Ultimate Error Research Articles

Identifying Objects at the Quantum Limit for Superresolution Imaging.

We consider passive imaging tasks involving discrimination between known candidate objects and investigate the best possible accuracy with which the correct object can be identified. We analytically compute quantum-limited error bounds for hypothesis tests on any library of incoherent, quasimonochromatic objects when the imaging system is dominated by optical diffraction. We further show that object-independent linear-optical spatial processing of the collected light exactly achieves these ultimate error rates, exhibiting scaling superior to spatially resolved direct imaging as the scene becomes more severely diffraction limited. We apply our results to example imaging scenarios and find conditions under which superresolution object discrimination can be physically realized.

Hybrid analog/digital signal detector with reduction in number of receive antennas for multiuser uplink massive MIMO systems

Low-complexity signal detection with a large number of receive antennas is crucial to the success of multiuser uplink massive multiple-input multiple-output (MIMO) systems. In this paper, we introduce a new hybrid analog/digital signal detector with a reduction in the number of receive antennas (RN-RA) for this case. Specifically, a convex optimization problem is formulated to decrease the number of active antennas used for receiving signals. With the proposed hybrid structure, the number of radio-frequency (RF) chains is reduced to equal the number of uplink users, and the tuning of phase shifters in the analog part is free from optimization. Besides, an efficient decision-aided Gauss-Seidel (DA-GS) iteration is used in the digital part to lower the implementation complexity and improve the ultimate error rate of the system at the same time. All these make our detector be comparable to the suboptimal fully-digital minimum-mean-squared error (MMSE) detector in terms of the error-rate performance, and become a complete low-complexity solution for signal detection in this kind of usage.

Political Trust and the Ultimate Attribution Error in Explaining Successful and Failed Policy Initiatives

This study examines how the ultimate attribution error (group attribution bias) plays out in the interaction between trust/distrust in a political actor and the success or failure of the actor’s proposed policy initiative. We conducted an experiment where student participants ( n = 222) from Latvian universities evaluated reasons for the success versus failure of a policy initiative proposed by a trusted versus untrusted political party in terms of the perceived benevolence, competence, and integrity of the political party as dispositional factors contributing to the initiative’s outcome, or external circumstances not under the political party’s control. The results showed evidence of the ultimate attribution error in the participants’ answers. The success of a policy initiative was explained more in terms of positive dispositions of the authoring party when the initiative came from a trusted political party than when it came from a distrusted party, and an initiative’s failure was explained more in terms of a lack of these positive dispositions when the initiative came from a distrusted party. There were no indications of the ultimate attribution error when explaining an initiative’s success or failure by external factors not controlled by the party authoring the initiative. The results provide additional insight into how the mechanisms of intergroup attribution play out in the context of political trust and may influence both overall trust in political actors and the evaluation of specific policy initiatives authored by these actors.

Event-triggered dynamic surface control of uncertain nonlinear systems

In this paper, an event-triggered dynamic surface controller is proposed for strict-feedback nonlinear networked systems with mismatched uncertainties. Towards this aim and first of all, an event-based dynamic surface control law is designed. Then, the closed-loop error dynamics is derived and rewritten as a linear dynamics with nonlinear perturbation terms. Next, these terms are classified into vanishing and nonvanishing perturbations. Finally, by imposing some constraints on the nonvanishing terms, an event-triggering mechanism is constructed. By formulating the imposed constraints in the form of linear matrix inequalities (LMIs) and using the ultimate boundedness theory, the ultimate error boundedness and quadratic tracking objectives are addressed in the framework of convex optimisation. The absence of the Zeno behaviour, which is an important feature of any event-triggered methodology, is also proven. The validity of the theoretical results is illustrated by applying the proposed method to a remotely operated underwater vehicle in a simulation study as well as an experimental implementation on a magnetic levitation system.

Adaptive Algorithms for Measuring the Parameters of Low-Frequency Noise of Semiconductor Devices Under the Conditions of Mass Control

We solve the problem of increasing the reliability and efficiency of quality control for semiconductor devices and present the analysis of the conditions of measuring the power spectral density of low-frequency noise in semiconductor devices with spectra of the form G(f) ~ f–γ (γ is the parameter of shape of the spectrum) under the conditions of mass quality control. The measurement error of the power spectral density under given conditions of measurements strongly depends on the value of the parameter of form of the spectrum. We propose adaptive algorithms aimed at measuring the parameters of low-frequency noise in the cases of a given ultimate measurement error of power spectral density and a given duration of a single measurement. The proposed algorithms include the preliminary evaluation of the parameter of shape of the spectrum with subsequent measurements of the power spectral density of noise for the optimal bandwidth of the filter. The optimal bandwidth of the filter is established according to the results of preliminary evaluation of the parameter of shape of the spectrum. In both cases, we obtain estimates of the gain in a sense of the mean value over the set (ensemble) of controlled products. We also discussed the possibility of adaptive or cognitive adjustment of the parameters of measuring system in the control process based on the results of evaluation of sample means in the training sample.

Optimal environment localization

Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multi-mode system. We derive bounds for the ultimate error probability affecting this multi-ary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).

Ultimate Limits for Multiple Quantum Channel Discrimination

Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication. Although the limits of hypothesis testing between quantum states have been completely clarified by the pioneering works of Helstrom in the 1970s, the more difficult problem of hypothesis testing with quantum channels, i.e., channel discrimination, is less understood. This is mainly due to the complications coming from the use of input entanglement and the possibility of employing adaptive strategies. In this Letter, we establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries. As an example, we apply our results to the problem of channel position finding, where the goal is to identify the location of a target channel among multiple background channels. In this general setting, we find that the use of entanglement offers a great advantage over strategies without entanglement, with nontrivial implications for data readout, target detection, and quantum spectroscopy.

Hate begets hate: anti-refugee violence increases anti-refugee attitudes in Germany

ABSTRACT How does ethnic violence affect the perpetrator group’s attitudes towards the victim group? Combining the security threat and ultimate attribution error, I expect that perpetrator group members react to security threats caused by ethnic violence to form negative attitudes towards the victim group. This study tests this hypothesis using the case of ethnic violence against refugees who came to Germany during the “migrant crisis” in 2015. Results show that a higher rate of anti-refugee violence in a German state is associated with more negative attitudes towards refugees among German natives. The effect of ethnic violence is more prominent among Germans with higher concerns for security, pinpointing the threat mechanisms. A series of additional tests, including instrumental variable strategy, Bayesian analysis, and robustness checks support the conclusion. The results of this study indicate that ethnic violence induces negative attitudes among the perpetrator group towards the victim group.

LMI-based criterion for global Mittag-Leffler lag quasi-synchronization of fractional-order memristor-based neural networks via linear feedback pinning control

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo’s fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems.

Analysis and Rectification of the Asynchronous Sampling Effect in the Pulse-Position Modulation Systems

Although the clock synchronization is of utmost importance in communications, it is quite difficult to achieve in practice. Consequently, the asynchronous effect emerges as a critical problem for all pulse-position modulation (PPM) systems. In this paper, the impact of the sampling-period misalignment is studied and evaluated. A new analytical model is established to govern the misalignment between the slot periods of the transmitted and received signals. The ultimate error rate related to this kind of unfavorable misalignment is also derived theoretically. Besides, we propose a new algorithm, which can adjust the onsets of the slot periods dynamically, to mitigate this misalignment and improve the error performance. To justify our new analysis and algorithm, a visible-light communication system using single-pulse PPM is taken as a practical example. Simulation results demonstrate that the effectiveness of our proposed algorithm is very promising. The frame-error rate of the rectified PPM signal is around 10−5 across all of the misalignment values.

Disturbance observer-based control of UAVs with prescribed performance

ABSTRACTThis work proposes a novel robust nonlinear control method for trajectory tracking of a quadrotor unmanned aerial vehicle using the prescribed performance control technique and disturbance observers, in the presence of external disturbances and uncertainties of physical parameters. By exploiting the cascaded structure of the position subsystems and the attitude subsystems, the controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid the explosion of the controller complexity. For each axis of the subsystem with uncertainties, the prescribed performance control technique is adopted to ensure a moderate control performance. Then a disturbance observer is constructed to enhance the corresponding controller to achieve a sufficiently small ultimate error. Not only the control performance of the overall control system, but also the behaviour of all the internal error signals are analysed rigorously. Finally, the performance of the proposed controller is confirmed by simulation studies.

Study of Mechanical Properties of Carbon Steel Plate SA-516 Gr. 70 Welded by SAW Using V-Shape Joint Design

Submerged arc welding (SAW) is a fusion type welding and it is considered one of the most important welding types due to its inherent capabilities of high welding speed, high deposition rate, welding large thickness plates owing to its deep penetration characteristic and many other advantages. In this study, the goal was to investigate the effect of welding parameters, namely (welding current and welding speed) as well as the joint design on the mechanical properties (yield stress, bending force on the face of the weldment and hardness of the weld metal. Experiments were conducted employing Design of Expert (DOE) software and Response Surface Methodology (RSM) technique. The experiments were conducted by welding ASME SA-516 Gr. 70 steel plate with dimension (300 mm × 150 mm × 10 mm) depending upon the design matrix developed via the DOE. Results manifested that the optimum process parameters for maximum yield stress, maximum bending force and minimum hardness were at (425 amps) welding current and (35 cm/min) welding speed, where the arc voltage was held constant at (37 volts). The optimum values for the yield stress, bending force and hardness were (474.447 MPa, 36.997 kN and 150 HV), respectively. Finally, it was found that the predicted and experimental results of yield stress, bending force and hardness agree very well according to the ultimate error (1.05%, 1.92%, and 4.25 %), respectively.

Delay-Tolerant Adaptive Robust Tracking Control of Uncertain Time-Delay Systems

The simultaneous presence of parameter variations, time-varying disturbances, and delay in the control loop of an $n{\text{th}}$ -order (possibly unstable) dynamical system makes formal tracking control design difficult. Existing model-based control methodologies can handle only a subset of the above-mentioned complexities, and hence, become insufficient to accurately track the desired trajectory. In this paper, a prediction-based adaptive robust control framework is proposed for high performance control of dynamical systems subject to the above-mentioned complexities, which involves the following. First, prediction-based projection-type adaptation laws with model compensation to reduce the effect of parameter uncertainties under delay and time-varying disturbances. Second, a robust prediction scheme that factors in both unknown parameters and disturbance uncertainties under delay to handle the resulting unmatched disturbances. Third, prediction-based continuous robust feedback to attenuate the cumulative effect of disturbance terms due to uncertain prediction. The controller guarantees semiglobal, exponential convergence of the tracking error with an ultimate error bound proportional to delay, disturbance, and controller gain. The controller effectiveness is demonstrated with an illustrative flight control example and compared with the baseline adaptive robust controller.

Optimal state observation using quadratic boundedness: Application to UAV disturbance estimation

Abstract This paper presents the design of a state observer which guarantees quadratic boundedness of the estimation error. By using quadratic Lyapunov stability analysis, the convergence rate and the ultimate (steady-state) error bounding ellipsoid are identified as the parameters that define the behaviour of the estimation. Then, it is shown that these objectives can be merged in a scalarised objective function with one design parameter, making the design problem convex. In the second part of the article, a UAV model is presented which can be made linear by considering a particular state and frame of reference. The UAV model is extended to incorporate a disturbance model of variable size. The joint model matches the structure required to derive an observer, following the lines of the proposed design approach. An observer for disturbances acting on the UAV is derived and the analysis of the performances with respect to the design parameters is presented. The effectiveness and main characteristics of the proposed approach are shown using simulation results.

Robust consensus tracking of second-order nonlinear systems using relative position information by K-filter and disturbance observer based control

ABSTRACTThis work considers the problem of distributed consensus tracking control of second-order uncertain nonlinear systems under a directed communication graph which contains a spanning tree, where the leader node is the root. It is assumed that the followers receive only the relative positions from the neighbours. For the purpose of consensus tracking controller design, in each follower, a group of K-filters is introduced so that the necessity of velocity estimating is avoided. Then we can express each follower's tracking error dynamics as a second-order system with mismatched uncertainties. And hence we can design a robust consensus tracking controller for each follower by using the combination of the backstepping design and the disturbance observer based control using only relative position information. Theoretical analysis is performed to show that the DOBs' estimation errors can be made to decay to be sufficiently small very quickly before the system states escape from the feasible region. Then we show that all the followers' states track those of the leader with arbitrarily small ultimate error bounds. And simulation examples are provided to demonstrate the performance of the proposed method.

Study of the Ultimate Error of the Axis Tolerance Feature and Its Pose Decoupling Based on an Area Coordinate System

Manufacturing error and assembly error should be taken into consideration during evaluation and analysis of accurate product performance in the design phase. Traditional tolerance analysis methods establish error propagation model based on dimension chains with tolerance values being regarded as error boundaries, and obtain the limit of target feature error through optimization methods or conducting statistical analysis with the tolerance domain being the boundary. As deviations of the tolerance feature (TF) on degrees of freedom (DOF) have coupling relations, accurate deviations on all DOF may not be obtained, even though these deviations constitute the basis for product performance analysis. Therefore, taking the widely used shaft-hole fit as an example, a pose decoupling model of the axis TF was proposed based on an area coordinate system. This model realized decoupling analysis of any pose of the axis TF within the tolerance domain. As proposed by the authors, by combining a tolerance analysis model based on tracking local coordinate systems, ultimate pose analysis of the closed-loop system, namely the target feature, as well as statistical analysis could be further implemented. This method contributed to analysis of true product performance with arbitrary error in the product design phase from the angle of tolerance, therefore, shortening the product research and development cycle. This method is demonstrated through applying it to a real-life example.

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Improved Models of Systematic and Random Errors

The literature contains many studies on assessment of DIC uncertainties, particularly in the ultimate error regime, when the shape function used to describe the material transformation perfectly matches the actual transformation. For pure sub-pixel translations, bias and random errors obtained for experimental or synthetic images show more complex evolution versus the fractional part of displacement than those predicted by the existing theoretical models. Indeed, small deviations arise, mainly around integer values of imposed displacements for noisy images, and they are interpreted as the unrepresentativeness of the underlying hypotheses of the theoretical models. In a first step, differences between imposed and measured displacements are analysed: random error is independent of fractional displacement, and systematic error does not decrease for values close to integer displacements whatever the noise level. Therefore, new prediction models are proposed based on the analysis of identified phenomena from synthetic speckle-pattern 8-bit images. The statistical approach used in this paper generalizes the methods proposed in the literature and mimics the experimental methodology usually used for displacement measurements performed in different subsets in the same image. Two closed-form expressions for the systematic and random errors and a linear interpolation scheme are developed. These models, depending only on image properties and the imposed displacement, are built with a very limited number of parameters. It is then possible to predict the evolution of bias and random errors from one to four images.

Te Ture Whenua MMMori Reform When Poor Problem Definition Leads to Illegitimate Policy

Achieving policy legitimacy is incredibly challenging. One key element includes input legitimacy which includes the early review stages that seek to define the problem the resulting policy will address. The recent proposed reform of the Te Ture Whenua Māori Act 1993 demonstrates the importance of problem definition in achieving policy legitimacy. In order to effectively define the problem in this case, an assessment of the Act was required to determine whether the regulatory framework and the Māori Land Court were inhibiting utilisation of Māori land. The Review Panel tasked with undertaking the review of the 1993 Act chose to rely on current research to design a policy that sought to address what it perceived as the barriers to utilisation of land, rather than determine whether the current framework was in fact inhibitory. This choice was the ultimate error and resulted in a policy perceived as illegitimate overall. The Panel effectively ignored history, relied disproportionately on poor quality evidence, and used this evidence incorrectly.

Robust consensus tracking control of higher‐order uncertain non‐linear systems via cascaded finite‐time estimation of reference states

This work considers the problem of distributed consensus tracking control of higher-order uncertain non-linear systems on a directed graph which contains a spanning tree with the leader node being the root. To facilitate controller design, in each agent of the network, a group of distributed and cascaded finite-time estimators is constructed for estimating the reference trajectory and its higher-order derivatives by information exchange among the local neighbours. Only the highest-order derivative estimator is discontinuous, whereas the estimators of the other reference states are continuous. Finite-time convergence property of each estimator is analysed. Then by utilising the estimated reference states, in each agent, a robust controller composed of some non-linear damping terms, a disturbance observer and a sliding mode control term is designed, so that the agent's states track the estimated reference states with an arbitrarily small ultimate error bound. The tracking performance is theoretically analysed. And simulation examples are provided to demonstrate the performance of the finite-time reference estimators and the tracking controllers.

Modeling and Optimal Design of a Glass RTP System

The problem of modeling and generating an optimal design of a rapid thermal processing (RTP) system for flat panel display glass was addressed. An RTP system using bulb-type tungsten-halogen lamps was considered, and a dynamic model to describe the glass temperature distribution was established. The power dispersion function comprising the model was established in an experimental RTP setup for 2G display glass. The model was used to determine an optimal lamp arrangement for a 4G glass RTP system such that the maximum temperature error meets the specifications while both heating power and lamp occupation area are moderate. An iterative learning control method was applied and found to be able to closely match the predicted ultimate temperature error in dynamic situations with model uncertainty.