Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Privacy Protection in COVID Data Tracking: Textual Analysis of the Literature

The literary review presented in the following paper aims to analyze the tracking tools used in different countries during the period of the COVID-19 pandemic. Tracking apps that have been adopted in many countries to collect data in a homogeneous and immediate way have made up for the difficulty of collecting data and standardizing evaluation criteria. However, the regulation on the protection of personal data in the health sector and the adoption of the new General Data Protection Regulation in European countries has placed a strong limitation on their use. This has not been the case in non-European countries, where monitoring methodologies have become widespread. The textual analysis presented is based on co-occurrence and multiple correspondence analysis to show the contact tracing methods adopted in different countries in the pandemic period by relating them to the issue of privacy. It also analyzed the possibility of applying Blockchain technology in applications for tracking contagions from COVID-19 and managing health data to provide a high level of security and transparency, including through anonymization, thus increasing user trust in using the apps.

FPGA and computer-vision-based atom tracking technology for scanning probe microscopy

Atom tracking technology enhanced with innovative algorithms has been implemented in this study,utilizing a comprehensive suite of controllers and software independently developed domestically.Leveraging an on-board field-programmable gate array(FPGA)with a core frequency of 100 MHz,our system facilitates reading and writing operations across 16 channels,performing discrete incremental proportional-integral-derivative(PID)calculations within 3.4 microseconds.Building upon this foundation,gradient and extremum algorithms are further integrated,incorporating circular and spiral scanning modes with a horizontal movement accuracy of 0.38 pm.This integration enhances the real-time performance and significantly increases the accuracy of atom tracking.Atom tracking achieves an equivalent precision of at least 142 pm on a highly oriented pyrolytic graphite(HOPG)surface under room temperature atmospheric conditions.Through applying computer vision and image processing algorithms,atom tracking can be used when scanning a large area.The techniques primarily consist of two algorithms:the region of interest(ROI)-based feature matching algorithm,which achieves 97.92%accuracy,and the feature description-based matching algorithm,with an impressive 99.99%accuracy.Both implementation approaches have been tested for scanner drift measurements,and these technologies are scalable and applicable in various domains of scanning probe microscopy with broad application prospects in the field of nanoengineering.

Beam Training and Tracking in mmWave Communication:A Survey

Communicating on millimeter wave(mmWave)bands is ushering in a new epoch of mobile communication which provides the availability of 10 Gbps high data rate transmission.However,mmWave links are easily prone to short transmission range communication because of the serious free space path loss and the blockage by obstacles.To overcome these challenges,highly directional beams are exploited to achieve robust links by hybrid beamforming.Accurately aligning the transmitter and receiver beams,i.e.beam training,is vitally important to high data rate transmission.However,it may cause huge overhead which has negative effects on initial access,handover,and tracking.Besides,the mobility patterns of users are complicated and dynamic,which may cause tracking error and large tracking latency.An efficient beam tracking method has a positive effect on sustaining robust links.This article provides an overview of the beam training and tracking technologies on mmWave bands and reveals the insights for future research in the 6th Generation(6G)mobile network.Especially,some open research problems are proposed to realize fast,accurate,and robust beam training and tracking.We hope that this survey provides guidelines for the researchers in the area of mmWave communications.

A Retrodirective Array Enabled by CMOS Chips for Two-Way Wireless Communication with Automatic Beam Tracking

This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic complementary metal-oxide semiconductor(CMOS)process.The highly integrated CMOS chip includes a receiving(Rx)chain,a transmitting(Tx)chain,and a unique tracking phaselocked loop(PLL)for the crucial conjugated phase recovery in the RDA.This article also proposes a method to reduce the beam pointing error(BPE)in a conventional RDA.To validate the above ideas simply yet without loss of generality,a 2.4 GHz RDA is demonstrated through two-way communication links between the Rx and Tx chains,and an on-chip quadrature coupler is designed to achieve a nonretrodirective signal suppression of 23 dBc.The experimental results demonstrate that the proposed RDA,which incorporates domestically manufactured low-cost 0.18 lm CMOS chips,is capable of automatically tracking beams covering±40with a reduced BPE.Each CMOS chip in the RDA has a compact size of 4.62 mm^(2) and a low power consumption of 0.15 W.To the best of the authors’knowledge,this is the first research to demonstrate an RDA with a fully customized CMOS chip for wireless communication with automatic beam tracking。

Quantifying the agreement and accuracy characteristics of four satellite-based LULC products for cropland classification in China

Various land use and land cover(LULC)products have been produced over the past decade with the development of remote sensing technology.Despite the differences in LULC classification schemes,there is a lack of research on assessing the accuracy of their application to croplands in a unified framework.Thus,this study evaluated the spatial and area accuracies of cropland classification for four commonly used global LULC products(i.e.,MCD12Q1V6,GlobCover2009,FROM-GLC and GlobeLand30)based on the harmonised FAO criterion,and quantified the relationships between four factors(i.e.,slope,elevation,field size and crop system)and cropland classification agreement.The validation results indicated that MCD12Q1 and GlobeLand30 performed well in cropland classification regarding spatial consistency,with overall accuracies of 94.90 and 93.52%,respectively.The FROMGLC showed the worst performance,with an overall accuracy of 83.17%.Overlaying the cropland generated by the four global LULC products,we found the proportions of complete agreement and disagreement were 15.51 and 44.72% for the cropland classification,respectively.High consistency was mainly observed in the Northeast China Plain,the Huang-Huai-Hai Plain and the northern part of the Middle-lower Yangtze Plain,China.In contrast,low consistency was detected primarily on the eastern edge of the northern and semiarid region,the Yunnan-Guizhou Plateau and southern China.Field size was the most important factor for mapping cropland.For area accuracy,compared with China Statistical Yearbook data at the provincial scale,the accuracies of different products in descending order were:GlobeLand30,FROM-GLC,MCD12Q1,and GlobCover2009.The cropland classification schemes mainly caused large area deviations among the four products,and they also resulted in the different ranks of spatial accuracy and area accuracy among the four products.Our results can provide valuable suggestions for selecting cropland products at the national or provincial scale and help cropland mapping and reconstruction,which is essential for food security and crop management,so they can also contribute to achieving the Sustainable Development Goals issued by the United Nations.

Urea breath test for Helicobacter pylori infection in adult dyspeptic patients: A meta-analysis of diagnostic test accuracy

BACKGROUND Helicobacter pylori(H.pylori)infection has been well-established as a significant risk factor for several gastrointestinal disorders.The urea breath test(UBT)has emerged as a leading non-invasive method for detecting H.pylori.Despite numerous studies confirming its substantial accuracy,the reliability of UBT results is often compromised by inherent limitations.These findings underscore the need for a rigorous statistical synthesis to clarify and reconcile the diagnostic accuracy of the UBT for the diagnosis of H.pylori infection.AIM To determine and compare the diagnostic accuracy of 13C-UBT and 14C-UBT for H.pylori infection in adult patients with dyspepsia.METHODS We conducted an independent search of the PubMed/MEDLINE,EMBASE,and Cochrane Central databases until April 2022.Our search included diagnostic accuracy studies that evaluated at least one of the index tests(^(13)C-UBT or ^(14)C-UBT)against a reference standard.We used the QUADAS-2 tool to assess the methodo-logical quality of the studies.We utilized the bivariate random-effects model to calculate sensitivity,specificity,positive and negative test likelihood ratios(LR+and LR-),as well as the diagnostic odds ratio(DOR),and their 95%confidence intervals.We conducted subgroup analyses based on urea dosing,time after urea administration,and assessment technique.To investigate a possible threshold effect,we conducted Spearman correlation analysis,and we generated summary receiver operating characteristic(SROC)curves to assess heterogeneity.Finally,we visually inspected a funnel plot and used Egger’s test to evaluate publication bias.endorsing both as reliable diagnostic tools in clinical practice.CONCLUSION In summary,our study has demonstrated that ^(13)C-UBT has been found to outperform the ^(14)C-UBT,making it the preferred diagnostic approach.Additionally,our results emphasize the significance of carefully considering urea dosage,assessment timing,and measurement techniques for both tests to enhance diagnostic precision.Nevertheless,it is crucial for researchers and clinicians to evaluate the strengths and limitations of our findings before implementing them in practice.

Automatic velocity picking based on optimal key points tracking algorithm

Picking velocities from semblances manually is laborious and necessitates experience. Although various methods for automatic velocity picking have been developed, there remains a challenge in efficiently incorporating information from nearby gathers to ensure picked velocity aligns with seismic horizons while also improving picking accuracy. The conventional method of velocity picking from a semblance volume is computationally demanding, highlighting a need for a more efficient strategy. In this study, we introduce a novel method for automatic velocity picking based on multi-object tracking. This dynamic tracking process across different semblance panels can integrate information from nearby gathers effectively while maintaining computational efficiency. First, we employ accelerated density clustering on the velocity spectrum to discern cluster centers without the requirement for prior knowledge regarding the number of clusters. These cluster centers embody the maximum likelihood velocities of the main subsurface structures. Second, our proposed method tracks key points within the semblance volume. Kalman filter is adopted to adjust the tracking process, followed by interpolation on these tracked points to construct the final velocity model. Our synthetic data example demonstrates that our proposed algorithm can effectively rectify the picking errors of the clustering algorithm. We further compare the performances of the clustering method(CM), the proposed tracking method(TM), and the variational method(VM) on a field dataset from the Gulf of Mexico. The results attest that our method offers superior accuracy than CM, achieves comparable accuracy with VM, and benefits from a reduced computational cost.

Diagnostic Accuracy of Computerized Bowel Sound Analysis with Non-Invasive Devices for Irritable Bowel Syndrome:A Systematic Review and Meta-Analysis

Objective To assess the diagnostic accuracy of bowel sound analysis for irritable bowel syndrome(IBS)with a systematic review and meta-analysis.Methods We searched MEDLINE,Embase,the Cochrane Library,Web of Science,and IEEE Xplore databases until September 2023.Cross-sectional and case-control studies on diagnostic accuracy of bowel sound analysis for IBS were identified.We estimated the pooled sensitivity,specificity,positive likelihood ratio,negative likeli-hood ratio,and diagnostic odds ratio with a 95% confidence interval(CI),and plotted a summary receiver operat-ing characteristic curve and evaluated the area under the curve.Results Four studies were included.The pooled diagnostic sensitivity,specificity,positive likelihood ratio,nega-tive likelihood ratio,and diagnostic odds ratio were 0.94(95%CI,0.87‒0.97),0.89(95%CI,0.81‒0.94),8.43(95%CI,4.81‒14.78),0.07(95%CI,0.03‒0.15),and 118.86(95%CI,44.18‒319.75),respectively,with an area under the curve of 0.97(95%CI,0.95‒0.98).Conclusions Computerized bowel sound analysis is a promising tool for IBS.However,limited high-quality data make the results'validity and applicability questionable.There is a need for more diagnostic test accuracy studies and better wearable devices for monitoring and analysis of IBS.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Investigation of Inside-Out Tracking Methods for Six Degrees of Freedom Pose Estimation of a Smartphone in Augmented Reality

Six degrees of freedom(6DoF)input interfaces are essential formanipulating virtual objects through translation or rotation in three-dimensional(3D)space.A traditional outside-in tracking controller requires the installation of expensive hardware in advance.While inside-out tracking controllers have been proposed,they often suffer from limitations such as interaction limited to the tracking range of the sensor(e.g.,a sensor on the head-mounted display(HMD))or the need for pose value modification to function as an input interface(e.g.,a sensor on the controller).This study investigates 6DoF pose estimation methods without restricting the tracking range,using a smartphone as a controller in augmented reality(AR)environments.Our approach involves proposing methods for estimating the initial pose of the controller and correcting the pose using an inside-out tracking approach.In addition,seven pose estimation algorithms were presented as candidates depending on the tracking range of the device sensor,the tracking method(e.g.,marker recognition,visual-inertial odometry(VIO)),and whether modification of the initial pose is necessary.Through two experiments(discrete and continuous data),the performance of the algorithms was evaluated.The results demonstrate enhanced final pose accuracy achieved by correcting the initial pose.Furthermore,the importance of selecting the tracking algorithm based on the tracking range of the devices and the actual input value of the 3D interaction was emphasized.

Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution

Parking difficulties have become a social issue that people have to solve.Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents.The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method(RF-LNMPC)in order to improve the overall path tracking accuracy in parking conditions.Firstly,A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively.Secondly,the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization,of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution.Thirdly,the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented.The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically.Finally,the proposed RF-LNMPC is implemented on a selfdriving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions.The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.

Accurately tracking hypersonic gliding vehicles via an LEO mega-constellation in relay tracking mode

In order to effectively defend against the threats of the hypersonic gliding vehicles(HGVs),HGVs should be tracked as early as possible,which is beyond the capability of the ground-based radars.Being benefited by the developing megaconstellations in low-Earth orbit,this paper proposes a relay tracking mode to track HGVs to overcome the above problem.The whole tracking mission is composed of several tracking intervals with the same duration.Within each tracking interval,several appropriate satellites are dispatched to track the HGV.Satellites that are planned to take part in the tracking mission are selected by a new derived observability criterion.The tracking performances of the proposed tracking mode and the other two traditional tracking modes,including the stare and track-rate modes,are compared by simulation.The results show that the relay tracking mode can track the whole trajectory of a HGV,while the stare mode can only provide a very short tracking arc.Moreover,the relay tracking mode achieve higher tracking accuracy with fewer attitude controls than the track-rate mode.

Practical Prescribed Time Tracking Control With Bounded Time-Varying Gain Under Non-Vanishing Uncertainties

This paper investigates the prescribed-time control(PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbances makes PTC synthesis nontrivial. In this work, a control method that does not involve infinite time-varying gain is proposed, leading to a practical and global prescribed time tracking control solution for the strict-feedback systems, in spite of both the mismatched and nonvanishing uncertainties. Different from methods based on control switching to avoid the issue of infinite control gain that involves control discontinuity at the switching point, in our method a softening unit is exclusively included to ensure the continuity of the control action. Furthermore, in contrast to most existing prescribed-time control works where the control scheme is only valid on a finite time interval, in this work, the proposed control scheme is valid on the entire time interval. In addition, the prior information on the upper or lower bound of gi is not in need,enlarging the applicability of the proposed method. Both the theoretical analysis and numerical simulation confirm the effectiveness of the proposed control algorithm.

Accuracy of FreeStyle Libre flash glucose monitoring in patients with type 2 diabetes who migrated from highlands to plains

BACKGROUND The FreeStyle Libre flash glucose monitoring(FGM)system entered the Chinese market in 2017 to complement the self-monitoring of blood glucose.Due to its increased usage in clinics,the number of studies investigating its accuracy has increased.However,its accuracy has not been investigated in highland populations in China.AIM To evaluate measurements recorded using the FreeStyle Libre FGM system compared with capillary blood glucose measured using the enzyme electrode method in patients with type 2 diabetes(T2D)who had migrated within 3 mo from highlands to plains.METHODS Overall,68 patients with T2D,selected from those who had recently migrated from highlands to plains(within 3 mo),were hospitalized at the Department of Endocrinology from August to October 2017 and underwent continuous glucose monitoring(CGM)with the FreeStyle Libre FGM system for 14 d.Throughout the study period,fingertip capillary blood glucose was measured daily using the enzyme electrode method(Super GL,China),and blood glucose levels were read from the scanning probe during fasting and 2 h after all three meals.Moreover,the time interval between reading the data from the scanning probe and collecting fingertip capillary blood was controlled to<5 min.The accuracy of the FGM system was evaluated according to the CGM guidelines.Subsequently,the factors influencing the mean absolute relative difference(MARD)of this system were analyzed by a multiple linear regression method.RESULTS Pearson’s correlation analysis showed that the fingertip and scanned glucose levels were positively correlated(R=0.86,P=0.00).The aggregated MARD of scanned glucose was 14.28±13.40%.Parker's error analysis showed that 99.30%of the data pairs were located in areas A and B.According to the probe wear time of the FreeStyle Libre FGM system,MARD_(1 d) and MARD_(2-14 d) were 16.55%and 14.35%,respectively(t=1.23,P=0.22).Multiple stepwise regression analysis showed that MARD did not correlate with blood glucose when the largest amplitude of glycemic excursion(LAGE)was<5.80 mmol/L but negatively correlated with blood glucose when the LAGE was≥5.80 mmol/L.CONCLUSION The FreeStyle Libre FGM system has good accuracy in patients with T2D who had recently migrated from highlands to plains.This system might be ideal for avoiding the effects of high hematocrit on blood glucose monitoring in populations that recently migrated to plains.MARD is mainly influenced by glucose levels and fluctuations,and the accuracy of the system is higher when the blood glucose fluctuation is small.In case of higher blood glucose level fluctuations,deviation in the scanned glucose levels is the highest at extremely low blood glucose levels.

Demagnetization Analysis and Velocity Tracking Control of In-wheel Motor

The error caused by irreversible demagnetization damages the accurate velocity tracking of an in-wheel motor in a mobile robot.A current feedforward vector control system based on ESO is proposed to compensate it for the demagnetization motor.A demagnetization mathematical model is established to describe a permanent magnet synchronous motor,which took the change of permanent magnet flux linkage parameters as a factor to count the demagnetization error in velocity tracking.The uncertain disturbance estimation model of the control system is built based on ESO,which eliminates the system error by the feedforward current compensation.It is compared with the vector control method in terms of control accuracy.The simulation results show that the current feedforward vector control method based on ESO reduces the velocity tracking error greatly in conditions of motor demagnetization less than 30%.It is effective to improve the operation accuracy of the mobile robot.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

Hydrodynamic characteristics and particle tracking of 90° lateral intakes at an inclined river slope

Lateral intakes are common in rivers.The pump effciency and sediment deposition are determined by the local hydrodynamic characteristics and mainstream division width.The hydraulic characteristics of lateral withdrawal from inclined river slopes at different intake elevations should be investigated.Meanwhile,the division width exhibits significant vertical non-uniformity at an inclined river slope,which should be clarified.Hence,a three-dimensional(3-D)hydrodynamic and particle-tracking model was developed with the Open Source Field Operation and Manipulation(Open FOAM),and the model was validated with physical model tests for 90°lateral withdrawal from an inclined side bank.The flow fields,withdrawal sources,and division widths were investigated with different intake bottom elevations,withdrawal discharges,and main channel velocities.This study showed that under inclined side bank conditions,water entered the intake at an oblique angle,causing significant 3-D spiral flows in the intake rather than two-dimensional closed recirculation.A lower withdrawal discharge,a lower bottom elevation of the intake,or a higher main channel velocity could further strengthen this phenomenon.The average division width and turbulent kinetic energy were smaller under inclined side bank conditions than under vertical bank conditions.With a low intake bottom elevation,a low withdrawal discharge,or a high main channel velocity,the sources of lateral withdrawal were in similar ranges near the local inclined bank in the vertical direction.Under inclined slope conditions,sediment deposition near the intake entrance could be reduced,compared to that under vertical slope conditions.The results provide hydrodynamic and sediment references for engineering designs for natural rivers with inclined terrains.

Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

Guaranteed Cost Attitude Tracking Control for Uncertain Quadrotor Unmanned Aerial Vehicle Under Safety Constraints

In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.