The purpose of this paper is on the use of cloud computing for efficiently planning autonomous real-time prespecified trajectory tracking and obstacle avoidance control for an omnidirectional wheeled robot using fuzzy adaptive predictive control algorithm. The autonomous trajectory tracking control includes dynamic simulation, omnidirectional wheeled robot control, and the feedback signal mainly provided by the sensor object surface and depth measurement. The robot is equipped with three independent-driven omnidirectional wheels and six ultrasonic sensors. The Jacobian between Cartesian space corresponding to the joint space of the robot is setup for ellipse motion planning so that it can autonomously follow the prespecified trajectory tracking, obstacle avoidance, and other sports. An architecture is setup to split computation between the remote cloud and the robot so that a robot can interact with a computing cloud. Given this robot/cloud architecture, the stability of the closed-loop control system from the Lyapunov theorem for the fuzzy adaptive predictive control algorithm and trajectory planning is guaranteed with satisfactory performance on the cloud during a periodically updated preprocessing phase efficiently, and manipulation queries on the robots given changes in the workspace can achieve real-time trajectory tracking and obstacle avoidance with ellipse motion planning control. Finally, tradeoffs arising between path quality and computational efficiency are evaluated through simulation, and experiments are given for analyzing the control performance.

This paper is to design a visual servo control for a hexapod robot with obstacle avoidance. The implementation of the motion control for the hexapod robot using the inverse kinematics and visual recognition system is used to achieve the trajectory tracking with obstacle avoidance. The control structure is composed of three parts: a tilt camera based on the concepts of mechanical geometry, visual servo control systems, and motion dynamics for trajectory tracking and obstacle avoidance. First, the depth between the obstacle and robot based on the proportion of the size of the area is constructed. Then, the image processing is used to identify whether there are any obstacles in the front, and make it as a feedback to the servo control system. For image recognition, we use OpenCV to process environment to the grayscale and binarization, filter noise through erosion and dilation, and then fill all of the contours using Sobel edge detection, and finally calculate the area and compare that with each other. Finally, some experiments for a hexapod robot with obstacle avoidance are used to validate the performance of the proposed control scheme.

It is proposed here to use a robust tracking design neural-based adaptive integral sliding mode control technique to control nonlinear interconnected systems with unknown coupled uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. A neural network for nonlinear interconnected systems is then proposed for solving the uncertainties of nonlinear interconnected systems. On-line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty, simultaneously. By the concept of parallel distributed compensation (PDC), we combine adaptive neural scheme the integral sliding mode control scheme to resolve the system uncertainties, unknown coupled uncertainties, and the external disturbances such that H∞tracking performance is achieved. Simulation results are further presented to show the effectiveness and performance of the proposed control scheme.

In this paper, the design problem of a delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno-type fuzzy linear model with an online update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to overcome the nonlinearities, time delays, and external disturbances such that H∞tracking performance is achieved. The linguistic information is developed by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly using linear analytical results instead of estimating nonlinear system functions. The tracking error dynamics are designed to enable our adaptive controller to avoid the filtering of the basis vectors whose dimension is much larger than that of the state vector of the controlled system. This is achieved by not imposing the strictly positive real condition. Based on the Lyapunov stability criterion and linear matrix inequalities, some sufficient conditions are derived so that all the states of the system are uniformly ultimately bounded. Therefore, the effect of the external disturbances on the tracking error can be attenuated to any prescribed level, and H∞tracking control is achieved. Building on our previous work in this area, the proposed control scheme is extended to handle a class of uncertain nonlinear systems with state and output delays and external disturbances. This is achieved through the use of a robust variable structure scheme and H∞control techniques. Finally, a numerical example of a two-link robot manipulator is studied to illustrate the effectiveness of the proposed control scheme.

In this paper, an H∞adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics, external disturbances, and approximation errors. First, the parallel manipulator is formulated as an error dynamics according to a specified reference model. Then, an adaptive fuzzy integral sliding mode control scheme is developed to tackle the unmodeled dynamics and approximation errors. The integral sliding mode control with time-varying exponent in terms of error is proposed to eliminate the reaching phase in the sliding manifold such that the error state approach the equilibrium point in a finite time period as quickly as possible. Based on Lyapunov stability theorem, the proposed control scheme can guarantee the stability of the closed-loop system and achieve the H∞performance. Finally, we will use a 2-dof parallel robot system to verify the effectiveness of the proposed control scheme.

Robotic systems have inherently nonlinear phenomena as joints undergo sliding and/or rotating. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the robot states by applying observer-based adaptive wavelet neural network (OBAWNN) tracking control scheme to tackle these phenomena such as system uncertainties, multiple time-delayed state uncertainties, and external disturbances such that the closed loop system signals must obey uniform ultimate boundedness and achieve H∞tracking performance. The recurrent adaptive wavelet neural network model is used to approximate the dynamics of the robotic system, while an observer-based adaptive control scheme is to stabilize the system. The advantage of employing adaptive wavelet neural dynamics is that we can utilize the neuron information by activation functions to on-line tune the hidden-to-output weights, and the adaptation parameters to estimate the robot parameters and the bounds of the gains of delay states directly using linear analytical results. It is shown that the stability of the closed-loop system is guaranteed by some sufficient conditions derived from Lyapunov criterion and Riccati-inequality. Finally, a numerical example of a three-links rolling cart is given to illustrate the effectiveness of the proposed control scheme.

In this paper, a trajectory tracking control strategy by elliptic collision-Free approach is proposed for guiding and following mobile robots. Each robot is setup with a single eye camera to capture the image of a guiding robot or obstacle. The image between them is converted to a gray form, and then to the gradient for each pixel of Gaussian pyramid level to estimate the motion parameters, disturbances, or obstacles. Successive images for a moving object are used to estimate or recognize the foreground, guiding robot, and obstacles by calculating the gravity of the moving object, and then the following mobile robot will follow the trajectory of the guiding one. On the contrary, the following mobile robot turns out to serve as a guiding one when there is no gravity. Furthermore, the elliptic collision-free path will be used for obstacle gravity and keep going until the final destination is achieved. Finally, experimental results will be used to show the effectiveness of the proposed method.

In this paper, steering and balance controls of an unmanned electrical bicycle (e-bicycle) using an integral sliding mode control scheme including adaptive neural network disturbance elimination is proposed. The e-bicycle has three degrees of freedom in the space, and they are driven by an in-wheel brushless motor setup in the rear wheel and a servomotor on the saddle seat post steers for handlebar grip control via a planar four-bar linkage, while keeping the lean angle to be zero. Some unknown underactuated uncertainties are approximated by the adaptive neural network. The constrained Lagrangian's equations are derived to simulate the motion of the e-bicycle in state-space form with uncertainty. Based on Lyapunov stability theorem, the proposed control scheme can ensure the stability of the system and parameter estimations convergence, and achieve steering and balance controls. Finally, some simulation examples are given to show the effectiveness and validity of the proposed control scheme.

In this paper, an H∞control performance via interval type-2 fuzzy adaptive tracking control scheme for a class of nonlinear systems with dead-zones is proposed. The Takagi-Sugeno (T-S) fuzzy model is used for representing a nonlinear system, where the parameters of the fuzzy model are obtained from both the fuzzy rules and online updates. An inverse function is cascaded with the plant to cancel the effects of dead-zone. Based on the fuzzy model, a state feedback controller is developed to override the nonlinearities and external disturbances such that the uniform ultimate boundedness of all signals in the closed loop and the H∞tracking performance are achieved. From Lyapunov stability and linear matrix inequalities (LMIs), the effect of the external disturbance on the tracking error can be attenuated to any prescribed level. An inverted pendulum system is used to illustrate the effectiveness of the proposed method.

Rolling cart system is a highly nonlinear phenomenon in which links undergo tipping and rolling with no fixed base. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the rolling cart states by applying observer-based adaptive wavelet neural network (OBAWNN) tracking sliding mode control scheme with system uncertainties, multiple time-delayed state uncertainties, and external disturbances. Based on a recurrent adaptive wavelet neural network model for approximating the dynamics of the rolling cart, an observer-based adaptive control scheme is developed to override the nonlinearities, time delays, and external disturbances such that the uniform ultimate boundedness of all signals in the closed loop and the H∞tracking performance are achieved. The advantage of employing adaptive wavelet neural dynamics is that we can utilize the neuron information by activation functions to on-line tune the parameters of dilation and translation of wavelet basis functions and hidden-to-output weights, and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently an H∞tracking control is achieved. Finally, a numerical example of a rolling cart is given to illustrate the effectiveness of the proposed control scheme.

In this paper, an observer-based indirect adaptive fuzzy output feedback control scheme is proposed for a biped robotic system. Fuzzy logic systems are employed to approximate the biped unknown nonlinear functions. Based on the fuzzy system, a state observer is designed for estimating the states of the controlled system. In addition, we use a regularized inverse function to overcome the control singularity problem. Based on Lyapunov stability analysis, convergence of the system states and boundedness of tracking errors can be achieved by the proposed control scheme. The experiment results are used to demonstrate the effectiveness and robustness of the proposed control scheme, and the tracking performance.

In this paper, an adaptive fuzzy integral sliding mode control scheme with H∞tracking performance is proposed for parallel manipulators to attenuate the effects caused by nonlinear unmodeled dynamics, external disturbances, and approximation errors. First, the parallel manipulator is formulated as an error dynamics according to a specified reference model. Then, an adaptive fuzzy integral sliding mode control scheme is developed to attenuate the effects caused by unmodeled dynamics, disturbances, approximation errors, and restrain the external disturbances. The integral sliding mode control is used not only to provide one more degree of freedom to eliminate the steady-state error but to make the state error approach the equilibrium point in a finite time period quickly. Based on Lyapunov stability theorem, the proposed control scheme can guarantee the stability of the closed-loop system and achieve the H∞tracking performance. Finally, we will use a 2-dof parallel robot system to verify the effectiveness of the proposed control scheme.

In this paper, a delay-based H∞tracking performance scheme for chaotic systems with output delays is proposed. The Takagi and Sugeno fuzzy model with adaptation capability is employed to approximate the chaotic system. Based on the fuzzy model, a fuzzy observer-based controller is developed to achieve the H∞control performance when system with external disturbance rejection. The fuzzy adaptive observers consist of a two-layer fuzzy observer is used to reconstruct the system states cause by system with delayed output. Furthermore, the delayed time is partitioned and the fuzzy sub-observer is set at each partitioned time instant. Estimation errors and tracking errors can convergence to a bounded region by using the Lyapunov synthesis approach and linear matrix inequalities (LMIs) and the H∞tracking performance in the closed-loop system can be achieved. Finally, a Chua's chaotic circuit system is used to verify the validity of theoretical derivations.

In this paper, we propose an adaptive fuzzy sliding mode control scheme (AFSCS) for continuous-time multiple-input-multiple-output (MIMO) linear time-varying uncertain systems. The AFSCS consists of a fuzzy controller with adaptive mechanism to reconstruct the system states using the tracking error and to make the state error reach the equilibrium point in finite time period quickly. The sliding surface is first employed to represent the state error to reach the equilibrium point in a finite time period. Then, an adaptive fuzzy controller using sliding mode is developed to achieve the control performance and the state tracking errors performance quickly. The reaching mode of the uncertain system using the proposed adaptive fuzzy sliding mode controller is guaranteed. Moreover, the chattering around the sliding surface for the proposed adaptive fuzzy sliding mode control can be reduced. A 2-dof parallel robot system will be used to verify the effectiveness of the proposed method.

In this paper, we present Takagi-Sugeno (T-S) fuzzy logic control scheme for a class of large-scale time-varying uncertain systems. The proposed control scheme is comprised of a fuzzy system for the given system with uncertainties and a state feedback fuzzy controller. The parameters of the fuzzy system are updated by learning rules. The state feedback fuzzy controller is used to restrain the external disturbances. Based on the Lyapunov stability theorem, we will prove that the closed-loop control system is uniformly ultimately bounded. The main point of the proposed control scheme is that we can use the P matrix in Riccati-like LMI equation for each rule to synthesize the state feedback control gain K other than that to find a common P of the traditional approach. Finally, a numerical example and a TMD system is given to validate the proposed scheme.

In this paper, a novel observer-based adaptive fuzzy control scheme is proposed for nonaffine nonlinear systems with unknown structure of nonlinearities. The Takagi-Sugeno (T-S) fuzzy model is used for representing the nonaffine part of the system, where the parameters of the fuzzy model are updated online according to Lyapunov stability theorem. Based on Lyapunov theory, the stability of the closed-loop system can be guaranteed, and all signals involved are bounded. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.

In this paper, an observer-based adaptive fuzzy control scheme for rolling carts with time delays and external disturbances is proposed. A simplify fuzzy modelling that can avoid complicated Lagrange's equations is used to approximate the dynamics of the rolling cart. The observer-based fuzzy adaptive control scheme is developed to override the external disturbances such that theH∞tracking performance is achieved. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently anH∞tracking control is achieved. Finally, a numerical example of a rolling cart is given to illustrate the effectiveness of the proposed control scheme.

In this paper, an adaptive fuzzy control scheme for fuzzy systems with multiple delayed state perturbations, time- varying uncertain parameters, and disturbances. These delayed state perturbations, uncertainties, and external disturbances in the fuzzy systems are assumed to be any uncertain bounded but unknown continuous functions. An improved adaptation law with sigma-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a continuous memoryless state feedback controller is constructed for achieving robust stability of the closed-loop system. Based on Lyapunov stability theorem, the proposed adaptive robust fuzzy controller can guarantee that the state converges asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with sigma-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, an inverted pendulum system is given to demonstrate the validity of the proposed design method.

In this paper, a fuzzy logic controller with Hinfintracking performance for uncertain nonlinear descriptor systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances, and approximation errors. First, the nonlinear descriptor system is represented by an equivalent Takagi-Sugeno type fuzzy model. Then, a state feedback fuzzy control scheme is developed to restrain the external disturbances such that the model reference Hinfintracking performance is achieved. Furthermore, based on Lyapunov stability theorem, the proposed fuzzy control system can guarantee the stability of the whole closed-loop system and obtain good tracking performance as well. Stability conditions are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example of a nonlinear descriptor system control problem is given to illustrate the effectiveness of the proposed control scheme.

In this paper, a fuzzy adaptive output feedback control design method for a class of nonlinear output-delayed single-input single-output systems with guaranteed control performance is proposed. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based controller is developed to achieve the control performance with a desired disturbance rejection constraint. The fuzzy adaptive observers consist of a serial-observation algorithm to reconstruct the system states at different delayed time instants for state estimation. Based on the Lyapunov synthesis approach, a global uniform ultimate boundedness property (UUB) of the state estimation errors and tracking errors in the closed-loop system can be achieved. According to some conditions, global exponential convergence to a bounded value for the observation error is ensured for any given delay in the measurements. Finally, an inverted pendulum system is used to illustrate the effectiveness of the proposed method.

In this paper, an adaptive fuzzy PID control scheme is investigated for a class of nonlinear systems with Hinfintracking performance. Stability and robustness of the control scheme is analyzed in Lyapunov sense and a modified Riccati-like equation. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with Hinfintracking performance for any prescribed level. Moreover, the simplicity of the scheme provides a new approach for implementing PID controller for a variety of nonlinear problems. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.

In this paper, the problem of fuzzy model ref- erence adaptive control (FMRAC) for a class of continuous- time multiple-input-multiple-output (MIMO) nonlinear uncer- tain systems with state delays and external disturbances is investigated. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy system is used to approximate an unknown optimal control law from the strategic manipulation of the model following tracking errors. The proposed FMRAC scheme uses on-line estimations for the control gains. Based on the Lyapunov stability theorem, a fuzzy adaptive control strategy using Takagi-Seguno (TS) fuzzy system with proportional-integral (PI) type can guarantee parameter estimation convergence and stability robustness of the closed-loop system. The performance of the proposed scheme is evaluated through the simulation results. A 2 DOF parallel robot control problem is simulated to demonstrate the validity of the proposed scheme.

In this paper, an observer-based fuzzy sliding mode adaptive control design algorithm with Hinfintracking performance is presented for a class of nonlinear SISO delayed systems. To facilitate this concept, an observer is developed for the error dynamics and Lyapunov type stability is established under certain condition. The fuzzy approximators equipped with adaptive algorithms are introduced to learn the behaviors of the uncertain dynamics. It is shown that all the states and signals of the system are bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently an Hinfintracking performance is achieved. Finally, simulation examples by the application to control of a car-like inverted pendulum are included to confirm the validity and performance of the proposed algorithm.

In this paper, we present an algorithm using distance-based two-layer fuzzy sliding mode control (DBTLF-SMC) to achieve the prespecified trajectory for a class of nonlinear systems. The tracking trajectory is composed of a set of sequentially-operated piecewise continuous sliding surfaces which the system's state can follow to the equilibrium in phase plane. The algorithm using the boundary layer technique is capable of handling the reaching phase (RP) of the trajectory and chattering effects inherent to the VSC easily and effectively. By using distance-based two-layer fuzzy sliding mode controller, the state would follow the sliding surfaces in turn, and the parametric uncertainties or disturbances can be reduced effectively and the response of the tracking error will be small than that of the distance-based single-layer fuzzy sliding mode control. It is shown that the stability of the control system is guaranteed in the Lyapunov sense. Finally, an inverted pendulum control problem subject to external disturbance is simulated to demonstrate the validity of the proposed algorithm

In this paper, a robust adaptive neural-based sliding-mode observer for achieving H∞tracking performance is proposed for a class of single-output nonlinear systems with unknown internal parameters and bounded external disturbances. The nonlinear system is first transformed by state-space change of coordinates into a special observable canonical form. Then, the adaptive neural networks and the sliding-mode control action are used for plant parameters estimation and to eliminate the effect of approximation error, respectively. Sufficient conditions are developed for achieving the H∞tracking performance in terms of linear matrix inequality (LMI) formulations. Our main contribution is nonlinear observers analysis and design methods that can effectively deal with model/plant mismatches. Finally, simulation results for a single-link robot are given to show the effectiveness of the proposed scheme.

In this paper, an algorithm using an artificial neural network (ANN)-based direct adaptive control algorithm is presented for multi-input multi-output (MIMO) nonlinear systems with unknown output delays. This algorithm contains two parameter estimations, one for estimating unknown plant delays and the other for unknown control parameters. If the number of center frequency is enough, the predicted output signal can approximate the true delayed output, especially for large output delays. It is shown that the proposed algorithm not only can guarantee control parameter estimation convergence but can achieve the tracking purposes. Simulation studies are presented to validate the theoretical findings.

In this paper, an approach for robust stability analysis of a digital closed-loop system for digital controller implementations subject to finite word length (FWL) effects is proposed. Uncertainties caused by the roundoff and computational errors subject to FWL effects are expressed in function of mantissa bit number when the mode of floating-point arithmetic is used in the process. Then, based on the Small Gain Theorem and the Bellman-Grownwall Lemma, a sufficient stability criterion for the digital closed-loop system is derived. The eigenvalue sensitivity of the closed-loop system is developed in terms of mixed matrix-2/Frobenius norms. Then, by minimizing this eigenvalue sensitivity and using orthogonal Hermitian transform as well, an optimal similarity transformation can be obtained. By substituting this optimal transformation into the stability criterion, a minimum mantissa bit number used for implementing the stabilizing digital controllers can be determined. The main contributions are that this approach provides an analytical closed-form solution for obtaining the optimal transformation and, in addition to the stability criterion, leads to the implementation of the stabilizing controllers with a lower mantissa bit number when using this optimal one. Finally, detailed numerical design processes and simulation results are used to illustrate the effectiveness of the proposed scheme.

In this paper, a novel adaptive fuzzy-neural control (AFNC) scheme for uncertain dynamical systems is proposed to suppress the effects caused by multiple time-delayed state uncertainties, unmodeled dynamics, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy-neural (FN) system is used to represent the unknown controlled system from the strategic manipulation of the model following tracking errors. The proposed AFNC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FN system simultaneously. Stability and robustness of the AFNC scheme is analyzed in Lyapunov sense. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.

In this paper, a fuzzy-neural identification and control for uncertain robotic systems with time delays is proposed for H/sub /spl infin// tracking performance and to suppress the effects caused by multiple time-delayed state uncertainties, unmodeled dynamics, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy-neural (FN) system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors. The proposed AFNC scheme uses two online estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FN system simultaneously. Stability and robustness of the AFNC scheme is analyzed in Lyapunov sense. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system with H/sub /spl infin// tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties.

Presents the design of a fuzzy sliding mode control algorithm to achieve the specified trajectory tracking on mechatronic arms. The tracking paths are composed of a set of sequentially-operated piecewise sliding surfaces which the system's state can follow to the equilibrium point in phase plane and from which the total tracking time can be obtained directly. It is shown that each fuzzy controller will refer to a stable closed-loop subsystem in the sense of Lyapunov stability under a common Lyapunov function, and then the overall system is also stable in the sense of Lyapunov stability. Further, the reaching phase of the trajectory which is sensitive to parameter uncertainties or disturbances can be reduced effectively and the system's state traveling on the paths and finally to the equilibrium point be ensured. The main advantages of the proposed algorithm, in contrast to the conventional sliding-mode control design, are that the tracking time in the reaching phase no longer exists, and the tracking time the first time the system's state hitting each sliding surface can be evaluated, and that the theoretic total tracking time and the true total one are in good agreement.

In this paper, an adaptive control algorithm via delayed dynamical neural nets (DDNNs) for a class of nonlinear systems is presented. We identify the nonlinear system by updating the weights of the DDNNs and then design the controller adaptively based on the neural networks model to achieve the model following purpose. An analysis via Lyapunov stability criteria shows that the proposed control algorithm guarantees parameter estimation convergence and system stability, with the output of the system following the specified reference model. Finally, a series of simulations are performed to demonstrate the effectiveness of the proposed scheme.

A fuzzy model based adaptive control algorithm for a class of continuous-time nonlinear dynamic systems is presented. The fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems. Each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system. The proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching-/spl sigma/ modification adaptive controller to adaptively compensate for the plant nonlinearities. Stability robustness of the closed-loop system is analyzed in Lyapunov sense. It is shown, that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties, converging to the neighborhood of the origin for all realizations of uncertainties and disturbances. The simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method.