroneous training data. As a result, the robust function approximation can rapidly converge to the desired tolerable error scope. In other words, the learning iterations will decrease greatly. We realize the function approximation not only in one dimension (curves), but also in two dimension (surfaces). Several examples are simulated in order to confirm the efficiency and feasibility of the proposed approach in this paper.

A general methodology for constructing fuzzy membership functions via B-spline curves is proposed. By using the method of least-squares, the authors translate the empirical data into the form of the control points of B-spline curves to construct fuzzy membership functions. This unified form of fuzzy membership functions is called a B-spline membership function (BMF). By using the local control property of a B-spline curve, the BMFs can be tuned locally during the learning process. For the control of a model car through fuzzy-neural networks, it is shown that the local tuning of BMFs can indeed reduce the number of iterations tremendously. This fuzzy-neural control of a model car is presented to illustrate the performance and applicability of the proposed method.>