Set Of Auxiliary Variables Research Articles

Scaled Event-Triggered Resilient Consensus Control of Continuous-Time Multi-Agent Systems Under Byzantine Agents

This paper investigates the scaled event-triggered consensus control for the continuous-time multi-agent system under Byzantine agents. The Byzantine agents do not follow the desired control strategy, which may influence the consensus performance of the multi-agent systems. To realize the scaled consensus under the Byzantine agents, a novel continuous-time scaled event-triggered mean-subsequence-reduced algorithm is constructed. First, a scaled resilient consensus controller is developed, where every cooperative agent removes the most different event-triggered transmitted values from the in-neighbors and obtains the associated scaled resilient consensus control input. Besides, a novel dynamic event-triggered condition is designed based upon the associated discontinuous and non-differentiable Lyapunov function candidate. In addition, two sets of auxiliary variables are introduced into the event-triggered condition, to prevent the usage of the global topology information and to exclude the Zeno behavior simultaneously. The proposed control algorithm can realize the scaled consensus of the continuous-time multi-agent systems, resist the Byzantine agents, and decrease the communication burden simultaneously. The simulation results verify the effectiveness of the proposed algorithm.

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control (FSC) method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics. The key feature of the proposed method is the design of two dynamic parameters. Specifically, a set of auxiliary variables is first introduced through state transformation. These variables combine the original system states and the two introduced dynamic parameters, facilitating the closed-loop system stability analyses. Then, the two dynamic parameters are delicately designed by utilizing the Lyapunov method, ensuring that all the closed-loop system states are globally fixed-time stable. Compared with existing results, the “explosion of complexity” problem of backstepping control is avoided. Moreover, the two designed dynamic parameters are dependent on system states rather than a time-varying function, thus the proposed controller is still valid beyond the given fixed-time convergence instant. The effectiveness of the proposed method is demonstrated through two practical systems.

Robust Dynamic TEP With an Security Criterion: A Computationally Efficient Model

This paper presents a hybrid column-and-constraint-generation augmented-Lagrangian algorithm to efficiently solve the robust security-constrained dynamic transmission expansion planning (TEP) problem. The column-and-constraint generation algorithm separates the TEP problem into a master problem and a set of subproblems decomposable by time period. Additionally, the computationally expensive master problem is decomposed into three computationally efficient sub-master problems: an upper-master quadratic problem, a middle-master quadratic unconstrained binary problem, and a lower-master quadratic unconstrained problem. A set of auxiliary variables are used to relax as real ones the binary variables corresponding to the status of candidate transmission lines enabling the master problem decomposition. The solutions of the three sub-master problems are coordinated using a three-block alternating direction method of multipliers algorithm to enforce binary variables to be binary. An initialization strategy based on load shedding is used to enhance the performance of the proposed algorithm. Simulation results on the IEEE 118-bus test system show the efficient performance of the proposed algorithm for solving security-constrained dynamic TEP problems.

Adjusting for Unmeasured Confounding Variables in Dynamic Networks

This letter presents a technique to identify a certain transfer function in a dynamic network when the input and the output of the transfer function are influenced by an unmeasured confounding variable. It is assumed that in an observational framework, only a subset of the variables of the network are measured and the topology of the interconnections between the variables is partially known. The focus of this letter is the challenging scenario where it is not possible to measure any variables on the directed paths from the confounding variable to either the input or the output of the transfer function of interest. Sufficient conditions are derived to determine a set of instrumental variables and a set of auxiliary variables that guarantee consistent identification of the transfer function using an algorithm based on prediction error method for the class of acyclic networks. It is also shown that similar ideas could be applied to cyclic networks. In particular, we show how consistent estimates of some transfer functions in a network with feedback loops could be used to identify some other transfer functions whose inputs and outputs are influenced by unmeasured confounding variables.

Robust Neural Network Consensus for Multiagent UASs Based on Weights’ Estimation Error

We propose a neural network consensus strategy to solve the leader–follower problem for multiple-rotorcraft unmanned aircraft systems (UASs), where the goal of this work was to improve the learning based on a set of auxiliary variables and first-order filters to obtain the estimation error of the neural weights and to introduce this error information in the update laws. The stability proof was conducted based on Lyapunov’s theory, where we concluded that the formation errors and neural weights’ estimation error were uniformly ultimately bounded. A set of simulation results were conducted in the Gazebo environment to show the efficacy of the novel update laws for the altitude and translational dynamics of a group of UASs. The results showed the benefits and insights into the coordinated control for multiagent systems that considered the weights’ error information compared with the consensus strategy based on classical σ-modification. A comparative study with the performance index ITAE and ITSE showed that the tracking error was reduced by around 45%.

Generalised calibration with latent variables for the treatment of unit nonresponse in sample surveys

Sample surveys may suffer from nonignorable unit nonresponse. This happens when the decision of whether or not to participate in the survey is correlated with variables of interest; in such a case, nonresponse produces biased estimates for parameters related to those variables, even after adjustments that account for auxiliary information. This paper presents a method to deal with nonignorable unit nonresponse that uses generalised calibration and latent variable modelling. Generalised calibration enables to model unit nonresponse using a set of auxiliary variables (instrumental or model variables), that can be different from those used in the calibration constraints (calibration variables). We propose to use latent variables to estimate the probability to participate in the survey and to construct a reweighting system incorporating such latent variables. The proposed methodology is illustrated, its properties discussed and tested on two simulation studies. Finally, it is applied to adjust estimates of the finite population mean wealth from the Italian Survey of Household Income and Wealth.

Shaped-Beam Pattern Synthesis With Sidelobe Level Minimization via Nonuniformly-Spaced Sub-Array

This article deals with the low-sidelobe shaped-beam pattern synthesis (SBPS) problem using two nonuniformly spaced subarray configurations, including amplitude and amplitude–phase subarray configurations. An optimization model is proposed for the SBPS problem to minimize the peak sidelobe level by jointly optimizing the subarray configuration and element excitations/positions. A typical advantage of the proposed model is to reduce the system control points while maintaining the benign array performance. However, the formulated problem is a mixed-integer nonconvex one, which makes it challenging. Besides, this problem cannot be directly solved due to the existence of coupling optimization variables. Thus, a set of auxiliary variables is introduced to move the coupling optimization variables into equality constraints. These equality constraints are converted into quadratic penalty forms and are added to the objective function. Then, an efficient iterative algorithm is proposed using the penalty-based optimization method, which solves the original problem by iteratively solving a series of subproblems based on the inexact block coordinate descent technique. Numerical examples with different beam patterns are performed to verify the effectiveness of the proposed algorithm.

Low-Sidelobe Shaped-Beam Pattern Synthesis With Amplitude Constraints

The article deals with the low-sidelobe shaped-beam pattern synthesis (SBPS) problem under amplitude constraints, including the controllable dynamic range ratio (DRR) and the predetermined excitation amplitude. The formulated problem is nonconvex owning to the existing nonconvex constraints. To this end, a set of auxiliary variables are introduced to reformulate the original problem, and then a double-loop iterative algorithm based on the penalty dual decomposition method (PDD) framework is proposed. The proposed approach solves the reformulated problem by updating primal variables with block successive upper-bound maximization (BSUM) algorithm in the inner loop and updating the dual variables and penalty parameter with the constraint violation strategy in the outer loop. One important advantage of the proposed approach is that all of its subproblems have closed-form solutions, which guarantees that the reformulated problem can be effectively solved. Numerical simulations are carried out to validate the proposed approach’s superiority with both isotropic element pattern and active element pattern (AEP). The results show that the proposed approach can obtain a lower sidelobe level (SLL) and a smaller DRR when compared with the state-of-the-art approaches.

Sum/Difference Pattern Synthesis With Dynamic Range Ratio Control for Arbitrary Arrays

This article proposes a method which generates a set of weights to synthesize sum or difference pattern with precisely controlled sidelobe level (SLL), null, and dynamic range ratio (DRR) for arbitrary arrays. Our pattern synthesis approach reduces mutual coupling (MC) between the neighboring elements and complexity of the feeding network design. However, the formulated optimization problem is nonconvex due to the nonconvex objective function and fractional DRR constraint. To tackle it, we first introduce two sets of auxiliary variables: one for DRR constraint and the other for sidelobe and null constraints. By doing so, we then decompose the original optimization problem into three sets of subproblems characterized by the auxiliary variables and weight variables. To facilitate the subproblem with weight variables reaching its optimum values, we derive an appropriate range of step size. Finally, we iteratively solve these subproblems to obtain the solution to the original problem. Extensive experiments employing non-equispaced linear and rectangular arrays, concentric ring array, and cylinder array, are implemented to demonstrate that the developed approach can accurately control SLLs, null and DRR for arbitrary arrays.

CL-ADMM: A Cooperative-Learning-Based Optimization Framework for Resource Management in MEC

We consider the problem of the intelligent and efficient resource management framework in mobile-edge computing (MEC), which can reduce delay and energy consumption, and features distributed optimization and efficient congestion avoidance. In this article, we present a cooperative learning framework for resource management in MEC from an alternating direction method of multipliers (ADMMs) perspective, named the CL-ADMM framework. First, computing a task requires both the user personal data and corresponding program that processes it, to efficiently cache program in a group, a novel program popularity estimation scheme is proposed, which is based on a semi-Markov process model. Then, a greedy program cooperative caching mechanism is established, which can effectively reduce delay and energy consumption. Second, to address group congestion, a dynamic task migration scheme based on improved cooperative Q-learning is proposed, which can effectively reduce delay and alleviate congestion. Third, to minimize delay and energy consumption for resource allocation in a group, we formulate it as an optimization problem with a large number of variables, and then exploit a novel ADMM-based scheme to solve this problem, which can reduce the complexity of the problem with a new set of auxiliary variables, these subproblems are all convex problems that can be solved by using a primal-dual approach, which guarantees its convergence. Finally, we prove its convergence by using the Lyapunov theory. The numerical results demonstrate the effectiveness of the CL-ADMM framework in reducing delay and energy consumption in MEC.

Discrete topology optimization in augmented space: integrated element removal for minimum size and mesh sensitivity control

A computational strategy is proposed to circumvent some of the major issues that arise in the classical threshold-based approach to discrete topology optimization. These include the lack of an integrated element removal strategy to prevent the emergence of hair-like elements, the inability to effectively enforce a minimum member size of arbitrary magnitude, and high sensitivity of the final solution to the choice of ground structure. The proposed strategy draws upon the ideas used to arrive at mesh-independent solutions in continuum topology optimization and enables efficient imposition of a minimum size constraint onto the set of non vanishing elements. This is achieved via augmenting the design variables by a set of auxiliary variables, called existence variables, that not only prove very effective in addressing the aforementioned issues but also bring in a set of added benefits such as better convergence and complexity control. 2D and 3D examples from truss-like structures are presented to demonstrate the superiority of the proposed approach over the classical approach to discrete topology optimization.

Time-domain simulation of wave propagation across resonant meta-interfaces

Meta-interface models stem from the homogenization, in a low-frequency dynamic regime, of thin heterogeneous layers that are structured to achieve uncommon properties at the macroscopic level. When the layer is composed of a thin periodic array of highly-contrasted inclusions embedded within a homogeneous background medium then the corresponding effective interface model is characterized by jump conditions that, in the harmonic regime, involve some singular frequency-dependent terms. In this context, the article is concerned with the simulation of transient waves across such resonant meta-interfaces and a numerical method is proposed to handle the associated resonant jump conditions. To do so, a set of auxiliary variables is introduced locally along the interface and an augmented system of first-order equations in time accompanied with local-in-time jump conditions is derived. This system is then discretized on a Cartesian grid and solved using a high-order finite-difference scheme while the complexity associated with the geometry of the interface and the jump conditions is handled using an immersed interface method. A set of numerical examples in 1D and 2D is proposed to illustrate and validate the overall numerical approach, and quantitative comparisons with semi-analytical solutions are also provided.

Identification and estimation of average causal effects when treatment status is ignorable within unobserved strata

This paper extends matching and propensity-score reweighting methods to settings in which unobserved variables influence both treatment assignment and counterfactual outcomes. Identification proceeds under the assumption that counterfactual outcomes are independent of treatment status conditional on observed covariates and membership in one of a finite set of latent classes. Individuals are first assigned to latent classes according to posterior probabilities of class membership derived from a finite-mixture model that relates a set of auxiliary variables to latent class membership. Average causal effects are then identified by comparing outcomes among treated and untreated individuals assigned to the same class, correcting for misclassifications arising in the first step. The identification procedure suggests computationally attractive latent-class matching and propensity-score reweighting estimators that obviate the need to directly estimate the distributions of counterfactual outcomes. In Monte Carlo studies, the resulting estimates are centered around the correct average causal effects with minimal loss of precision compared to competing estimators that misstate those effects. I apply the methods to estimate the effect of gang membership on violent delinquency.

A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling

Abstract Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If n denotes the fixed sample size, the n units are drawn independently with probabilities that may vary from unit to unit and the samples in which all units are not distinct are rejected. More generally, in rejective sampling, we select repeated samples according to a basic sampling design until a selected sample meets a specified balancing tolerance. Given a set of auxiliary variables, we consider a procedure in which the probability sample is rejected unless the sample mean of the auxiliary variables is within a specified distance of its corresponding population mean. The procedure represents an alternative to the well-known balanced cube method. In this article, we propose an estimator of the variance under the rejective sampling design. We also present the results of a Monte Carlo simulation study.

An efficient implementation of two-component relativistic density functional theory with torque-free auxiliary variables

An integration and assembly strategy for efficient evaluation of the exchange correlation term in relativistic density functional theory within two-component Kohn–Sham framework is presented. Working equations that both take into account all the components of the spin magnetization and can exploit parallelism, optimized cache utilization, and micro-architecture specific-floating point operations are discussed in detail in this work. The presented assembly of the exchange correlation potential, suitable for both open and closed shell systems, uses spinor density and a set of auxiliary variables, ensuring easy retrofitting of existing density functionals designed for collinear density. The used auxiliary variables in this paper, based on the scalar and non-collinear density, can preserve non-zero exchange correlation magnetic field local torque, without violating the required overall zero torque, even for GGA functionals. This is mandatory to obtain accurate spin dynamics and proper time evolution of the magnetization. Spin frustrated hydrogen rings are used to validate the current implementation and phenoxy radicals of different sizes are used to monitor the performance. This approach is a step towards extending the applicability of relativistic two-component DFT to systems of large size (>100 atoms).

Estimating The Impact Of R&D Spending On Total Factor Roductivity For OECD Countries: Pooled Mean Group Approach

Growth accounting models consider technology as exogenous which are determined outside the model. Even though Solow type model measures the contribution of technology as residual which is left over from the contribution of labor and capital, it does not provide tool to directly assess the role of technology. Endogenous growth models emerged to overcome this shortcoming. In the recent decades, many empirical studies have explored the direct role of technological change in economic growth in the long-run. Researchers have used various variables to endogenously study factors affecting economic productivity. R&D spending is considered one of those factors. However, since it takes a longer time to see the impact of R&D spending, many developing countries do not truly appreciate its importance for economic growth. This paper is aimed to provide further evidence by exploring the relationship between total factor productivity (TFP), information and communication technology (ICT) capital services, R&D expenditures, and a set of auxiliary variables (labor quantity, labor quality, non-ICT capital services) using the Pooled Mean Group approach for OECD countries. The objective is to show if and to what extent TFP is sensitive to ICT and R&D over both long- and short-term periods by controlling for auxiliary determinants. The study has found a positive significant relationship between TFP and ICT capital services over the long-run, and between TFP and both ICT capital services and R&D expenditures over the short-run. It is also found that TFP positively responds to changes in all auxiliary determinants over the short-run. The impact of all variables on TFP is smaller for short-term than long-term. The study highlights the great importance of investing in R&D by developing countries to catch up with the developed countries. The findings are expected to encourage developing countries to invest more in R&D to accomplish long-term sustainable and competitive economic growth.

Two-Component Noncollinear Time-Dependent Spin Density Functional Theory for Excited State Calculations.

We present a linear response formalism for the description of the electronic excitations of a noncollinear reference defined via Kohn-Sham spin density functional methods. A set of auxiliary variables, defined using the density and noncollinear magnetization density vector, allows the generalization of spin density functional kernels commonly used in collinear DFT to noncollinear cases, including local density, GGA, meta-GGA and hybrid functionals. Working equations and derivations of functional second derivatives with respect to the noncollinear density, required in the linear response noncollinear TDDFT formalism, are presented in this work. This formalism takes all components of the spin magnetization into account independent of the type of reference state (open or closed shell). As a result, the method introduced here is able to afford a nonzero local xc torque on the spin magnetization while still satisfying the zero-torque theorem globally. The formalism is applied to a few test cases using the variational exact-two-component reference including spin-orbit coupling to illustrate the capabilities of the method.

Parametric Dual Maximization for Non-Convex Learning Problems

We consider a class of non-convex learning problems that can be formulated as jointly optimizing regularized hinge loss and a set of auxiliary variables. Such problems encompass but are not limited to various versions of semi-supervised learning,learning with hidden structures, robust learning, etc. Existing methods either suffer from local minima or have to invoke anon-scalable combinatorial search. In this paper, we propose a novel learning procedure, namely Parametric Dual Maximization(PDM), that can approach global optimality efficiently with user specified approximation levels. The building blocks of PDM are two new results: (1) The equivalent convex maximization reformulation derived by parametric analysis.(2) The improvement of local solutions based on a necessary and sufficient condition for global optimality. Experimental results on two representative applications demonstrate the effectiveness of PDM compared to other approaches.

Joint Source-Relay Design for Full-Duplex MIMO AF Relay Systems

The performance of full-duplex (FD) relay systems can be greatly impacted by the self-interference (SI) at relays. By exploiting multi-antenna in FD relay systems, the spectral efficiency of FD relay systems can be enhanced through spatial SI mitigation. This paper studies joint source transmit beamforming and relay processing to achieve rate maximization for FD MIMO amplify-and-forward (AF) relay systems with consideration of relay processing delay. The problem is difficult to solve due mainly to the SI constraint induced by the relay processing delay. In this paper, we first present a sufficient condition under which the relay amplification matrix has rank one structure. Then, for the case of rank one amplification matrix, the rate maximization problem is equivalently simplified into an unconstrained problem which can be locally solved using gradient ascent method. Next, we propose a penalty-based algorithmic framework, called P-BSUM, for a class of constrained optimization problems which have difficult equality constraints in addition to some convex constraints. By rewriting the rate maximization problem with a set of auxiliary variables, we apply the P-BSUM algorithm to the rate maximization problem in the general case. Finally, numerical results validate the efficiency of the proposed algorithms and show that the joint source-relay design approach under the rank one assumption could be strictly suboptimal as compared to the P-BSUM-based joint source-relay design approach.

Maximizing the Sum Rate in Cellular Networks Using Multiconvex Optimization

In this paper, we propose a novel algorithm to maximize the sum-rate in interference-limited scenarios where each user decodes its own message with the presence of unknown interferences and noise. The problem of adapting the transmit and receive filters of the users to maximize the sum-rate with a transmit power constraint is nonconvex. Our novel approach is to formulate the sum-rate maximization problem as an equivalent multiconvex optimization problem by adding two sets of auxiliary variables. An iterative algorithm, which alternatingly adjusts the system variables and the auxiliary variables is proposed to solve the multiconvex optimization problem and we show that the algorithm converges to a stationary point. The proposed algorithm is applied to a downlink cellular scenario consisting of several cells each of which contains a base station serving several mobile stations. We examine the two cases, with or without several half-duplex amplify-and-forward relays assisting the transmission. A sum power constraint at the base stations and at the relays are assumed. The applicability of our approach to the individual power constraints case is also shown. Finally, we show that the proposed multiconvex formulation of the sum-rate maximization problem is applicable to many other wireless systems in which the estimated data symbols are multiaffine functions of the system variables.