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Sophisticated predetermined ratios are used to allocate portfolio asset weights to strike a good trade-off between profitability and risk in trading. Rebalancing these weights due to market fluctuations without incurring excessive transaction costs and tracking errors is a vital financial engineering problem. Rebalancing strategies can be modeled by discretely enumerating portfolio weights to form a grid space and then optimized via the Bellman equation. Discretization errors are reduced by increasing the grid resolution at the cost of increased computational time. To minimize errors with constrained computational resources (e.g., grid nodes), we vary the grid resolution according to the probability distribution of asset weights. Specifically, a grid space is first divided into several areas, and each area's probability is estimated. Then, the discretization error's upper bound is minimized by inserting an adequate number of grid nodes determined by Lagrange multipliers in a non-uniform fashion. In experiments, the proposed multiresolution rebalancing outperforms traditional uniform-resolution rebalancing and popular benchmark strategies such as the periodic, tolerance-band, and buy-and-hold strategies. [ABSTRACT FROM AUTHOR]

This article presents a hybrid model to predict the positions of the ball screw drive system of machine tool and then modify the trajectory through constructing a pre-compensation method to reduce servo errors in machine motion axes. To achieve this objective, a flexible control model is initially developed to characterize the ball screw drive system, and by leveraging this model, a high-bandwidth controller is constructed, with its physical representation, i.e. the state-space equation, being derived. Subsequently, a data-driven hybrid model is proposed to predict the positions of the ball screw drive system concerning the next multiple time steps from the current time step, and then the predicted positions associated with these steps are utilized as initial conditions to adjust and compensate for the physical model's prediction errors corresponding to these multiple time steps. As a result, a compensated trajectory with high tracking accuracy is generated. Finally, experiments confirm that the proposed prediction method offers superior prediction accuracy and enhanced adaptability, and the pre-compensated trajectory leads to reduced tracking errors. [Display omitted] • A hybrid model is constructed to pre-compensate servo error in the ball screw system. • A high bandwidth controller is designed by incorporating the feedback of the velocity. • A compensated trajectory with high tracking accuracy is generated. • The method can achieve a nice tracking accuracy and improve the bandwidth. • A series of comparative experiments validate the proposed method. [ABSTRACT FROM AUTHOR]

Tracking error leads to nonuniform flux distribution, local high temperature, and thermal stress of cavity receiver. However, the effects of tracking error on the optical–thermal conversion of dish concentrator–cavity receiver (DCCR) system are unclear. In this article, the optical–thermal coupling model of the DCCR system considering the tracking error is established, and the variations of the thermal performance index (the thermal efficiency, cavity maximum temperature, and outlet temperature) of the DCCR system under different direct normal irradiance (DNI), mass flow rate, inlet temperature, and cavity material are studied in detail. In the results, it is shown that the working condition is constant, tracking error increases, the outlet temperature and thermal efficiency decrease slightly, and the cavity maximum temperature increases. When tracking error is constant, with the increase of DNI or inlet temperature, the outlet and cavity maximum temperature increase, and the thermal efficiency decreases. With the increase of mass flow rate, the outlet and cavity maximum temperature decrease, and thermal efficiency increases. The cavity material with high thermal conductivity is beneficial to reduce the cavity maximum temperature. In this work, guidance for realizing safe and efficient service support can be provided. [ABSTRACT FROM AUTHOR]

The impact of tracking errors over the vibration interference is investigated. A novel expression is presented for the bidirectional laser tracking mechanism which takes in account both periscope communication terminal and beam acquisition process with beaconless technology. In this paper, platform microvibrations are measured and compensated to improve the tracking characteristics of the optical communication terminal. An experiment was conducted to verify the high precision tracking system with the combination of coarse and fine tracking technologies, which represents that the fine tracking error is suppressed to 2.1 μrad. This high precision implementation demonstrates the effectiveness of the tracking control loop, and will contribute to the space laser communication. [ABSTRACT FROM AUTHOR]

In this paper, for the output tracking problem of nonlinear discrete-time systems, a performance index is newly defined using the adaptive dynamic programming (ADP) technique to completely eliminate tracking errors in theory. In contrast to traditional definitions of performance indices in other ADP-based methods, the proposed performance index is not only designed from the perspective of output tracking errors but also introduced errors of system states and control inputs at adjacent stages, which is suitable for practical situations in many industrial applications, such as the alumina production, the flotation process, and the mineral grinding process. We proved that the obtained controller can make the system output fully track the given reference trajectory by applying the iterative criteria of the ADP technique. In addition, the proposed algorithm was implemented using a data-driven technique and neural networks to avoid analyzing and deducing the complicated dynamics of actual industrial processes. Finally, using historical data for a forced-circulation evaporation system in the alumina production process, the effect of the proposed approach was verified through a numerical simulation and compared with that of the proportional-integral controller. [ABSTRACT FROM AUTHOR]

As the solar energy utilization technology for renewable clean energy, actual parabolic trough receivers are subject to tracking errors and absorber tube installation errors, and the bellows and Kovar ring under these errors have a significant impact on the receiver's safety. Based on the MCRT-FVM-FEM principles in this paper, a receiver's optical-thermal-stress mathematical model is modeled and the thermal-stress performance and safety of the receiver's key components under two errors are evaluated. The correlation between the bellows and Kovar ring's performance and the two errors is analyzed. The results demonstrate that the lower tracking errors and larger installation errors markedly increment the absorber's deformation and have a negative impact on the receiver safety. Bellows and Kovar ring's asymmetrical temperature distribution causes variable swell and uneven stress under tracking and installation errors. Temperature gradient variation of bellows is more sensitive under errors than Kovar rings. Kovar ring's compressive stress rises substantially as the Y-directional installation error varied from −15 mm to 15 mm compared to other errors. With tracking errors exceeding 8 mrad, bellows' tensile stress and Kovar ring's compressive stress diminish under installation error. Thus, larger tracking errors significantly reduce the threat to the receiver when installation errors exist. [ABSTRACT FROM AUTHOR]

Exchange Traded Funds (ETF's) are one of the beloved passively managed funds that offer both retail and institutional investors an access to highly profitable and wide- range of diversifiable financial assets. The study aims to assess the ability of Indian equity ETF's in replicating the performance of their benchmark indices using a sample of 27 equity ETF's traded on the National Stock Exchange of India during the pre-pandemic period from 01/01/2015 to 31/12/2019. Evaluation of the performance of sample ETF's through risk-return analysis, risk-adjusted performance measures, tracking error analysis and multi-factor regression have revealed that the majority of the sample ETF's outperformed their tracking indices but with notable tracking errors during the study period. Further, the study also indicates that the returns of the sample ETF's have a significant and positive relationship with the returns of the index but are inversely related to risk and management fees. The results of this study will have major implications for investors in evaluating the performance of ETF's and fund managers as well in taking suitable measures to reduce tracking errors that will help in successful replication of the benchmark along with undertaking initiatives that will enable the ETF's to become price efficient. [ABSTRACT FROM AUTHOR]

Introduction. Conical scanning is applied for optimizing hardware resources in new devices, as well as when upgrading existing systems. All this explains the relevance of studying this type of direction finding systems.Aim. To adjust and complement the known calculation relations for the variance of direction finding results – an indicator of the quality (accuracy) of direction finding, as well as to determine the possibilities of optimizing direction finding and automatic object tracking processes.Materials and methods. Factors limiting the accuracy of direction finding via conical scanning were analyzed using spectral analysis. Mathematical modeling followed by statistical processing of quantitative results makes it possible to determine the conditions under which the influence of certain factors is predominant, as well as the conditions under which adjustment (completion) of the known calculation relations is required. The specified conditions are the errors at which the objects of direction finding are tracked. New calculation relations for the mentioned adjustment were determined by the methods of statistical radio engineering.Results. The validity of the calculation relations found is confirmed by mathematical modeling. Calculations and modeling lead to the need to optimize parameters for automatic object tracking systems.Conclusion. The study shows that, when choosing parameters for auto-tracking systems with conical scanning, it is important to implement object tracking not with minimal, but rather with optimized tracking errors in angular coordinates, which are to be estimated during direction finding. Moreover, the optimized errors (the values of static errors and the most probable values of the dynamic tracking errors) will require adjustment of the known analytical estimates for the variance of the direction finding results – the qualitative indicator of the direction finder (accuracy indicator). The determined analytical relationships allow such an adjustment to be performed, leading to an increased variance estimate by 10 dB.

· We examine the size and time-varying features of 72 ETFs' tracking errors. · ETFs beat the market in China, contrary to theory and other regional evidence. · IPO is a source of ETFs' excess returns, suggesting inefficiency in China market. · Harder to track index in bear market when ETF tracking abilities are more dispersed. · ETFs with smaller tracking errors tend to survive longer. We adopt 72 passive equity exchange-traded funds (ETFs) from the Chinese A-share market to examine the size and time-varying characteristics of their tracking errors, identify their determinants, and gain insight into the persistent and positive excess returns. Net asset value traces index better than closing price does; surviving ETFs perform better than delisted ones. The common determinants are fund expenses, liquidity and volatility of the index. Many determinants asymmetrically influence the tracking errors in bull and bear markets. Further examination based on the capital asset pricing model indicates persistent positive excess return is a result of A-share market inefficiency. [ABSTRACT FROM AUTHOR]

The thermal performance of a new type of solar water heater system consists of an array of parabolic trough collectors was studied. In CFD simulation of the system, a practical mathematical model was proposed that the realistic non-uniform solar flux distribution obtained by optical analysis is implemented in thermal modeling of the system. The system performance was investigated in three different tracking modes, stationary south-face, tilted N–S axis with daily tilt adjustment, and full tracking mode under the complexity of non-uniform solar flux distribution on the outer surface of the water pipe. The system was studied experimentally in Isfahan, Iran, with latitude and longitude of 32.6539° N, 51.6660° E, respectively. In experiments, the inlet water mass rate in the range of 0.005–0.15 kg s−1, and inlet temperature in the range of 20–40 °C was investigated. The system's average daily thermal efficiency at full tracking mode is greater than 60%, and at optimal conditions, the efficiency of more than 70% is also achievable. For the N–S axis with daily tilt adjusted equal to noontime zenith angle, its performance is greater than 45% and for the system at stationary mode with a tilt angle equal to local latitude is less than 40%. Results indicate that the system performance is severely affected by tracking errors, and the effect of these errors in tilt adjustment is more significant than surface azimuth adjustment. At full tracking mode, an accuracy error of 6° in tilt adjustment leads to a reduction of 10% in the system thermal efficiency, while the accuracy error up to 20° in azimuth adjustment has no significant effect on its performance. [ABSTRACT FROM AUTHOR]

The three‐dimensional trajectory tracking of an underactuated autonomous underwater vehicle (AUV) under the complex unknowns including model uncertainties and time‐varying disturbances is studied. The reference pitch angle and yaw angle are designed in kinematics, based on the time‐varying reference trajectory. Dynamics controllers are developed by incorporating the first‐order filter into the dynamic surface control (DSC), which simplifies the design process and overcome differential explosion in the traditional backstepping. To reduce the influence of the complex unknowns, an adaptive fuzzy‐based DSC scheme is employed to identify the lumped disturbances with arbitrary accuracy and further enhance system robustness. Lyapunov stability analysis demonstrates that tracking errors are bounded and converge to an arbitrarily small neighbourhood of zero. Finally, simulation studies and comparisons with DSC scheme are carried out to illustrate the effectiveness and superiority of the proposed scheme.

This study addresses the finite‐time tracking control problem for autonomous airships with uncertainties and external disturbances. Six‐degree‐of‐freedom kinematics and dynamics equations are established by considering the model uncertainties and external disturbances. To handle the model uncertainties and external disturbances, a finite‐time sliding mode disturbance observer (DOB) is designed. To have a good tracking performance, a finite‐time command‐filtered backstepping‐supertwisting controller is proposed with DOB. By using Lyapunov theory, the finite‐time convergence of tracking errors and the stability of the control method is proved. Finally, the simulation results show that the controller can track the desired trajectory well in spite of model uncertainties and external disturbances.

Herein, the effect of the various errors associated with concentrator, receiver, and tracking unit has been investigated on the optical performance of the large aperture parabolic trough solar collector (PTSC). The various combinations of the PTSC aperture sizes with the commercially available receiver sizes are considered for the analysis. The best combinations are identified based on the receiver's availability and intercept factor of the collector configuration. The effects of both the random (slope and tracking error) and non‐random (receiver alignment) errors have been investigated. It is observed that the PTSC performance should not be predicted based on the geometrical concentration ratio alone, as the focal length, absorber diameter, and aperture size also affect the PTSC performance. The intercept factor of large aperture PTSC is marginally affected by the receiver alignment error as compared to 5.77 m aperture. The rightward and leftward receiver displacement has no effect on the intercept factor for all the PTSC configurations. The slope error drastically affects the flux distribution as a change in the slope error from 0 to 8 mrad, the peak local concentration ratio decreases from 62 to 47. There is a decrease in the intercept factor by 22%, including a tracking error up to 8 mrad. [ABSTRACT FROM AUTHOR]

In a vector tracking loop (VTL) architecture, non‐linearities exist in discriminator functions and pseudo‐range/pseudo‐range rate measurement expressions. Generally, normalisation functions are used in discriminators to export the desired code phase or carrier frequency error and the extended Kalman filter is adopted to estimate receiver's states. This process could be accurate enough when the code phase or carrier frequency error approaches zero in the signal moderate environment but begins to distort due to non‐linearity when the tracking errors become large in harsh situations. This finally narrows the applicable range of VTL. To overcome this issue, a square‐root cubature Kalman filter (CKF)‐based VTL is designed in this study. The discriminator functions are employed directly as measurements of navigation filter, and the non‐linear expressions of discriminator functions in terms of the receiver's position, velocity, and time states are derived without normalisation. Then the CKF, which is competitive in high‐dimensional non‐linear systems, is employed in its square‐root version to estimate the position, velocity, acceleration, and time states of the receiver. Comparison trial results between traditional and proposed VTL illustrate that the proposed algorithm can not only keep a superior tracking accuracy but also improves the tracking stability of VTL in <20 dB‐Hz signal harsh circumstances. [ABSTRACT FROM AUTHOR]

In this brief, the robust trajectory tracking control problem is addressed for uncertain quadrotor systems with time delays. The quadrotor dynamical model is an under‐actuated system subject to non‐linearity, unmodelled uncertainties, parametric perturbations, external disturbances, and state and input time delays. A robust cascade trajectory tracking controller is developed by the backstepping method and the robust compensation theory. Theoretical analysis is given to prove that the tracking errors can converge into the given neighbourhood of the origin ultimately. An on‐line unidirectional tuning method is given to determine the controller parameters. Experimental results are provided to verify the effectiveness of the proposed control approach and the parameter tuning method. [ABSTRACT FROM AUTHOR]

This study investigates the distributed fixed‐time consensus tracking for high‐order uncertain non‐linear multi‐agent systems with switching topologies. Each follower is assumed to be in strict‐feedback form with both unknown parameters and mismatched disturbances. Different from traditional centralised tracking control problem, only a subset of the agents can acquire the desired trajectory information. By adopting backstepping method and dynamic surface control technique, the distributed fixed‐time consensus protocol and appropriate adaptive laws are designed without requiring knowledge of the upper bounds of disturbances. Moreover, the problem of 'explosion of complexity' in standard backstepping design is avoided. Under the proposed control protocol, it is shown from the Lyapunov‐based analysis that the tracking errors between all followers and the leader can converge to a small neighbourhood of the origin within a fixed time, even though the communication structures among agents dynamically change over time. Finally, a numerical example is carried out to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In image-guided neurosurgery, a registration between the patient and their pre-operative images and the tracking of surgical tools enables GPS-like guidance to the surgeon. However, factors such as brainshift, image distortion, and registration error cause the patient-to-image alignment accuracy to degrade throughout the surgical procedure no longer providing accurate guidance. The authors present a gesture-based method for manual registration correction to extend the usage of augmented reality (AR) neuronavigation systems. The authors’ method, which makes use of the touchscreen capabilities of a tablet on which the AR navigation view is presented, enables surgeons to compensate for the effects of brainshift, misregistration, or tracking errors. They tested their system in a laboratory user study with ten subjects and found that they were able to achieve a median registration RMS error of 3.51 mm on landmarks around the craniotomy of interest. This is comparable to the level of accuracy attainable with previously proposed methods and currently available commercial systems while being simpler and quicker to use. The method could enable surgeons to quickly and easily compensate for most of the observed shift. Further advantages of their method include its ease of use, its small impact on the surgical workflow and its small-time requirement.

This study describes a 3D ray tracer model for analysis of a small-scale solar concentrating system where thermal heat is collected for cooking purposes. Emitted sun rays were traced from the source through all reflections until they intercepted with the receiver or were lost. The algorithm of the ray tracer and its implementation in MATLAB is clearly described. The ray tracer was programmed to contribute to the development of small-scale concentrating solar energy systems with integrated heat storage units. The ray tracer was demonstrated for selected cases where continuous reflecting surfaces and flat mirror-tiled surfaces were compared. Off-focus sensitivity analysis was shown and this could provide guidelines for the required solar tracking accuracy. The flux distribution on the absorber was analysed and found to be concentrated on a small area on the target for continuous reflecting surfaces and having high intensities. However, for reflectors with mirror tiles, an elongated image was formed centred on the focal point with low intensities. Small misalignment of the reflector in the order 0.2° had minimal impact on the interception ratio, but any further increase in the tracking errors caused a sudden drop in the interception ratio to zero. Results showed that there is close agreement in flux distribution and the tracking error impact on interception ratio, when compared with the literature. This model could be a useful tool when designing the reflection and absorption components of solar concentrators for complex systems with several components in a non-symmetric 3D arrangement. [ABSTRACT FROM AUTHOR]

Distributed cooperative consensus tracking problem for a class of uncertain multi‐agent systems with a high‐dimensional leader under a directed communication topology is concerned. Compared with related works, the dynamics of the leader agent is allowed to be different from those of the followers and may not be measured. Meanwhile, the dynamics of each follower is subject to un‐modelled dynamics, unknown time‐varying delays, as well as external disturbances, which makes the model more suitable in various practical applications. Based on the M ‐matrix and Lyapunov–Krasovskii functional method, a distributed robust radial basis function neural network controller as well as a local observer is designed for each follower so as to guarantee the ultimate boundness of the tracking errors to the leader's output signals. By appropriately cutting down the neural network parameters to be updated online, the computational burden can be greatly reduced. The effectiveness of the proposed consensus approach is testified via a numerical example. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a model to keep the cutting load induced tool tip position and tool orientation errors of five-axis CNC machines within the desired tolerance limit by scheduling the feed along the tool paths. The cutting forces at the tool tip are transmitted to three translational and two rotary servo drives of the machine tool using its kinematic model. Tracking errors of each axis contributed by cutting forces are modeled using the disturbance transfer function of servo drives. The tracking errors are mapped to the workpiece coordinate system to evaluate the tool tip position and tool axis orientation errors at discrete tool path locations. The cutting forces, therefore the tracking errors, are modeled as a linear function of tangential feed velocity. The feed is adjusted to constrain the tool tip position and tool axis orientation errors at the desired tolerance levels along the tool path. The proposed algorithm has been experimentally validated by milling a curved tool path on a five-axis commercial CNC machine tool. It is shown that the proposed algorithm can significantly improve the part machining accuracy without increasing the machining time. [ABSTRACT FROM AUTHOR]

This article considers the use of Exchange-Traded Funds (ETFs) for indexing the portfolios of pension funds in Brazil. A methodology is proposed to allow the portfolio managers to combine ETFs and the assets composing its benchmark. The methodology is based on a mathematical programming model, with the resulting problem solved by any global optimization algorithm. The results obtained for two ETFs – BOVA11 (indexed to the Ibovespa) and BRAX11 (indexed to the IBrX-100) – are presented for illustrative purposes. All constraints imposed by the Brazilian regulatory environment have been incorporated in the studies presented. The methodology proved to be an interesting alternative to pension fund managers, with good results with respect to the control of tracking errors.

Five-axis CNC machine tools are widely used in machining parts with free form surfaces. This paper presents optimal placement of parts on the five-axis machine tool tables to minimize the tracking errors of the rotary servo drives. The cutting forces along the tool path are first simulated at the workpiece coordinate system in Computer-Aided-Manufacture (CAM) environment. The cutting torques transmitted to the rotary and translational drives are predicted using the location of the part on the table and kinematic configuration of the machine tool. The optimal location of the part on the table is identified by minimizing the forces transmitted to the rotary drives as torque disturbances. The proposed model has been experimentally validated on a five-axis machine with tilt-table configuration. It has been shown that the tracking and contouring errors can be significantly reduced with the proposed strategy, which can be used by process planners in digital simulation environment. [ABSTRACT FROM AUTHOR]

This study investigates the robust fixed‐time consensus tracking problem of second‐order multi‐agent systems under fixed topology. A novel type of non‐linear protocol and the corresponding sufficient conditions for achieving robust fixed‐time consensus tracking are proposed with the aid of sliding mode technique and Lyapunov theory. Compared to finite‐time consensus tracking, the convergence time of the tracking errors is globally bounded for any initial conditions of the agents, which is also the global information for each agent. Furthermore, the results obtained for second‐order multi‐agent systems are also extended to deal with the fixed‐time formation tracking problem for unicycle‐type robots. Extensive numerical experiments are performed to illustrate the effectiveness of the present theoretical results. [ABSTRACT FROM AUTHOR]

This study addres,ses a distributed optimal integrated tracking control method with disturbance rejection for separate kinematic and dynamic uncertain non‐holonomic mobile mechanical multi‐agent (NM3) systems. Initially, based on the graph theory, the overall tracking systems of agents are defined and the distributed optimal tracking problem of separate kinematics and dynamics is transformed into an equivalent distributed optimal regulation problem of the integrated affine system. Then, neural network (NN)‐based adaptive dynamic programming and cooperative differential game theory is utilised for control, in which only one NN is required for each agent. The NN weight‐tuning law and the online algorithm is developed to approximate the value function, and synchronously update both optimal control and worst disturbance laws in only one iterative loop. The tracking errors and function approximation errors are proven to be uniformly ultimately bounded using Lyapunov theory. Finally, as applications of the proposed method, control of the wheeled mobile multi‐robot system is discussed. The effectiveness of the method is demonstrated by the results of the comparative numerical simulation. [ABSTRACT FROM AUTHOR]

A class of switched multi‐agent tracking problems with variable tracking number is explored. During the whole tracking course, tracking agents switch and the tracking number varies over different time intervals. Consequently, tracking errors jump and the dimension of Laplacian matrix of the multi‐agent system changes, which increase the difficulty of analysis. To solve this problem, the authors proposed a switched tracking strategy and designed an average norm of tracking errors as a Lyapunov function. Thereafter, conditions guaranteeing the stability of each subsystem and overall stability of the switched tracking system are obtained. Finally, the effectiveness of the proposed tracking strategy and validity of the theoretical results are verified by a numerical simulation. [ABSTRACT FROM AUTHOR]

An indirect adaptive fuzzy prescribed performance control scheme is developed for a class of uncertain multi‐input and multi‐output feedback linearisable non‐linear systems with unknown control direction and external disturbances. The properties of symmetric matrix and hyperbolic tangent function are exploited and the predefined tracking performance boundary is used to design the adaptive fuzzy prescribed performance controller, which can avoid the possible singularity problem and calculating the inverse of matrix. A robust controller equipped with a Nussbaum‐type function is constructed to compensate for the lumped errors and solve the unknown control direction problem. The proposed scheme guarantees that all the signals in the resulting closed‐loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. Simulation results are used to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This research work examines the application of different statistical and empirical analysis methods to quantify pilot performance. A realistic approach and landing flight scenario is executed using the reconfigurable flight simulator at National Aerospace Laboratories and both subjective and quantitative measures are applied to the pilot performance data. Simulations were repeated for different difficult landing conditions like landing with degraded visibility, with crosswinds, with degraded aircraft handling qualities and with emergency conditions. Relative assessment of the different applicable metrics is made and significance of task difficulties on pilot performance is investigated. Changes in the pilot's control strategy with respect to primary and secondary tasks are also discussed in detail. Results indicate that analysing pilot's control strategy together with his/her deviations from predetermined flight profile provides a means to quantify pilot performance. [ABSTRACT FROM AUTHOR]

This paper presents the first study on the measurement of tracking errors using daily figures for gold exchange-traded funds (ETFs) in China. Three methods are employed to measure tracking errors: 1) calculating the absolute error measure, 2) calculating the differences between the standard deviation of the benchmark index and the ETF, and 3) a regression analysis of empirical returns. In general, the results suggest that the tracking errors of these ETFs in China are lower than those of equitybased ETFs in Hong Kong, the US, and Australia. This study further applied two optimised replication portfolios (50-10-10-30 and 90-2-3-5) for a total of three types of simulation portfolio. The overall results suggest that the performances of the optimised replication portfolios were better than the performance of the full replication portfolio. Our results provide valuable insight for both institutional and retail investors and the opportunity for exposure to a wide range of commodity ETFs in China.

This study investigates the problem of global decentralised fault‐tolerant control for a class of non‐linear large‐scale systems with unknown time‐delayed interconnections. The authors propose a novel time‐delay replacement technique. With this technique, a delay‐assumption independent controller is then developed. In addition, the delayed input variables of the fuzzy approximator are replaced by the bounded reference signals so that the global stability is achieved for the approximation‐based fault tolerant control field. In doing so, it will eliminate the limitation which is posted in estimating unknown functions in the traditional approach. The proposed controller ensures that all the signals in the closed‐loop system are globally uniformly ultimately bounded, and the tracking errors can converge to a small neighbourhood of the original point by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This study proposes hybrid control strategies for aggregated thermostatically controlled loads (TCLs) in order to provide ancillary service. The on/off control strategy and the setpoint‐regulation strategy are two typical control strategies. In order to reduce the tracking errors of the two control strategies, two improved methods were developed. The first method dispatches the aggregated loads to the automatic generation control signal following a step rule based on the state of charge. The second method optimises the controller parameters of the setpoint‐regulation strategy by the Powell optimisation algorithm. Based on these two improved methods, the hybrid control strategies with parallel and cascade control structures were established by dividing the TCLs into two clusters, and the optimal allocations of the loads, the reference signal and the tracking error between the two clusters were obtained by the particle swarm optimisation algorithm. The simulation results demonstrate that the hybrid control strategies can reduce the errors in load following. [ABSTRACT FROM AUTHOR]

Purpose One potential barrier for using prospective motion correction (PMC) in the clinic is the unpredictable nature of a scan because of the direct interference with the imaging sequence. We demonstrate that a second set of 'de-corrected' images can be reconstructed from a scan with PMC that show how images would have appeared without PMC enabled. Theory and Methods For three-dimensional scans, the effects of PMC can be undone by performing a retrospective reconstruction based on the inverse of the transformation matrix used for real time gradient feedback. Retrospective reconstruction is performed using a generalized SENSE approach with continuous head motion monitored using a single-marker optical camera system. Results Reverse retrospective reconstruction is demonstrated for phantom and in vivo scans using an magnetization-prepared rapid gradient echo (MPRAGE) sequence including parallel and Partial Fourier acceleration. Conclusion Reverse retrospective reconstruction can almost perfectly undo the effects of prospective feedback, and thereby provide a second image data set with the effects of motion correction removed. In case of correct feedback, one can directly compare the quality of the corrected with that of the uncorrected scan. Additionally, because erroneous feedback during PMC may introduce artifacts, it is possible to eliminate artifacts in a corrupted scan by reversing the false gradient updates. Magn Reson Med 75:2341-2349, 2016. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This study presents an adaptive decentralised dynamic surface control (DSC) approach for a class of large‐scale non‐linear systems with unknown non‐linear functions, unknown control gains, time‐varying delays and in the presence of unknown actuator failures. The considered actuator failures are modelled to cover both loss of effectiveness and stuck at some time‐varying values where the values, patterns and time occurrences of the failures are unknown. With the help of neural networks to approximate the unknown non‐linear functions, a novel adaptive actuator failure compensation controller is developed based on the backstepping method and the DSC approach. The appropriate Lyapunov–Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown actuator failures as well as uncertainties from unknown non‐linearities and time delays. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed and the tracking errors are proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This study focuses on the design of fixed‐time consensus for first‐order multi‐agent systems with unknown inherent non‐linear dynamics. A distributed control protocol, based on local information, is proposed to ensure the convergence of the tracking errors in finite time. Some conditions are derived to select the controller gains in order to obtain a prescribed convergence time regardless of the initial conditions. Simulations are performed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the input–output feedback linearisation and the internal dynamics stability of an underactuated autonomous underwater vehicle (AUV) in three‐dimensional space. By taking the coordinates of a virtual reference point in front of AUV system as the output equation, the input–output feedback linearisability of AUV kinematics and dynamics is guaranteed. A non‐linear controller is designed to make the reference point track a desired trajectory which is generated by an open‐loop path planner. Then, it is shown that the resulting internal dynamics of the system is stable. Neural network approximation capabilities and adaptive techniques are also adopted to compensate for unknown vehicle parameters, and constant or time‐varying disturbances induced by waves and ocean currents. A Lyapunov‐based stability analysis is used to show uniform ultimate boundedness of tracking errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed control system as a qualified candidate for real implementations in offshore applications. [ABSTRACT FROM AUTHOR]