Problem Of Error Control Research Articles

A Direct Contour Control Method for Free-Form Surface Machining Trajectories Based on Coordinate Transformation

The requirement for high-speed and high-precision contouring with free-form surfaces in the CNC machining process is increasing. The contour error is an essential criterion for the quality of CNC machining. For the problem of contour error control, the present research is mainly based on position tracking, and the control method directly aiming at contour control has not been well studied. This paper proposed a new type of coordinate transformation-based direct contour control method (CT-DCC) for free-form surface machining trajectories. By real-time monitoring of the contour error and the foot point of the free-form parametric trajectory, the contouring task is decomposed into the contour error control task in the normal direction and the velocity control problem in the feed direction. Using coordinate transformation, the output commands of the two tasks are converted to the axial motion command. CT-DCC completely eliminates position tracking in the traditional control to achieve direct control of the contour error, which provides a new solution for the contour control problem of free-form surface machining. Both the axial velocity control and the axial torque control-based CT-DCC scheme were studied, and the two-axis and three-axis direct contour controllers were tested. The simulation and experiment results show the feasibility of the proposed method.

Scaled average bioequivalence methods for highly variable drugs: Leveling-off soft limits and the EMA's 2010 guideline (some ways to improve its type I error control).

The regulatory EMA's reference scaled average bioequivalence (RSABE) approach for highly variable drugs suffers from some type I error control problems at the neighborhood of the 30% coefficient of variation (CV), where the bioequivalence (BE) limits change from constant to linearly scaled. This paper analyses BE inference methods based on the "Leveling-off" (LO) soft sigmoid expanding BE limits that were proposed as an appealing surrogate for the EMA's limits and compares both approaches, on the replicated and partially replicated crossover designs. The initially proposed version of the LO method also has type I error inflation problems, albeit attenuated. But given its more mathematically regular character, it is more suitable for analytical corrections. Here we introduce two improvements over LO, one based on the application of Howe's method and the other based on correcting the estimation error. They further reduce the type I error inflation, although it does not disappear completely. Finally, the effect of heteroscedasticity on the above results is studied. It leads to inflation or deflation of the type I error, depending on the design and the type of heteroscedasticity (variability of the test product greater than that of the reference product or the opposite). The replicated design is much more stable against these effects than the partially replicated design and maintains these improvements much better.

Network Decoding

We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proper subset</i> of the network edges. We model this problem via an adversarial noise, presenting a formal framework and a series of techniques to obtain upper and lower bounds on the network’s (1-shot) capacity, improving on the best currently known results. In particular, we show that traditional cut-set bounds are not tight in general in the presence of a restricted adversary, and that the non-tightness of these is caused precisely by the restrictions imposed on the noise (and not, as one may expect, by the alphabet size). We also show that, in sharp contrast with the typical situation within network coding, capacity cannot be achieved in general by combining linear network coding with end-to-end channel coding, not even when the underlying network has a single source and a single terminal. We finally illustrate how network <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decoding</i> techniques are necessary to achieve capacity in the scenarios we examine, exhibiting capacity-achieving schemes and lower bounds for various classes of networks.

Convex optimization of asteroid landing trajectories driven by solar radiation pressure

High-area/mass ratio landers driven by Solar Radiation Pressure (SRP) have potential applications for future asteroid landing missions. This paper develops a new convex optimization-based method for planning trajectories driven by SRP. A Minimum Landing Error (MLE) control problem is formulated to enable planning SRP-controlled trajectories with different flight times. It is transformed into Second Order Cone Programming (SOCP) successfully by a series of different convexification technologies. A trust region constraint and a modified MLE objective function are used to guarantee the convergence performance of the optimization algorithm. Thereafter, the SRP-driven trajectory optimal control problem is converted equivalently into a sequence of convex optimal control problems that can be solved effectively. A set of numerical simulation results has verified the effectiveness and feasibility of the proposed optimization method.

Secure network coding for data encoded using subspace codes

Subspace coding is a solution to the error-control problem in noncoherent networks using Random Linear Network Coding (RLNC) as a transmission mechanism. In this paper, we propose a secure error-correction scheme based on a codeword selection method called the Subspace Coding Strategy (SCS) along with a permutation step, as a possible solution for secure transmission of data encoded using subspace codes. Our scheme also makes use of the correction capability of the used code to induce correctable random errors to further mislead the wiretapper. Numerical results and comparative analysis with other schemes from the literature are presented as a verification of the impact of the proposed scheme on transmission security.

Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification

In this paper, we address the numerical posterior error control problem for the Bayesian approach to inverse problems or recently known as Bayesian Uncertainty Quantification (UQ). We generalize the results of Capistrán et al. (2016) to (a priori) expected Bayes factors (BF) and in a more general, infinite-dimensional setting. In this inverse problem, the unavoidable numerical approximation of the Forward Map (FM, i.e., the regressor function), arising from the numerical solution of a system of differential equations, demands error estimates of the corresponding approximate numerical posterior distribution. Our approach is to make such comparisons in the setting of Bayesian model selection and BFs. The main result of this paper is a bound on the absolute global error tolerated by the numerical solver of the FM in order to keep the BF of the numerical versus the theoretical posterior near one. For two examples, we provide a detailed analysis of the computation and implementation of the introduced bound. Furthermore, we show that the resulting numerical posterior turns out to be nearly identical from the theoretical posterior, given the control of the BF near one.

Nested Implicit Runge–Kutta Pairs of Gauss and Lobatto Types with Local and Global Error Controls for Stiff Ordinary Differential Equations

The problem of efficient global error estimation and control is studied in embedded nested implicit Runge–Kutta pairs of Gauss and Lobatto types as applied to stiff ordinary differential equations (ODEs). Stiff problems may arise in many areas of engineering, and their accurate numerical solution is an important issue of computational and applied mathematics. A cheap global error estimation technique designed recently for the mentioned Runge–Kutta pairs can severely overestimate the global error when applied to stiff ODEs and, hence, this reduces the efficiency of those solvers. In the present paper, we explain the cause of that error overestimation and show how to improve the mentioned computation techniques for stiff problems. Such modifications not only boost the efficiency of numerical integration of stiff ODEs, but also make the embedded nested implicit Runge–Kutta pairs with scaled modified local and global error controls superior to stiff built-in MATLAB ODE solvers with only local error control when applied to important test examples.

A tracking error–based fully probabilistic control for stochastic discrete-time systems with multiplicative noise

This article proposes the exploitation of the Kullback–Leibler divergence to characterise the uncertainty of the tracking error for general stochastic systems without constraints of certain distributions. The general solution to the fully probabilistic design of the tracking error control problem is first stated. Further development then focuses on the derivation of a randomised controller for a class of linear stochastic Gaussian systems that are affected by multiplicative noise. The derived control solution takes the multiplicative noise of the controlled system into consideration in the derivation of the randomised controller. The proposed fully probabilistic design of the tracking error of the system dynamics is a more legitimate approach than the conventional fully probabilistic design method. It directly characterises the main objective of system control. The efficiency of the proposed method is then demonstrated on a flexible beam example where the vibration quenching in flexible beams is shown to be effectively suppressed.

Controlling type I error in the reference-scaled bioequivalence evaluation of highly variable drugs.

Reference-scaled average bioequivalence (RSABE) approaches for highly variable drugs are based on linearly scaling the bioequivalence limits according to the reference formulation within-subject variability. RSABE methods have type I error control problems around the value where the limits change from constant to scaled. In all these methods, the probability of type I error has only one absolute maximum at this switching variability value. This allows adjusting the significance level to obtain statistically correct procedures (that is, those in which the probability of type I error remains below the nominal significance level), at the expense of some potential power loss. In this paper, we explore adjustments to the EMA and FDA regulatory RSABE approaches, and to a possible improvement of the original EMA method, designated as HoweEMA. The resulting adjusted methods are completely correct with respect to type I error probability. The power loss is generally small and tends to become irrelevant for moderately large (affordable in real studies) sample sizes.

A LADRC based fuzzy PID approach to contour error control of networked motion control system with time‐varying delays

AbstractThis paper investigate the contour error control problem for networked multi‐axis motion system (NMAMS) with time‐varying delays. Firstly, the uncertainties induced by the delays are modeled as a part of the total disturbance, and a linear active disturbance rejection controller (LADRC) is designed for the uniaxial trajectory tracking control. In the LADRC, a linear extended state observer (LESO) is designed to estimate the system state and the total disturbance simultaneously, and the effect of the total disturbance is eliminated by the designed linear feedback error control law. Then, the classical contour error estimation method is adopted, and a fuzzy PID controller is designed to compensate the contour error to achieve a better contour tracking performance. Finally, experiments are provided to verify the effectiveness of the proposed method.

A Simple Frequency-Domain Negative Acknowledgment Feedback for Automatic Repeat on reQuest Underwater Acoustic Networks

Bidirectional underwater acoustic communications usually request the transmission of some control information among nodes to govern the data flow. Control signaling, employed as frame reception validation, is also a peculiarity of the Automatic Repeat on reQuest (ARQ) schemes. An alternative solution to the error control problem is using forward error correction, even though high redundancy is needed to obtain the low error rate, hence leading to a sensible throughput reduction. Furthermore, no control on data integrity is allowed. For the above reasons, we explore the possibility of implementing three different ARQ schemes by considering only the use of an explicit negative acknowledgment (NACK) for requiring frames retransmission. Specifically, the NACK frame index is related to a frequency-dependent message and the information frame(s) to be retransmitted are recognized, owing to a frequency-domain detection mechanism. Moreover, the proposed solution is very efficient when applied in a broadcast environment since it overcomes the necessity of performing a multiuser detection at the centralized broadcaster. In this context, we report both simulations and experimental tests results to show the effectiveness of the proposed scheme.

Codes in the Space of Multisets—Coding for Permutation Channels With Impairments

Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted in the form of multisets of symbols from a given finite alphabet. A general channel model is assumed in which the transmitted multisets are potentially impaired by insertions, deletions, substitutions, and erasures of symbols. Several constructions of error-correcting codes for this channel are described, and bounds on the size of optimal codes correcting any given number of errors derived. The construction based on the notion of Sidon sets in finite Abelian groups is shown to be optimal, in the sense of the asymptotic scaling of code redundancy, for any "error radius" and any alphabet size. It is also shown to be optimal in the stronger sense of maximal code cardinality in various cases.

Disturbance observer-based control for consensus tracking of multi-agent systems with input delays from a frequency domain perspective

The consensus tracking controller design of multi-agent systems with diverse input delays is studied in this paper. A universal block diagram is established to describe the linear multi-agent systems based on transfer functions. The stabilization of the whole system is decomposed into the zero steady-state error control problem of each independent agent. A sufficient and necessary condition is accordingly deduced to impose on each controller. Based on the H2 performance index of each subsystem, both the optimal consensus controller and disturbance observer (DOB) are derived analytically. The distributed H2 DOB-based consensus controller can not only achieve consensus tracking for the reference input, but also reject the effects of external disturbance and model uncertainty. Some simulations are performed to illustrate the validity of the proposed design approach.

Embedding Bandwidth-Guaranteed Network-Based Virtual Ethernet Switches in SDN Networks

In this paper, we present a design for implementing network-based virtual Ethernet switches (NVESs) on top of a physical substrate consisting of a software-defined networking (SDN) network. An NVES has the same capability as a real Ethernet switch. A user makes a request to provision an NVES by specifying the number of ports and the maximum bandwidth for each port. The substrate network considered in this study is an Open Flow network. The entire network is controlled by an Open Flow controller. The controller is responsible for performing admission control, resource allocation, routing, address learning, and spanning tree protocol. To enhance the resource utilization of the substrate network, multipath routing is applied. Although using multipath routing can significantly improve bandwidth utilization, this approach results in out-of-order packet delivery and introduces additional error-control problems. To resolve these problems, we design a multipath agent to enhance the edge switch capability. The multipath agent is responsible for bandwidth metering, flow splitting, sequence number management, and packet reordering. We evaluated our virtual switches on top of a testbed network that includes not only commercial Open Flow switches but also a GPON-based virtual Open Flow switch. Multiple NVESs share the testbed network. The experimental results show that the user experience when using an NVES is identical to using a real Ethernet switch. In addition to the provision of guaranteed bandwidth for each NVES, traffic isolation among the NVESs is achieved. All NVESs are free of interference from others in the same network.

Multi‐tracking control of heterogeneous multi‐agent systems with single‐input– single‐output based on complex frequency domain analysis

This paper studies the multi-tracking control for high-order heterogeneous multi-agent systems under a directed acyclic graph. The authors first convert the multi-tracking control problem for multi-agent systems into the zero steady-state error control problem of some independent subsystems. Based on final-value theorem and Mason's rule, a sufficient condition for achieving the multi-tracking control is proposed. It explicitly reveals how the system dynamic and desired object dynamic jointly affect the multi-tracking control of heterogeneous multi-agent systems. Meanwhile, a new result on the steady-state error for multi-subnetworks is established. Moreover, the multi-tracking control for heterogeneous multi-agent systems with time delay is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.

A Convolution Method for Numerical Solution of Backward Stochastic Differential Equations

We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast Fourier transform (FFT). The problem of error control is addressed and a local error analysis is provided. We consider the extension of the method to forward-backward stochastic differential equations (FBSDEs) and reflected FBSDEs. Numerical examples are considered from finance demonstrating the performance of the method.

On stepwise control of directional errors under independence and some dependence

In this paper, the problem of error control of stepwise multiple testing procedures is considered. For two-sided hypotheses, control of both type 1 and type 3 (or directional) errors is required, and thus mixed directional familywise error rate control and mixed directional false discovery rate control are each considered by incorporating both types of errors in the error rate. Mixed directional familywise error rate control of stepwise methods in multiple testing has proven to be a challenging problem, as demonstrated in Shaffer (1980). By an appropriate formulation of the problem, some new stepwise procedures are developed that control type 1 and directional errors under independence and various dependencies.

Frequency Error and Voltage Control by using PI and Fuzzy Logic Controllers for Multi Area Inter Connected Power System

paper deals with the power system operation, frequency error and voltage control problems. In actual power system operations the load is changing continuously and randomly. As the ability of the generation to trace the change in load is limited due to physical/technical considerations. They result an imbalance between actual and the scheduled generation quantities. This imbalance leads to a frequency error and voltage problems. In general, as the speed of the machine depends on the frequency, any deviation in the frequency may lead to mal-operation of the system. So load frequency control is the key problem in the power system. For specified power rating of the machine the voltage should maintain constant otherwise the system insulation may get damage. In modern power system multi area inter connected systems are used for more reliability and economic purpose. In the multi area inter connected systems the frequency errors and voltage problems can be effectively decreased by using fuzzy logic controller with either of the 3, 5 or 7 membership functions. Here this fuzzy logic controller action also compared with automatic generation control and PI controllers also. By using fuzzy logic controller the frequency error, settling time, peak overshoot, under overshoots are effectively reduced.

A Convolution Method for Numerical Solution of Backward Stochastic Differential Equations

We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast Fourier transform (FFT). The problem of error control is addressed and a local error analysis is provided. We consider the extension of the method to forward-backward stochastic differential equations (FBSDEs) and reflected FBSDEs. Numerical examples are considered from finance demonstrating the performance of the method.

Time-varying neuro-fuzzy model using probability density function techniques for batch processes

A time-varying neuro-fuzzy model (TNFM) based on the probability density function (PDF) technique is proposed in this paper. It is able to describe the characteristics of repetition of batch process by using the input–output data information of batch axes and time axes separately. More specifically, the parameters of time-varying neuro-fuzzy are functions of time during one batch, while it can be looked as uniform values from the viewpoint of batch to batch. Moreover, it converts the modelling problem into a PDF shape of modelling error control problem. The adjustable parameters of TNFM are updated to make the PDF shape of modelling error to follow the targeted PDF. As a result, the proposed method not only describes the characteristics of repetition of batch process, but also guarantees the generalization and robustness, especially when uncertainty and disturbance exist. Lastly, to verify the effectiveness of the proposed identification method, it is applied to a benchmark batch process, in comparison with the traditional identification algorithm based on minimum variance and zero mean.