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The purpose of this paper is to address a fractional order fuzzy PID (FOFPID) control approach for solving the problem of enhancing high precision tracking performance and robustness against to different reference trajectories of a 6-DOF Stewart Platform (SP) in joint space.

For the optimal design of the proposed control approach, tuning of the controller parameters including membership functions and input-output scaling factors along with the fractional order rate of error and fractional order integral of control signal is tuned with off-line by using particle swarm optimization (PSO) algorithm. For achieving this off-line optimization in the simulation environment, very accurate dynamic model of SP which has more complicated dynamical characteristics is required. Therefore, the coupling dynamic model of multi-rigid-body system is developed by Lagrange-Euler approach. For completeness, the mathematical model of the actuators is established and integrated with the dynamic model of SP mechanical system to state electromechanical coupling dynamic model. To study the validness of the proposed FOFPID controller, using this accurate dynamic model of the SP, other published control approaches such as the PID control, FOPID control and fuzzy PID control are also optimized with PSO in simulation environment. To compare trajectory tracking performance and effectiveness of the tuned controllers, the real time validation trajectory tracking experiments are conducted using the experimental setup of the SP by applying the optimum parameters of the controllers. The credibility of the results obtained with the controllers tuned in simulation environment is examined using statistical analysis.

The experimental results clearly demonstrate that the proposed optimal FOFPID controller can improve the control performance and reduce reference trajectory tracking errors of the SP. Also, the proposed PSO optimized FOFPID control strategy outperforms other control schemes in terms of the different difficulty levels of the given trajectories.

To the best of the authors’ knowledge, such a motion controller incorporating the fractional order approach to the fuzzy is first time applied in trajectory tracking control of SP.

The purpose of this paper is to analyse the performance of UK property funds using the dual sources of active management, Active Share and tracking error, to distinguish between the types of active management styles used by funds.

The authors use data on 38 UK real estate funds and classify them into five active management categories using the dual sources of active management, Active Share and tracking error. Then, the authors compare their return performance against Active Share, tracking error, fund size and leverage. Therefore the paper is able to answer two of the fundamental questions of investment: does active management add value and what form of active management, stock selection or factor risk, is better at adding value to the fund?

There are three main conclusions. First, the approach of Cremers and Petajisto (2009) and Petajisto (2010) is able to classify real estate funds in the UK on their management activity into categories that makes intuitive sense and seem stable over time. Second, balanced funds show relatively low Active Shares and particularly low tracking errors, due to the benefits of property-type diversification. In contrast, specialists funds display higher Active Shares and both low and high tracking errors depending on their stock-picking approach; diversified or concentrated. Third, an analysis over different time periods confirmed that funds in the sample essentially remained in the same categories within the sample period, even during markedly different market return periods. This implies that investors need to constantly monitor changes in the market and switch between fund management styles, if at all possible.

The analysis was only based on 38 funds with complete data over the sample period and the relationship between fees and active management was not examined, even though ultimately investors are concerned with returns after management fee. It would be instructive therefore if the number of funds and time period was expanded to see if the results are robust and to see whether management fees outweigh the benefits of active manager.

The findings should enable investors to make a more informed investment decisions in the future.

To the best of the author’s knowledge this is the first paper to apply the dual sources of active management, Active Share and tracking error, in the UK real estate market.

With the increasing demands of industrial applications, it is imperative for robots to accomplish good contact-interaction with dynamic environments. Hence, the purpose of this research is to propose an adaptive fractional-order admittance control scheme to realize a robot–environment contact with high accuracy, small overshoot and fast response.

Fractional calculus is introduced to reconstruct the classical admittance model in this control scheme, which can more accurately describe the complex physical relationship between position and force in the interaction process of the robot–environment. In this control scheme, the pre-PID controller and fuzzy controller are adopted to improve the system force tracking performance in highly dynamic unknown environments, and the fuzzy controller is used to improve the trajectory, transient and steady-state response by adjusting the pre-PID integration gain online. Furthermore, the stability and robustness of this control algorithm are theoretically and experimentally demonstrated.

The excellent force tracking performance of the proposed control algorithm is verified by constructing highly dynamic unstructured environments through simulations and experiments. In simulations and experiments, the proposed control algorithm shows satisfactory force tracking performance with the advantages of fast response speed, little overshoot and strong robustness.

The control scheme is practical and simple in the actual industrial and medical scenarios, which requires accurate force control by the robot.

A new fractional-order admittance controller is proposed and verified by experiments in this research, which achieves excellent force tracking performance in dynamic unknown environments.

Trajectory tracking error of robotic manipulator has limited its applications in trajectory tracking control systems. This paper aims to improve the trajectory tracking accuracy of robotic manipulator, so a linear-extended-state-observer (LESO)-based prescribed performance controller is proposed.

A prescribed performance function with the convergence rate, maximum overshoot and steady-state error is derived for the output error transformation, whose stability can guarantee trajectory tracking accuracy of the original robotic system. A LESO is designed to estimate and eliminate the total disturbance, which neither requires a detailed system model nor a heavy computation load. The stability of the system is proved via the Lyapunov theory.

Comparative experimental results show that the proposed controller can achieve better trajectory tracking accuracy than proportional-integral-differential control and linear active disturbance rejection control.

In the LESO-based prescribed performance control (PPC), the LESO was incorporated into the PPC design, it solved the problem of stabilizing the complex transformed system and avoided the costly offline identification of dynamic model and estimated and eliminated the total disturbance in real-time with light computational burden. LESO-based PPC further improved control accuracy on the basis of linear-active-disturbance-rejection-control. The new proposed method can reduce the trajectory tracking error of the robotic manipulators effectively on the basis of simplicity and stability.

This study discusses the tracking trajectory issue of the exoskeleton under the bounded disturbance and designs an useful tracking trajectory control method to solve it. By using the proposed control method, the tracking error can be successfully convergence to the assigned boundary. Meanwhile, the chattering effect caused by the actuators is already reduced, and the tracking performance of the pneumatic artificial muscles (PAMs) elbow exoskeleton is improved effectively.

A prescribed performance sliding mode control method was developed in this study to fulfill the joint position tracking trajectory task on the elbow exoskeleton driven by two PAMs. In terms of the control structure, a dynamic model was built by conforming to the adaptive law to compensate for the time variety and uncertainty exhibited by the system. Subsequently, a super-twisting algorithm-based second-order sliding mode control method was subjected to the exoskeleton under the boundedness of external disturbance. Moreover, the prescribed performance control method exhibits a smooth prescribed function with an error transformation function to ensure the tracking error can be finally convergent to the pre-designed requirement.

From the theoretical perspective, the stability of the control method was verified through Lyapunov synthesis. On that basis, the tracking performance of the proposed control method was confirmed through the simulation and the manikin model experiment.

As revealed by the results of this study, the proposed control method sufficiently applies to the PAMs elbow exoskeleton for tracking trajectory, which means it has potential application in the actual robot-assisted passive rehabilitation tasks.

The purpose of this paper is to improve the tracking performance of the carrier phase lock loop (PLL) in the strapdown inertial navigation system/global positioning system (SINS/GPS) integrated system with an innovative scheme of ultra‐tight integration.

First, providing the Doppler frequency for PLL using SINS velocity could enlarge the loop equivalent bandwidth and reduce the dynamic effect on the carrier loop. Meanwhile, lowering the filter bandwidth could increase the immunity to noise. Second, the relationships between the PLL and SINS errors have been analyzed, and then the PLL error model is established to eliminate the correlation between the pseudo‐range‐rate error and SINS velocity error. Third, the carrier frequency is regulated to improve the tracking accuracy, according to the error estimations of Kalman filter.

The innovative ultra‐tightly integrated system could not only enhance the anti‐jamming capability and the dynamic tracking performance of the tracking loops, but also improve the pseudo‐range‐rate measurements accuracy for the integrated filter.

This paper provides further study on the method of enhancing the carrier‐tracking performance and improving the integration mode in the ultra‐tightly integrated system based on the software‐defined GPS receiver.

The purpose of this paper is to improve the tracking performance of the tracking loops under high dynamic and severe jamming conditions.

First, as the two dominant measurement error sources of the tracking loops, the thermal noise jitter and the dynamic stress error are thoroughly analyzed. Second, a scheme of adaptive tracking loops, which could adaptively adjust the order and the bandwidth of tracking loops, is proposed. Third, real-time detections of the vehicle dynamics and the carrier-to-noise density ratio, and the adaptive bandwidth of the carrier loop are presented, respectively. Finally, simulations are operated to validate the excellent tracking performance of the adaptive tracking loops.

Based on the principle of minimizing the measurement errors, the loop order and bandwidth are adaptively adjusted in the proposed scheme. Thus, the anti-jamming capability and dynamic tracking performance of the tracking loops could be effectively enhanced.

This paper provides further study on the method of improving the tracking capability under complexly applied conditions of high dynamics and severe jamming.

The detections of carrier-to-noise density ratio and vehicle dynamics are used to adaptively adjusting the loop order and bandwidth, which could not only improve the measurement accuracy but also ensure the stable operation of tracking loops.

The aim of this study is to examine the tracking performance and tracking error (TE) of New Zealand exchange traded fsunds (ETFs).

The authors use regression methods and cointegration analysis to examine tracking performance. Multivariate regressions are used to examine the determinants of TE.

At the daily frequency, the authors observe that the ETFs have substantially different exposures to their underlying indexes from what they should be, which is confirmed by cointegration analysis. At the monthly frequency, tracking performance improves but still shows significant differences between the ETF and its underlying index. When the authors examine the TEs of the ETFs, the authors observe that these are substantial and that there is considerable variation in TE. Regression analysis shows that both characteristics of the ETF and the constituents of the index the ETF tracks, as well as the volatility of the underlying benchmark are determinants of the TE of the ETFs.

This is the first study to examine New Zealand-based ETFs. The findings contribute to understanding the performance of these ETFs and are of relevance to academics, investors and the ETF provider.

The purpose of this paper is to gain trajectory-tracking controllers for autonomous aircraft are optimized using a modified evolutionary, or genetic algorithm (GA).

The GA design utilizes real representation for the individual consisting of the collection of all controller gains subject to tuning. The initial population is generated randomly over pre-specified ranges. Alternatively, initial individuals are produced as random variations from a heuristically tuned set of gains to increase convergence time. A two-point crossover mechanism and a probabilistic mutation mechanism represent the genetic alterations performed on the population. The environment is represented by a performance index (PI) composed of a set of metrics based on tracking error and control activity in response to a commanded trajectory. Roulette-wheel selection with elitist strategy are implemented. A PI normalization scheme is also implemented to increase the speed of convergence. A flexible control laws design environment is developed, which can be used to easily optimize the gains for a variety of unmanned aerial vehicle (UAV) control laws architectures.

The performance of the aircraft trajectory-tracking controllers was shown to improve significantly through the GA optimization. Additionally, the novel normalization modification was shown to encourage more rapid convergence to an optimal solution.

The GA paradigm shows much promise in the optimization of highly non-linear aircraft trajectory-tracking controllers. The proposed optimization tool facilitates the investigation of novel control architectures regardless of complexity and dimensionality.

The addition of the evolutionary optimization to the WVU UAV simulation environment enhances significantly its capabilities for autonomous flight algorithm development, testing, and evaluation. The normalization methodology proposed in this paper has been shown to appreciably speed up the convergence of GAs.

The paper provides a flexible generalized framework for UAV control system evolutionary optimization. It includes specific novel structural elements and mechanisms for improved convergence as well as a comprehensive PI for trajectory tracking.

The problem of multi‐branch and multi‐functional financial service organisations in obtaining timely and actionable information in a manner that can enhance co‐ordination among operational units and personnel is addressed. Tracking systems are proposed as a vehicle for improving organisational integration through both the process of managing the system and using the information. A tracking system can aid decision and functional levels to learn from each other and co‐ordinate service activities. An approach for developing and maintaining an effective tracking system is summarised, and its contribution to organisational integration discussed.