It is known that the advantageous feature of Mecanum wheel vehicle (MWV) is its perfect trajectory tracking in a narrow space. For an AI platform, appropriate sensors, e.g., vision and LiDAR, are installed along the planned head direction to obtain human/object recognition tasks. However, most works of MWV only discussed their trajectory tracking in an indoor congested environment. In this article, a mathematical model including kinematics, dynamics with friction, and motor dynamics of a four Mecanum-wheel vehicle (FMWV) for smooth indoor ground or complex outdoor asphalt, bumpy, and uneven surface roads is first derived. To accomplish pose tracking tasks of sensor-based FMWV under different terrain and uncertain conditions, the more efficient and resilient fuzzy finite-time pose tracking control (FFTPTC) using edge computing is proposed. The FFTPTC comprises two portions: 1) a nominal control based on the derived model to achieve the planned tasks and 2) fuzzy enhanced control (FEC) with a new nonlinear output scale factor (NOSF) to contend with lumped uncertainties and the discontinuity of the desired and initial poses. Not only is robust stability improved but also are robust pose tracking simulation and experiment performances obtained in comparison to the state-of-the art methods.

To implement the specific human following (SHF) task in a global GPS-denied environment (e.g., airport, hotel, hospital, inventory area, office, library), a distributed module ultra wideband network (DM-UWBN) is deliberated on residual-bi-long short-term memory (RBLSTM) model. It possesses these advantages: maintain its gradient signal for more effective learning, reduce the overfitting weight, and improve localization accuracy. Besides the dynamic localizations of omnidirectional service robot (ODSR) and specific human, a residual-recurrent neural network -based finite-time control (RRNN-FTC) based on the relative degree of ODSR's output is designed. It has a dominant advantage in the converging weight learning compensation of aggregately dynamic uncertainties. Based on these valuable characteristics, outstanding tracking performance with reducing average power or fluctuation of control input in contrast to previous research is achieved. Due to the multiprocessing times of RRNN-FTC (e.g., 5 ms) and RBLSTM-DM-UWBN (e.g., 150 ms), the SHF is more arduous. Finally, the SHF of ODSR by the RRNN-FTC in the global GPS-denied environment with two pillars and a mat on the reference path validates the supremacy of the proposed approach.

To satisfy the required recognition accuracy from a far distance, an adjusted attention-based YOLOX for face recognition (AA-YOLOX-FR) is designed by an appropriate segmentation of the original image, so that faces' pixels (e.g., 20 × 20 at 15m) effectively train, validate, and test. Based on an edge computing platform (e.g., NVIDIA Jetson-AGX), the processing time for the image 2208 × 1242 with 8 segmentations of 640 × 640 equals 296.3ms in comparison to 95.4ms for its down-sampling to 640 × 640. Although the down-sampling technique achieves a faster processing speed, its recognition rate decreases as a face is at a far distance or with different lighting conditions. The average online video-based recognition rate of AA-YOLOX-FR for a distance from 10m to 15 m and different lighting conditions is 92.5%.

In this article, an online RNN-based finite-time formation tracking control (ORNN-FTFTC) is designed to quickly accomplish an assigned formation of nonlinear generalized and heterogeneous multiagent systems with input fault and saturation. Each agent, including the leader and the followers, can possess different relative degrees and control input numbers but the same output for easy task planning. At least one agent must communicate with the leader and the information of neighborhood agents is required to accomplish the assigned formation task. To fulfill the task under the uncertain environment, the proposed ORNN-FTFTC possesses nonlinear filtering formation error with dynamic fractional exponent, nonlinear filtering gain, and the RNN learning compensation of the aggregately uncertain dynamics in each agent. Not only does the nonlinear filtering gain increase as the nonlinear filtering formation error is in the vicinity of zero to achieve its finite-time convergence, but also the new e-modification learning can cover all the value of formation error such that learning weights are stabilized even in an uncertain environment. Finally, an application to a 3D pose from take-off to a steady-formation of hexa-copter unmanned aerial vehicles and unmanned helicopters with initial formation error certifies the feasibility and robustness of the proposed control.

To implement the human–robot interactions in a noisy environment, the speech improvement-based (SIB) stratified adaptive finite-time saturation control (SAFTSC) for omnidirectional service robot (OSR) is developed. From the outset, the feature vectors of nine designed speech commands are extracted from their frequency signals and then trained by multiclass support vector machine. Two background noises are on-line filtered with the characteristic: “the smaller error in power spectrum is, the larger recovery from noisy power spectrum is.” Comparisons among without or with noise, and filtering are addressed. To achieve the zero pose error of OSR in finite time, an adaptive finite-time indirect trajectory (AFTIT) is constructed. To track the AFTIT with the zero error in finite time, the adaptive finite-time saturation control (AFTSC) is also established. Both AFTIT and AFTSC possess nonlinear switching gain increasing the high-frequency motion capability to fulfill the classified speech command. Simply put, the proposed SIB stratified AFTSC includes the speech improvement for classification, the AFTIT, and the AFTSC. Besides the stability of the closed-loop system is verified by the Lyapunov stability theory, three categories of SIB experiments are compared.

Only partial system knowledge for the generalized robotic dynamics with input saturation, i.e., the regression matrix for the specific robot, is required to design the proposed adaptive finite-time saturated tracking control (AFTSTC). It contains a nonlinear auxiliary tracking error, which can shape the system frequency response. As the operating point is in the neighborhood of the zero auxiliary tracking error, nonlinear filtering gains can be increased to accelerate its tracking ability. Moreover, the traditional skew-symmetric matrix's condition for the time derivative of inertia matrix and the Coriolis and centrifugal force matrix is not necessarily required such that the uncertainties and the finite-time convergence are reduced. The computational complexity as compared with the fuzzy neural network adaptive control is also addressed. The stability of the closed-loop system is verified by the Lyapunov stability theory. Finally, two practical robotic examples are given to validate the effectiveness and robustness of the proposed control.

A class of generalized nonlinear dynamic systems is first approximated by N fuzzy-based linear subsystems using the identification of input-output data or the linearizing system with respect to suitable operating points. To obtain null trajectory tracking error in fixed time, a fuzzy fixed-time control (FFTC) with nonlinear switching surface and switching gain is first designed. It can be said that the FFTC is based on a class of passive and distributive models with uncertainties. To compensate enormous uncertainties, a fuzzy fixed-time learning control (FFTLC) by learning two unknown coefficients for the upper bound of uncertainties in each subsystem is designed. As compared with radial basis function neural network, the computational complexity for the compensated uncertainties is much simple. It can be said that an FFTLC is based on a class of online active and distributive uncertain models. Due to the fixed-time control design, the transients often occur, particularly for the larger uncertainties or initial tracking error. Hence, the saturated input of nonlinear dynamic system is addressed and online compensated. Finally, the compared simulations and application to two-link robot manipulator confirm the effectiveness, robustness, and less computation as compared with previous studies.

To begin with, the target human (TH) in the face of a mid-size humanoid robot performs 3-D motions captured by the servo-cradle-head RGB-D vision system (SCH-RGB-D-VS) on its head. During imitation processing, the SCH-RGB-D-VS can maintain a suitable field of view in the pitching and rolling directions to acquire the correct images of the TH's motion. Its necessity is first confirmed by the experimental result. Based on the 3-D coordinates of the head and two feet, 11 stable motions of the lower body (LB) are classified by the proposed improved support vector machine. Two pairs of hands and elbows for upper body (UB) imitation are approximated by eight pretrained multilayer neural network models to enhance one-to-one mapping, reduce the modeling complexity of inverse kinematics, and imitate complex motion. Finally, three categories of experiments by integrated motion of UB and LB confirm the effectiveness and robustness of the proposed method.

Owing to advantageous feature of omnidirectional drive service robot (ODSR), i.e., simultaneous translation and rotation, the human-robot collaborations are more reliable and satisfactory. The path tracking model of an ODSR includes mechanism kinematics, mechanical dynamics with friction of each wheel and transformation between ODSR and world coordinates, and motor dynamics. To track the desired pose of ODSR in finite time, the adaptive finite-time virtual desired path (AFTVDP) is designed. To make the direct output track the AFTVDP in finite time, an adaptive finite-time control (AFTTC) is designed to execute high frequency motions. In summary, the proposed hierarchical adaptive finite-time control (HAFTC) contains AFTVDP and AFTTC. Finally, experiment validates the effectiveness of the proposed control.

A hierarchically improved fuzzy dynamical sliding-model control (HIFDSMC) is presented to address the autonomous ground vehicle (AGV) path tracking problem. The proposed controller has two portions: one is the virtual desired input (VDI), and the second is the path tracking control (PTC). In addition to the equivalent control in VDI and PTC, an improved fuzzy dynamical sliding-mode control (IFDSMC) is designed to deal with the system uncertainties, e.g., different payloads. Contributions of this paper include the following four parts: 1) Based on the nominal system response, the fuzzy rules and scaling factors of the IFDSMCs in the VDI and PTC are easily chosen. In contrast, a conventional fuzzy logic control approach requires more trial-and-error tuning to obtain a satisfactory performance. 2) The proposed HIFDSMC possesses the tuning mechanism (the coefficients of two sliding surfaces, the scaling factors in indirect and direct modes, and the fine tuning in fuzzy table) such that the uncertainties are tackled without a larger computational burden. 3) The stability of the closed-loop system is verified by the Lyapunov stability with hierarchical concept. 4) Different payloads not at the mass center of the AGV (e.g., greater than 25% in the total weight of the AGV) are tackled by the IFDSMCs to obtain a satisfactory performance. Finally, the application to the assembly line of the AGV with different payloads to track the circular and piecewise straight-line paths by the proposed HIFDSMC is compared with the hierarchical fuzzy decentralized PTC.

First, the received signal strength indications (RSSIs) of the three tags on a triangular apparatus surrounding a target human (TH) are read by two perpendicular antennas with one reader. These 6 RSSIs and their corresponding pose and the azimuth angle of the TH with respect to the autonomous guided vehicle (AGV) or antenna are attained. Since the relations of these pairs of input and output are nonlinear, coupled, and stochastic, it is difficult to obtain an effective model. A 1st-order low-pass filter with unit dc gain and suitable cut-off frequency is applied to remove the unnecessary high frequencies of 6 RSSIs. Due to the advantageous features of neural network modeling, e.g., stochastic approximation, insensitive to noise, different numbers of input and output, the multilayer neural network (MLNN) with Levenberg-Marquard Back-Propagation (LMBP) learning law is applied to obtain the model between six filtered RSSIs and three outputs (i.e., the pose and the azimuth angle of the TH). Then the static and dynamic estimations of the TH w.r.t. the AGV are first investigated. To confirm the robustness of the proposed MLNN-based mobile RFID localization system, another human walks through a specific zone between the TH and the AGV with different velocities are also addressed. Then the path to track the TH is on-line planned and predicted from the output of MLNN.

The proposed hierarchical sliding mode control (HSMC) for the car-like automated guided vehicle (CLAGV) includes two parts: one is virtual control input (VCI), the other is sliding mode tracking control (SMTC) [1]. Moreover, a single software/hardware based platform develops the software for the control, image processing and trajectory planning algorithms, and the hardware for the control signal (e.g., the PWM for driving the motor) and for the sensor inputs (e.g., the decoder for obtaining the position or velocity of motor, the USB interface for capturing the image). The RGB-D vision system can detect the obstacle(s) through the depth image and recognize the specific object through the SURF (Speed-Up Robust Feature) method. The estimated distance with respect to the vehicle can execute the task of obstacle avoidance (OA) and target approach (TA). Finally, the experiments of the straight-line and circular trajectory tracking with the simultaneous OA and TA of the vehicle confirm the effectiveness, efficiency, and robustness of the proposed system.

Due to the nature of the complete model with motor dynamics, virtual control input (i.e., desired motor current) is designed by the first sliding surface so that the indirect output (i.e., 3-D pose of mobile robot) is controlled by the direct output (i.e., motor current). Subsequently, the linear dynamic tracking error of the virtual control input is employed to establish the second sliding surface. Then, the hierarchical path tracking control (HPTC) is constructed so that the direct output asymptotically and robustly tracks the virtual control input. In the meanwhile, the asymptotic tracking of the indirect output is achieved. To improve only asymptotical tracking to convex set due to the existence of huge uncertainties (e.g., different ground conditions, time-varying system parameters, external disturbances), two online fuzzy models of uncertainties are plunged into the HPTC with a switching mechanism to design the so-called global fuzzy adaptive HPTC for a mobile robot. Moreover, the global adaptive path tracking control for different initial system states outside of approximated set is achieved. The simulations confirm the effectiveness, efficiency, and practicality of the proposed technique. Two compared experiments also validate the consistence with the simulation result.

At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

In the beginning, a dynamic sensing system including the hardware and the low-pass and Kalman filtering is designed. It is then installed at the center of gravity (CoG) of the humanoid robot (HR) and can capture the responses of the pitch and roll axes during the execution of specific task. After the analytic design, a set of desired pitch and roll trajectory for a specific task is achieved. In addition, the 3D coordinates of four tips (i.e., two hands and feet) with respect to the neck and waist centers of HR are computed by the kinematics of 4-DoFs of two arms and 6-DoFs of two legs. Based on these 3D coordinate, the total 36 classes are achieved. Without measuring the contact force of two feet, without unnecessarily interfering the original task, the incremental proportion-derivative dead-zone control of the pitch and roll directions for each class is designed by the control of different suitable motors. It is cost-effective as compared with other methods. Finally, the experiments of continuous walking motion in the presence of external disturbances are presented to evaluate the effectiveness and robustness of the proposed method.

In this paper, a nonlinear time-varying dynamic system is first approximated by N fuzzy-based linear state-space subsystems. To track a trajectory dominant by a specific frequency, the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule. It is known that linear state feedback control for each fuzzy subsystem is inferior to that using nonlinear feedback control. It is also known that most of the fuzzy adaptive controls must be in a specific domain for the function approximation. To overcome the above shortcomings, we propose a globally fuzzy model based adaptive variable structure control with a switching function to determine when the learning law should be used. As the norm of the switching surface is inside of a defined set, the learning law starts; simultaneously, as it is outside of the other set which is larger than the previous defined set, the learning law stops. In this situation, the proposed control is verified to converge into a convex set, which is smaller than the set for the function approximation. For the purpose of smoothing the discontinuity of control input, a transition between outside and inside of approximated set is also assigned. Under these circumstances, the proposed control can automatically tune as a control without or with the learning compensation of uncertainties. Finally, the stability of the overall system is verified by Lyapunov stability theory.

The trajectory tracking of uncertain underactuated nonlinear dynamic systems is tackled by an adaptive fuzzy hierarchical sliding-mode control (AFHSMC). First, one of the subsystems is assigned as the first layer sliding surface. Next, a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem is constructed. In this paper, the nth layer is supposed to be the top layer (or hierarchical layer) for including the sliding surfaces of all subsystems. Because two nonlinear system functions and the time-varying external disturbance of each subsystem are supposed to be unknown, different online fuzzy models are employed to approximate these nonlinear system functions and the upper bounded functions of external disturbances. Moreover, the upper bound of uncertainties caused by these fuzzy modeling errors is estimated online. Based on these learning fuzzy models and the estimated upper bound of these modeling errors, an AFHSMC is developed. The stability analysis and tracking performance of the closed-loop system are verified by Lyapunov stability theory. Finally, two simulation examples including different amplitudes of external disturbance and comparison with hierarchical sliding-mode control confirm the effectiveness and robustness of the proposed control.

At beginning, the dynamic model of QUAV at low speed including translational and rotational motions is derived by Newton-Euler formulation. Four control inputs generated by four rotors are employed to accomplish the up-down, translation, roll, pitch and yaw motions. In this total, the proposed system produces six outputs that will affect the trajectory and pose of a QUAV: its 3D position and angular position with respect to the world-fixed coordinate. Based on the data of input-output, two scaling factors are first used to normalize each sliding surface and its derivative. According to the concept of if-then rule, an appropriate rule table for the ith subsystem is obtained. Then the output scaling factor based on Lyapunov stability is determined. The purpose of using the proposed fuzzy decentralized sliding-mode under-actuated trajectory-tracking control (FDSMUTC) is the huge uncertainties of a QUIAV often caused by different flight conditions. Finally, the simulation example is applied to illustrate the corresponding procedure of controller design.

In the beginning, the kinematic model, dynamic model of a differential mobile robot (DMR), and the dynamic model of left- and right-wheel DC motors are combined to be a controlled system. The control inputs of the proposed controlled system include the input voltages for the left- and right-wheel motors, i.e., two inputs. On the other hand, the system outputs contain two-dimension position and its orientation, i.e., three outputs. Due to the under-actuated characteristic, the sliding surface using directly controlled output is designed so that the number of control input and sliding surface is the same, and that the indirectly controlled output is also controlled. Under uncertain environment including friction and uncertainty, the sliding-mode under-actuated control (SMUC) with suitable conditions is designed such that an asymptotical tracking result is obtained. To enhance system performance, an on-line fuzzy modeling of friction and uncertainty is employed to design a fuzzy model-based sliding-mode under-actuated control (FSMUC). Finally, the proposed hybrid fuzzy sliding-mode under-actuated control (HFSMUC) combining SMUC and FSMUC with a transition maintains both advantages of SMUC and FSMUC and simultaneously avoids the disadvantages coming from SMCU and FSUMC.

Due to the under-actuated characteristic of quadrotor unmanned aerial vehicle (QUAV), the sliding surface using measurable output (i.e., 3D position and attitude), whose number is larger than that of control input (i.e., total thrust force, roll, pitch and yaw torques), is designed. Hence, the number of control input and sliding surface is the same, and the indirectly controlled mode (e.g., x- and y-axes) is controlled. Under uncertain environment, the sliding-mode under-actuated control (SMUC) with suitable conditions is first derived so that asymptotical and bounded tracking results are achieved. To improve system performance, an on-line recurrent neural network modeling for dynamical uncertainty of QUAV is employed to design a recurrent-neural-network-based sliding-mode under-actuated control (RNNSMUC). Then the proposed hybrid neural-network-based sliding-mode under-actuated control (HNNSMUC) combining SMUC and RNNSMUC with a transition maintains both advantages of SMUC and RNNSMUC and simultaneously avoids the disadvantages coming from SMCU and RNNSMUC.

This paper realizes a humanoid robotic system to execute target grasping (TG) in the 3-D world coordinate. At the outset, the HR scans the field to find specific target(s), which is (are) randomly distributed in the 3-D coordinate before the HR. By an active stereo vision system (ASVS), the HR is navigated to the planned posture and then the task of TG is executed. The first feature of this paper is that the transform between the target in the left and right image plane coordinates of the ASVS and the target in the 3-D world coordinate is off-line approximated by multilayer neural network (MLNN) using Levenberg Marquardt Back Propagation (LMBP) training law. Because the computation of inverse kinematics (IK) of two arms is time consuming, another off-line modeling using MLNN is employed to approximate the transform between estimated ground truth of target and joint coordinate of two arms. This is the second feature of this paper. Finally, the grasping of three targets with different colors and different 3-D world coordinates via our HR is demonstrated to verify the effectiveness and efficiency of the proposed method.

Robots can adapt strides according to ground conditions and walk stably in different environments. This study uses fuzzy logic control and Linear Quadratic Regulator (LQR) control theory on biped robot system to achieve the development of balanced and fast footsteps. Traditional controllers are designed according to mathematical models of physical systems, while fuzzy controller is a physical system that uses inexact mathematical model involving sets and membership functions. Fuzzy controller includes theories in fuzzification, fuzzy control rules, and defuzzification.

Each subsystem of a nonlinear interconnected discrete dynamic delayed system is approximated by a weighted combination of L pulse transfer function delayed systems (PTFDS). To deal with large time-delay of the controlled system with acceptable performance, a two-degree-of-freedom control is designed. At beginning, the H2- norm of the difference between the transfer function of a reference model and the closed-loop transfer function of the jth PTFDS of subsystem i is minimized to obtain a suitable frequency response. In addition, the H∞- norm of the weighted sensitivity function between the output disturbance and its corresponding output of the jth PTFDS is simultaneously minimized to reduce its effect. In summary, the proposed control not only accomplishes the above mentioned optimizations but also attenuates the effect of time delay. Furthermore the comparisons between with and without discrete Smith predictor are presented. The main contributions of this paper are three folds. First, the large nominal time-delay is compensated by a discrete Smith predictor. Secondly, the proposed control can achieve the suitable response of the closed loop system with the attenuation of output disturbance and time varying delay. Thirdly, an observer is not needed and the discrete controller is more suitable for the implementation.

Due to the under-actuated feature, the reference signals using the combination of the system outputs, whose number is larger than that of reference signal, are designed so that the number of control inputs and sliding surfaces is the same, and that the uncontrollable mode is indirectly controlled. Under the uncertain environment, the sliding-mode under-actuated control (SMUC) with the satisfaction of suitable condition is designed to asymptotically track the reference signal. Otherwise, a bounded tracking result is obtained for the mild condition. In this situation, an on-line fuzzy modeling for the uncertainty is employed to design a fuzzy model-based sliding-mode under-actuated control (FSMUC) to improve the system performance; e.g., the bounded tracking result of SMUC becomes an asymptotical tracking. The proposed hybrid fuzzy sliding-mode under-actuated control (HFSMUC) combining SMUC and FSMUC with a transition can be applied to a class of generalized, under-actuated and uncertain nonlinear systems, e.g., the trajectory tracking control of a differential mobile robot (DMR). Finally, the simulations of the HFSMUC system are presented to confirm the efficiency and effectiveness of the proposed control.

In this study, a fuzzy control policy is presented for dynamic walking of a biped robot that is modeled as a simulated five-link biped robot. Due to complex ground contact models, it is difficult to precisely model its dynamics. Besides, a spring/damper ground model and a simplified inverted pendulum model are presented to represent the ground contact relation and the approximated model of biped robots as well. Moreover, Finite State Machine (FSM) is utilized to decompose a cycle of walking gait. Under zero moment point (ZMP) constraint, each joint follows desired trajectories in each state that are generated by quintic spline curve through the model free controller (i.e., fuzzy control). In addition, its robustness is investigated by imposing pulse perturbation on torso for some directions. The results are demonstrated in simulations as well as animation and then the proposed controller is compared with a PID controller as well.

In this paper, the functional commands based on hand gesture are designed by Hu moments and contour sequence moments, which are invariant to the translation, rotation and scale of a hand gesture. First, the original image with a hand gesture is transformed into the color space of YCrCb. The segmentation of the skin-like objects is obtained by suitable thresholds of Crand Cb. In sequence, the morphological filtering and the shape selection are employed to obtain various acceptable region-based and contour-based binary images of different hand gestures. Various feature vectors corresponding to different processed hand gestures are applied to train the input weight matrix and layer weight matrix of a probability neural network for classification. Furthermore different lighting conditions for Hu moments and contour sequence moments of eight hand gestures are compared to verify the robustness of the image processing and classification.

Due to the under-actuated feature, the reference signals using the combination of the system outputs, whose number is larger than that of reference signal, are designed so that the number of control inputs and sliding surfaces is the same, and that the uncontrolled mode is indirectly controlled. Under the uncertain environment, the variable structure under-actuated control (VSUC) with the satisfaction of suitable condition is designed to asymptotically track the reference signal. Otherwise, a bounded tracking result is obtained for the mild condition. In this situation, an on-line neural network modeling for the uncertainty is applied to construct a neural-network-based variable structure under-actuated control (NVSUC) to improve the system performance; e.g., the bounded tracking result of previous VSUC becomes an asymptotical tracking. The proposed hybrid neural-network-based variable structure under-actuated control (HNVSUC) combining VSUC and NVSUC with a transition can be employed to a class of under-actuated and uncertain nonlinear systems. Finally, the corresponding simulations of the balance control of a double inverted pendulum on a cart are undertaken to confirm the efficiency and effectiveness of the proposed method.

Each subsystem of a nonlinear interconnected dynamic delayed system is approximated by a weighted combination of L transfer function delayed systems (TFDSs). The H2-norm of the difference between the transfer function of a reference model and the closed-loop transfer function of the kth TFDS of subsystem i is then minimized to obtain a suitable frequency response without incurring oscillating and sluggish phenomena. Because of the existence of the disturbance at the output of the kth TFDS, which is not only large but also contains various frequency components, the H∞-norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth TFDS is simultaneously minimized to reduce its effect. Furthermore, with proper selection of weighted sensitivity functions, certain specific modes of the output disturbance can be eliminated. Finally, two simulations are performed; one is the simulation of our designed TFDSs with different delays or nonminimum phases, and the other is the simulation of an internet-based intelligent space for the trajectory tracking of a car-like wheeled robot system. We demonstrate the effectiveness and efficiency of the proposed control. The main contributions of this paper are twofold. First, the control can simultaneously attain robust performance through the mixed H2/H∞optimization with a Smith predictor and achieve the robust stability via L2Nstable with finite gain. Second, fuzzy observer is not needed.

In this paper, a robust adaptive fuzzy sliding mode controller is proposed to deal with the tracking control problem for a class of single-input single-output (SISO) perturbed strict-feedback nonlinear systems. It is known that the presence of perturbations is a very common problem in various kinds of engineering systems, and these perturbations involve unmodelled dynamics, external disturbances, and parameter variations. First, the unknown parameter vectors of strict-feedback system is on-line learned to compensate their effects. Besides the parameter variations, the upper bounds of these perturbations are often difficult to be obtained. Therefore, fuzzy logic systems and adaptive laws are applied to approximate the unknown upper bounds of the remained perturbations. In addition, the absolute minimum between the upper bound of perturbation and its learning function is updated to enhance the system performance. By introducing Lyapunov stability theorem as well as the theory of sliding mode control, not only the robust stability of the overall system can be ensured, but also good tracking performance can be obtained. Finally, an example of spring-mass-damper nonlinear system in the presence of perturbations confirms the effectiveness and the feasibility of the proposed control.

Hybrid under-actuated control for the autonomous dynamic balance of a running electrical bicycle including frictional torque and motor dynamics is developed, where includes two control inputs: steering and pendulum voltages, and three system outputs: steering, lean and pendulum angles. Due to the under-actuated feature, two novel reference signals using three system outputs are designed so that the number of control inputs and sliding surfaces is the same. The previous fuzzy decentralized sliding mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a running electrical bicycle system, caused by different ground conditions, gusts of wind, and interactions among subsystems, are often huge, an extra compensation of learning uncertainty is plunged into FDSMUC to enhance the system performance. We call it as “fuzzy decentralized sliding mode adaptive under-actuated control (FDSMAUC).” To avoid the unnecessary transience caused by uncertainties and control signal and to preserve the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., Hybrid FDSMUC) is designed. Finally, the compared simulations for the suggested control system among the FDSMUC, FDSMAUC and Hybrid FDSMUC validate the efficiency of the proposed method.

In this paper, a robust adaptive fuzzy control for a class of nonlinear uncertain systems preceded by an unknown dead-zone and with unknown upper bound of uncertainties is developed. The dead-zones are quite commonly encountered in many systems (e.g., DC servosystem, robot, and machine tools), are usually poorly known, and may severely limit the performance of control. In addition, the system uncertainties (e.g., parameter variations, or external load, unmodeled dynamics) often exist. Therefore, the controllers are required to deal with the robust stability and performance of the systems with unknown dead-zone and in the presence of uncertainties, whose upper bound is generally unknown. In the beginning, an adaptive dead-zone compensation is employed to improve system performance. Then the unknown system functions and the unknown upper bound of system uncertainties are respectively approximated by fuzzy logic systems with unknown weights. The unknown bounds caused by the learning error of the slope of dead-zone and the system functions are also tackled by an extra learning law. The above weights are all on-line learned to provide for the controller design. Moreover, the projection terms in these learning laws are designed such that the boundedness of the learning weight can be assured.

Based on the previous studies, the dynamic balance of an electrical bicycle includes two control inputs: steering and pendulum torques, and three system outputs: steering, lean and pendulum angles. Two novel reference signals are first designed so that the uncontrolled mode is simultaneously included into these two control modes. Two scaling factors for each subsystem are first employed to normalize the sliding surface and its derivative. The so-called fuzzy decentralized sliding-mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a bicycle system, caused by different ground conditions, gusts of wind, and interactions among subsystems, are often huge, an extra compensation of learning uncertainty is plunged into FDSMUC to enhance system performance. We call it as ldquofuzzy decentralized sliding-mode adaptive under-actuated controlrdquo (FDSMAUC). To avoid the unnecessary transient response and then destroy the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., fuzzy decentralized sliding-mode robust adaptive under-actuated control, FDSMRAUC) is designed. Finally, the compared simulations for an electrical bicycle among the FDSMUC, FDSMAUC and FDSMRAUC validate the efficiency of the proposed method.

Each subsystem of a nonlinear interconnected dynamic delay system (NIDDS) is first approximated by a weighted combination of L transfer function delay systems (TFDSs). The H2-norm of the difference between the transfer function of the reference model and the closed-loop transfer function of the kth TFDS of subsystem i is then minimized to obtain a suitable frequency response. Because the output disturbance of the kth TFDS, including the interconnections coming from the other subsystems, the approximation error of the ith subsystem, and the interactions resulting from the other TFDSs, is not small and includes various frequencies, the H℞-norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth TFDS is simultaneously minimized to attenuate its effect. In addition, an appropriate selection of the weighted function for the sensitivity can reject the specific mode of the output disturbance. Finally, the stability of the overall system is verified by the concept of L2n-stable with finite gain.

The purpose of this paper is to stabilize the running motion of an electrical bicycle. In order to do so, two strategies are employed in this paper. One is to control the bike’s center of gravity (CG), and the other is to control the angle of the bike’s steering handle. In addition, the proposed system produces three outputs that will affect the dynamic balance of an electrical bicycle: the bike’s pendulum angle, lean angle, and steering angle. Based on the data of input-output, two scaling factors are employed to normalize the sliding surface and its derivative. According to the concept of if-then rule, an appropriate rule table for the ith subsystem is obtained. Then the output scaling factor based on Lyapunov stability is determined. The proposed control method used to generate the handle torque and pendulum toque is called fuzzy sliding-mode under-actuated control (FSMUAC). The purpose of using the FSMUAC is the huge uncertainties of a bicycle system often caused by different ground conditions and gusts of wind; merely ordinary proportional-derivative-integral (PID) control method or other linear control methods usually do not show good robust performance in such situations.

To realize trajectory tracking and obstacle avoidance, two distributed CCD (charge-coupled device) cameras are constructed to obtain the dynamic poses of the car-like mobile robots (CLMRs) and the obstacles. Based on the control authority of these two CCD cameras, a suitable reference command including desired steering angle and translation velocity for the fuzzy decentralized variable structure control (FDVSC) in the client computer is on-line planned. Due to the delay of signal transmission through an internet network and wireless local area network (WLAN), suitable sampling time of the FDVSC is determined by the Quality of Service (QoS). The proposed control can track an on-line planning reference command without the requirement of a mathematical model of the CLMR. Only the information of the upper bound of system knowledge (including the dynamics of the CLMR, the delay feature of internet network and WLAN) is required to select the suitable scaling factors and the coefficients of switching surface so that an acceptable performance is achieved.

In an electric bicycle, two strategies are taken up to stabilize the running motion of a bicycle. One is the control of its center of gravity (CG), and the other is the control of its steering angle of handle. In general, the control of the CG is used a pendulum. In addition, the motion of a bicycle often possesses a lean angle with respect to vertical direction. In this situation, the proposed system contains three outputs: steering angle, lean angle, and pendulum angle, these will affect the dynamic balance of an electrical bicycle. The proposed control generating the handle torque and pendulum toque is called variable structure under-actuated control (VSUAC). The motivation of using the VSUAC is that the system uncertainties of a bicycle are often huge due to different ground conditions and a gust of wind. Merely use an ordinary proportional-derivative-integral (PID) control or other linear controls often can not have good robust performance. Finally, the compared simulations for the electrical bicycle among ordinary PID control, modified proportional-derivative control (MPDC), and VSUAC confirm the usefulness of our proposed control.

In this paper, the trajectory tracking and (dynamic) obstacle avoidance of a car-like mobile robot (CLMR) within distributed sensor-network spaces via fuzzy decentralized sliding-mode control (FDSMC) is developed. To implement trajectory tracking and (dynamic) obstacle avoidance, two distributed charge-coupled device (CCD) cameras are set up to realize the dynamic position of the CLMR and the obstacle. Based on the control authority of these two CCD cameras, a suitable reference trajectory including desired steering angle and forward-backward velocity for the proposed controller of the CLMR is planned. It is also transmitted to the CLMR by a wireless module. The proposed FDSMC can track a reference trajectory without the requirement of a mathematical model. Only the input-output data pairs of the CLMR and the upper bound of its dynamics are required for the selection of suitable scaling factors. The proposed control system includes two processors with multiple sampling rates. One is a personal computer employed to obtain the image of the CLMR and the obstacle, to plan a reference trajectory for the CLMR, and then to transmit the planned reference trajectory to the CLMR. The other is a digital signal processor (DSP) implementing in the CLMR to control two dc motors. Finally, a sequence of experiments is carried out to confirm the performance of the proposed control system.

In this paper, a navigation system is developed. The system includes path tracking and obstacle avoidance apparatus for a car-like wheeled robot (CLWR) within an Internet-based smart-space (IBSS) using fuzzy-neural adaptive control (FNAC). Two distributed charge-coupled device (CCD) cameras are installed to capture both the dynamic pose of the CLWR and the obstacle. Based on the control authority of these two CCD cameras, a suitable reference command that contains the desired steering angle and angular velocity for the FNAC built into the client computer is planned. Because of the delay encountered by the transmission through the Internet network (IN) and the wireless local area network (WLAN) and the nonlinear coupling features of the CLWR, a weighted combination ofNlinear subsystems that are described by a state-space model with average-delay is implemented to approximate the dynamics of an IBSS-CLWR. The proposed FNAC contains a neural network consisting of a radial basis function (RBFNN) to learn the uncertainties due to the fuzzy-model error (e.g., the random time-varying delays and the slippage of the CLWR) and the interactions caused by other subsystems. The stability of the overall system is then investigated by adopting the Lyapunov stability theory. Finally, a sequence of experiments including the control of the off-ground CLWR (i.e., the CLWR does not make contact with the ground) and the navigation of the IBSS-CLWR as compared with the conventional proportional-integral-derivative (PID) control is performed to demonstrate the advantage of the proposed control system.

In this paper, the trajectory tracking and obstacle avoidance for a car-like mobile robot (CLMR) within distributed active-vision network-space system (DAVNSS) via three fuzzy variable structure decentralized controls (FVSDCs) is developed. To implement trajectory tracking and obstacle avoidance, two distributed wireless CCD (charge-coupled device) cameras individually driven by two stepping motors, i.e., active CCD1 and active CCD2 (or ACCD1 and ACCD2), are constructed to capture the dynamic pose of the CLMR or obstacle. The proposed control system includes quad-processors with multiple sampling rates. One personal computer is first employed to receive the image of the CLMR or obstacle from ACCD1 or ACCD2 by wireless transmitter, and then to plan three reference commands for the CLMR, ACCD1, and ACCD2, which are individually received by three digital signal processors (DSPs). The six-step image processing and the calibration between the world coordinate and the image plane coordinate using multilayer perceptrons (MLP) are established. Finally, a sequence of experiments is carried out to confirm the performance of the proposed control system.

For implementing dynamic target tracking, two distributed CCD (charge-coupled device) cameras are set up to capture the poses of the tracking and target cars, which have the front-wheel for the steering orientation and the rear-wheel for the forward-backward motion. Based on the control authority of these two CCD cameras, a suitable reference command for the proposed controller of the tracking car is planned on a personal computer and then transmitted to the tracking car by a wireless device. Only the information of the upper bound of system knowledge is required to select the suitable scaling factors and coefficients of sliding surface for the proposed controller so that an acceptable performance is achieved. Since the target car is dynamic and the tracking car possesses dynamics, a grey prediction for the pose of the target car is employed to plan an effective reference command for the tracking car to enhance the performance of target tracking. Finally, a sequence of experiments is carried out to confirm the usefulness of the proposed control system.

In this paper, a decentralized model reference control via fuzzy mixed H2/Hinfinoptimization design was developed. Each subsystem contained L linear pulse transfer function systems (LPTFSs). The reference model for every LPTFS was first designed to shape the response of the ith closed-loop subsystem. Then the H2-norm of the output error (i.e., the difference between the output of the reference model and the system) and weighted control input of the jth LPTFS was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the jth LPTFS was achieved. However, an output disturbance of the jth LPTFS caused by the interactions among the LPTFSs, the interconnections among the subsystems, modeling errors, and external loads deteriorated system performance or even resulted in instability. In this situation, the Hinfin-norm of weighted sensitivity between output disturbance and output error of the jth LPTFS was minimized to attenuate its effect. A nonlinear control based on output error for every LPTFS was also established to improve robust performance. The stability of the overall system was then verified by Lyapunov stability criterion. The application to piezo-driven XY table system (PD-XY-TS) was carried out to confirm the usefulness of the proposed control

In this paper, a partially known nonlinear dynamic system with time-varying delays of the input and state is approximated by N fuzzy-based linear subsystems described by a state-space model with average delay. To shape the response of the closed-loop system, a set of fuzzy reference models is established. Similarly, the same fuzzy sets of the system rule are employed to design a fuzzy neural-based control. The proposed control contains a radial-basis function neural network to learn the uncertainties caused by the approximation error of the fuzzy model (e.g., time-varying delays and parameter variations) and the interactions resulting from the other subsystems. As the norm of the switching surface is inside of a defined set, the learning law starts; in this situation, the proposed method is an adaptive control possessing an extra compensation of uncertainties. As it is outside of the other set, which is smaller than the aforementioned set, the learning law stops; under this circumstance, the proposed method becomes a robust control without the compensation of uncertainties. A transition between robust control and adaptive control is also assigned to smooth the possible discontinuity of the control input. No assumption about the upper bound of the time-varying delays for the state and the input is required. However, two time-average delays are needed to simplify the controller design: 1) the stabilized conditions for every transformed delay-free subsystem must be satisfied; and 2) the learning uncertainties must be relatively bounded. The stability of the overall system is verified by Lyapunov stability theory. Simulations as compared with a linear transformed state feedback with integration control are also arranged to consolidate the usefulness of the proposed control.

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.

From the very beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent an unknown and multivariable nonlinear dynamic system. A recurrent neural network with a compensation of upper bound of its residue is applied to model the unknown functions in a compact subset. The linearly parameterized weight for the function approximation error of the proposed network is also derived. An e-modification learning law with projection for weight matrix is employed to guarantee its boundedness and the stability of network without the requirement of persistent excitation. The proposed controller contains an equivalent control and a switching control. The equivalent control uses the learning functions by RNN, switching surface, and a bounded reference input. To compensate the residue of RNN, a simple network is applied to estimate its upper bound for the design of the switching control. Under some conditions, the semi-globally ultimately bounded tracking with the boundedness of estimated weight matrix is accomplished by Lyapunov stability theory.

In this paper, the trajectory tracking of a two-dimensional piezo-driven system (2DPDS) using Internet-based fuzzy decentralized microprocessor control (IBFDMC) was developed. It was known that the piezoelectric actuator contained hysteresis, which was not one-to-one mapping and memory nonlinearity. Due to this nonlinearity and the coupling characteristic of 2DPDS, an effective decentralized control was difficult to design. From the very beginning, suitable coefficients of switching surface were assigned to stabilize the switching surface and to shape the response of tracking error. Based on the data of input-output, two scaling factors are employed to normalize the switching surface and its derivative. According to the concept of if-then rule, an appropriate rule table for theithsubsystem was then achieved. Finally, a sequence of experiments was carried out to confirm the usefulness of the proposed control.

In this paper, the trajectory tracking and obstacle avoidance of a car-like mobile robot (CLMR) within an intelligent space via mixed H2/ Hinfindecentralized control was developed. For implementing (dynamic) obstacle avoidance and trajectory tracking, two distributed CCD (charge-coupled device) cameras were established to realize the pose of the CLMR and the position of the obstacle. Based on the authority of these two CCD cameras, a suitable reference command for the proposed controller of the CLMR is planned by the information of the CCD camera with higher authority and then transmitted to the CLMR by a wireless device. The features of the proposed control included smaller energy consumption with bounded tracking error, attenuation of output disturbance, and improvement of control performance. The suggested control system contained two processors with multiple sampling rates. One personal computer (PC) was employed to capture the image of CLMR and obstacle, to plan a reference command for the CLMR, and then to transmit the reference command to the CLMR. The other was a DSP (digital signal processor) implementing in the CLMR to control two DC motors. A sequence of experiments was carried out to confirm the effectiveness of the proposed control system.

In this paper, a partially known nonlinear dynamic system with input and state time-varying delay was approximated by N fuzzy-based linear subsystems described by state-space model with average-delay. For tracking the trajectory with a primary frequency, the fuzzy reference models with desired amplitude and phase features were established. Similarly, the same fuzzy sets of the system rule were employed to design a fuzzy-neural variable structure control (FNVSC). The proposed control contained a radial basis neural network to learn the uncertainties caused by the fuzzy-model error and the interactions resulting from the other subsystems. As the norm of the switching surface was inside of a defined set (e.g., ||sigma(t)||sigma2) the learning law started; the proposed method was an adaptive control possessing a compensation of uncertainties. As it was outside of the other set (e.g., ||sigma(t)|| > nsigma1, where nsigma1> nsigma2) the learning law stopped; the proposed method became a robust control. A transition between robust control and adaptive control was also assigned to smooth the possible discontinuity of control input. In addition, no assumption about the upper bound of the time-varying delay for the state and the input is required; however, a time-average delay is needed for the controller design. The stability of the overall system was verified by Lyapunov stability theory

Based on a preload design and a suitable feedback gain for the piezo-driven x-y table system (PD-XY-TS), the system response was improved. It was called "enhanced piezo-driven x-y table system (EPD-XY-TS)". Each subsystem of the EPD-XY-TS was then approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the ith subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the ith subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. In this situation, the Hinfin-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be improved by a switching control. Finally, the compared experiments of the trajectory tracking of the piezo-driven x-y table were carried out to confirm the practicality of the proposed control

In this paper, the trajectory tracking of a car-like mobile robot (CLMR) via network-based fuzzy decentralized sliding-mode control (NBFDSMC) was developed. Based on the upper bound of system knowledge with a little trial-and-error, the fuzzy decentralized sliding-mode control (FDSMC) for the motor was achieved. The controls of steering angle and angular (or linear) velocity of a CLMR were obtained through the modified scaling factors of the motor. Due to the delay transmission of a signal through an Internet, a revision of FDSMC (i.e., NBFDSMC) with suitable sampling interval, according to the quality of service (QoS), was accomplished. Then the control input was transmitted to the CLMR by a wireless device. The proposed control could track a reference trajectory without the requirement of a mathematical model. Only the information of the upper bound of system knowledge was required to select suitable scaling factors sucb that an excellent performance was accomplished. A sequence of experiments was carried out to evaluate the usefulness of the proposed control system

In this paper, a decentralized discrete variable structure control via mixed H2/H infinity design was developed. In the beginning, the H2-norm of output error and weighted control input was minimized to obtain a control such that smaller energy consumption with bounded tracking error was assured. In addition, a suitable selection of this weighted function (connected with frequency) could reduce the effect of disturbance on the control input. However, an output disturbance caused by the interactions among subsystems, modeling error, and external load deteriorated system performance or even brought about instability. In this situation, the H infinity-norm of weighted sensitivity between output disturbance and output error was minimized to attenuate the effect of output disturbance. Moreover, an appropriate selection of this weighted function (related to frequency) could reject the corresponding output disturbance. No solution of Diophantine equation was required; the computational advantage was especially dominated for low-order system. For further improving system performance, a switching control for every subsystem was designed. The proposed control (mixed H2/H infinity DDVSC) was a three-step design method. The stability of the overall system was verified by Lyapunov stability criterion. The simulations and experiments of mobile robot were carried out to evaluate the usefulness of the proposed method.

Because the piezoceramic materials were ferroelectric, the inherent hysteretic nonlinearity always existed in the piezoelectric system (PES). Due to the existence of hysteresis and modeling error, the system performance by only PID control often deteriorated. Because not all of the states of the PES were measurable, a state estimator was required to obtain the unavailable state. To begin with, a feedback linearization using estimated state was employed to transform the PES to a new coordinate system. To track the trajectory with a primary frequency, the reference model with desired amplitude and phase features was also designed. In the mean while, a tracking error model was achieved for the system analysis. Then the feedback linearization with a sliding-mode control including equivalent control and switching control was established to enhance system performance. The equivalent control using the signals from state estimator and reference model was designed to gain the desired control behavior. The switching control was applied to ameliorate the robust performance. Finally, the stability of the overall system was verified by Lyapunov stability theory. The tracking result converged to a set in terms of system and control parameters. In summary, the state-estimator-based feedback control contained state estimator, feedback linearization, reference model, and sliding-model control. Experiments of the PES were also presented to verify the usefulness of the proposed control.

A proportional control is first applied to improve the dynamics of robotic system. It is called "improved robotic system (IRS)", containing N subsystems. Each subsystem is approximated by the weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the ith subsystem, a dead-beat to its sliding surface is first designed. The output disturbance is not small and contains various frequencies. In this situation, the H/sup /spl infin//-norm of the weighted sensitivity function between the mth sliding surface and the output disturbance is minimized. An appropriate selection of the weighted function can enhance the system robustness. Although the effect of the output disturbance is attenuated, a better performance can be improved by a fuzzy switching control. Finally, the experiments of the trajectory tracking of the IRS on the horizontal plane with (or without) payload are given to verify the usefulness of the proposed control.

In this paper, a nonlinear dynamic system is first approximated by N fuzzy-based linear state-space subsystems. To track a trajectory dominant by a specific frequency, the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule. Similarly, the same fuzzy sets of the system rule are employed to design robust fuzzy sliding-mode control (RFSMC) and adaptive fuzzy sliding-mode control (AFSMC). The difference between RFSMC and AFSMC is that AFSMC contains an updating law to learn system uncertainties and then an extra compensation is designed. It is different from the most previous papers to learn the whole nonlinear functions. As the norm of the sliding surface is inside of a defined set, the updating law starts; simultaneously, as it is outside of the other set, the updating law stops. For the purpose of smoothing the possibility of discontinuous control input, a transition between RFSMC and AFSMC is also assigned. Under the circumstances, the proposed control [robust adaptive fuzzy sliding-mode control (RAFSMC)] can automatically tune as a RFSMC or an AFSMC; then the advantages coming from the RFSMC and AFSMC are obtained. Finally, the stabilities of the overall system of RFSMC, AFSMC, and RAFSMC are verified by Lyapunov stability theory. The compared simulations among RFSMC, AFSMC, and RAFSMC are also carried out to confirm the usefulness of the proposed control scheme.

To begin with, each subsystem of a nonlinear interconnected system was approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the mth subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the mth subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. Under this circumstances, the H/sup /spl infin//-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be enhanced by a switching control based on the Lyapunov redesign. In addition, the stability of the overall system was verified by Lyapunov stability theory. The simulations for the LPTFSs with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control. Finally, the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control.

In this paper, a nonlinear stochastic system (NSS) is approximated by weighted combination of N subsystems, which are described by ARMAX model (autoregressive moving-average model with exogenous input). The approximation error between the NSS and the stochastic fuzzy-model system (SFMS) is represented by nonlinear time-varying uncertainties (NTVU) in every subsystem. In the beginning, a dead-beat to the switching surface for every nominal subsystem is designed. The total disturbance of the ith subsystem is caused by the white noise, the approximation error of SFMS, and the interaction dynamics resulting from the other subsystems. In general, it is not small. Then the H/sup /spl infin// -norm of the weighted sensitivity function between the switching surface and the total disturbance is minimized. For obtaining a better performance, a fuzzy switching control is also designed. Finally, the simulations are carried out to confirm the validity of the proposed control.

Due to the complexity of robot, its exact description is difficult. On the contrary, a linear model about a specific operating point for a nominal robot is easy Then, a nominal robot can be approximated by the weighted combination of N subsystems described by the pulse transfer function matrices. The approximation error between the robot and the fuzzy linear pulse transfer function matrix system (FLPTFMS) includes two categories: the structural one caused by parameter variations and the unstructural one caused by measurement noise and external disturbance. The approximation error is represented by the weighted combination of the output disturbance in every subsystem. In addition, the output response of the ith closed-loop subsystem is subjected to the uncertainties caused by the output disturbance and the interaction dynamics resulting from the other subsystems. Due to the existence of the (remaining) uncertainties, a disadvantageous response often occurs. Under the circumstances, a switching control in every subsystem is designed to reinforce the system performance. The experiments of two-joint robot in the horizontal plane with (or without) payload confirm the practicality of the proposed control.

In this paper, a piezoelectric actuator (PEA) system is approximated by N subsystems, which are described by pulse transfer functions. The approximation error between the PEA system and the fuzzy linear pulse transfer function system is represented by additive nonlinear time-varying uncertainties in every subsystem. First, a dead-beat to the switching surface for every ideal subsystem is designed. It is called the "variable structure tracking control". The output disturbance of the ith subsystem is caused by the approximation error of fuzzy-model and the interaction dynamics resulting from other subsystems. In general, it is not small. Then, the H/sup /spl infin//-norm of the sensitivity function between the switching surface and the output disturbance is minimized. It is the "optimal robustness". Although the effect of the output disturbance is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the final step for the robustness design of control, which is "reinforced robustness". The stability of the overall system is verified by Lyapunov stability theory. Experimental work of a PEA system was carried out to confirm the validity of the proposed control.

The theoretical and experimental studies of a reinforcement discrete neuro-adaptive control for unknown piezoelectric actuator systems with dominant hysteresis are presented. Two separate nonlinear gains, together with an unknown linear dynamical system, construct the nonlinear model (NM) of the piezoelectric actuator systems. A nonlinear inverse control (NIC) according to the learned NM is then designed to compensate the hysteretic phenomenon and to track the reference input without the risk of discontinuous response. Because the uncertainties are dynamic, a recurrent neural network (RNN) with residue compensation is employed to model them in a compact subset. Then, a discrete neuro-adaptive sliding-mode control (DNASMC) is designed to enhance the system performance. The stability of the overall system is verified by Lyapunov stability theory. Comparative experiments for various control schemes are also given to confirm the validity of the proposed control.

In this paper, a DSP-based fuzzy-linear-model robust tracking control (DFRTC) is developed for the piezoelectric servosystem (PS) with dominant hysteresis. The PS is approximated by the weighted combination of N fuzzy linear pulse transfer functions. The DFRTC contains equivalent control and switching control. Based on the fuzzy model, the equivalent control is designed by the dead-beat to the switching surface for every ideal subsystem. Then the H/sup /spl infin//-norm of the sensitivity function between the switching surface and the output disturbance is minimized. Although the effect of the output disturbance is attenuated, the control accuracy may not be good enough. The switching control based on the Lyapunov redesign is applied to improve the control performance. The stability of the overall system can be verified by Lyapunov stability theory. The experiments of the PS are given to confirm the usefulness of the proposed control.

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory.

A nonlinear discrete-time system is approximated by N subsystems described by pulse transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse transfer function system is represented by the additive nonlinear time-varying uncertainties in every subsystem. First, a dead-beat to the switching surface for every ideal subsystem is designed. If part of the approximation error can be modeled as a known pulse transfer function for output disturbance, a controller based on the "internal model principle" is given to reject the corresponding disturbance. It is called "rejected robustness". Then the H/sub /spl infin//-norm of the transfer function between switching surface and the remaining output disturbance, the interaction caused by the other subsystem, is minimized. It is the so-called "optimal robustness" for robust control. Although the effect of the remaining output disturbance and the interaction is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the third step for the robustness design of control, which is called "reinforced robustness".

First, a one-degree-of-freedom of the frictional direct-drive motor is approximated by nine linear state-space dynamic subsystems obtained by the local linearization about the operating point. Then the same fuzzy sets of the system rule are applied to design the fuzzy-linear-model-based robust variable structure control, including a fuzzy equivalent control and fuzzy switching control. The fuzzy equivalent control is designed to obtain the desired control behavior. The fuzzy switching control is applied to tackle the uncertainty caused by the approximation error of fuzzy-model and the interaction dynamics resulting from the other subsystems. The proposed control does not require the solution of linear matrix inequalities for obtaining a common positive definite matrix to ensure the stability of the closed-loop system. The simulations are also presented to confirm the usefulness of the proposed control.

In this paper, a stable adaptive fuzzy sliding-mode control for affine highly nonlinear systems is developed. First, the external part of a transformed system via a feedback linearizing control evolves a linear dynamic system with uncertainties. A reference model with the desired amplitude and phase properties is given to obtain an error model. Since the uncertainties are assumed to be large, a fuzzy model is employed to model these uncertainties. A learning law with e-modification for the weight of a fuzzy model is considered to ensure the boundedness of learning weight without the requirement of persistent excitation condition. Then, an equivalent control using the known part of system dynamics and the learning fuzzy model is designed to achieve the desired control behavior. Furthermore, the uncertainties caused by the approximation of fuzzy model and the error of learning weight are tackled by a switching control. Finally, the stability of the overall system is verified by the Lyapunov theory. Simulations and experiments of the velocity control of a four-bar-linkage system are presented to verify the usefulness of the proposed control.

First, we assume that the controlled systems contain a nonlinear matrix gain before a linear discrete-time multivariable dynamic system. Then, a forward control based on a nominal system is employed to cancel the system nonlinear matrix gain and track the desired trajectory. A novel recurrent-neural-network (RNN) with a compensation of upper bound of its residue is applied to model the remained uncertainties in a compact subset /spl Omega/. The linearly parameterized connection weight for the function approximation error of the proposed network is also derived. An e-modification updating law with projection for weight matrix is employed to guarantee its boundedness and the stability of network without the requirement of persistent excitation. Then a discrete-time multivariable neuro-adaptive variable structure control is designed to improve the system performances. The semi-global (i.e., for a compact subset /spl Omega/) stability of the overall system is then verified by the Lyapunov stability theory. Finally, simulations are given to demonstrate the usefulness of the proposed controller.