Auxiliary Vector Research Articles

A multipopulation cooperative coevolutionary whale optimization algorithm with a two-stage orthogonal learning mechanism

This paper designed a multipopulation cooperative coevolutionary framework with a two-stage orthogonal learning (OL) mechanism for the whale optimization algorithm (MCCWOA) to improve the performance of the whale optimization algorithm (WOA). In the framework, a prediction model of the neighborhood structure is established by discovering the guidance information of the following iteration process in the objective space at the first-stage OL. In the second-stage OL, an auxiliary vector pool with various features in the decision space is introduced to guide the candidates falling in the stagnant status to conduct more valuable exploration. According to the domain knowledge of the candidates, the population is divided into the elite population, the intermediate population, and the inferior population. The information of the subpopulations has interacted with the corresponding historical populations in the evolution processes to enhance the ability of cooperative coevolution among individuals. A standard set of comprehensive benchmark cases and three engineering cases are utilized to verify the advantages of the proposed algorithm. The results of the statistical analysis, diversity analysis, and convergence analysis testified that the MCCWOA outperforms the 15 state-of-the-art algorithms regarding efficiency and significance.

Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation

A general geometric construction of a generic null hypersurface in presence of torsion in the spacetime (Riemann-Cartan background), generated by a null vector $l^a$, is being developed here. We then explicitly define and structure various corresponding kinematical quantities. The dynamics of the null surface, particularly given by $\hat{G}_{ab}k^al^b$, is also discussed. The later one is constructed under the {\it geodesic constraint} condition. This yields a relation among the rate of change of expansion scalar corresponding to auxiliary null vector $k^a$ and various kinematical entities on the null surface. Using this relation we show that the Einstein-Cartan-Kibble-Sciama equation (which provides the dynamics of the metric and the torsion tensor) on this null hypersurface acquires a thermodynamic interpretation. The thermodynamic entities like temperature, entropy density, energy and pressure are properly identified. In the whole analysis we adopt the geometrical field interpretation of torsion and all discussions are done in a covariant manner.

Indirect adaptive control of multi-input-multi-output nonlinear singularly perturbed systems with model uncertainties

In this paper, two indirect adaptive control schemes for a class of multi-input-multi-output nonlinear singularly perturbed systems with partially unknown models and parameters are presented. Firstly, the original system dynamic equation is reformulated into a new form with identity control gain matrices, and a new multi-time-scale singularity-free neural network is employed to represent the new dynamic equation. Subsequently, an online identification scheme is proposed to update neural network weights where a set of auxiliary weight error vectors are used such that better convergence property can be achieved. Based on identification results, a singularity-free singular perturbation controller is developed to control the unknown nonlinear system. By using the singularity-free neural network and singular perturbation technique, the complexity in controller design for a singularly perturbed system is reduced, and the potential singularity problem is avoided. Moreover, a singularity-free dynamic surface control scheme is also proposed, and the “explosion of complexity” issue is relieved. Compared to conventional direct adaptive dynamic surface control schemes which use gradient-like updating laws and tracking errors to train the neural networks, the singularity-free dynamic surface controller is designed indirectly and the neural networks are updated using the identification errors. Therefore, better identification and control performance is achieved, and the potential singularity problem is also circumvented. The stability of the closed-loop system is rigorously proved via the Lyapunov approach, and the effectiveness of proposed identification and control schemes is demonstrated by simulations.

Group-symmetric consensus for nonholonomic mobile multirobot systems in coopetition networks

This paper proposes the concept of group-symmetric consensus for nonholonomic mobile multirobot systems (NMMRSs). Based on the thought of group-based coordination control, the framework of group-symmetric consensus for NMMRSs is developed in coopetition networks. Antagonistic interactions between robots therein can exist in the same group. Resorting to a novel auxiliary velocity vector embedded in the control algorithm, group-symmetric consensus can be realized with an integrated torque controller. By exploiting the Laplacian matrix associated with the coopetition networks in NMMRSs, the coordinate transformation technique is employed to execute stability analysis. Finally, the effectiveness of the group-symmetric consensus problem is verified by numerical simulations in two coopetition network types.

SYNTHESIS OF AUTO CALIBRATION SYSTEM IN NON MAINTENANCE WIRELESS SENSOR NETWORK

The methods of research and development of calibration of radio sensors with use of various models of parameters drift of radio sensors is solved. The main tasks and approaches to the development and synthesis of the autocalibration system in the network of radio sensors are determined. The proposed method of error detection and correction of measurement results of radio sensors in the network is based on the assumption of spatio-temporal correlation of measurement results in neighboring sensors and the lack of mutual correlation of drift processes of technical parameters. The use of the auxiliary regression vector, according to the equation of which the forecast of future measurement results is calculated, is proposed and substantiated for the analysis of the space-time correlation. It is established that there is a certain compromise in the choice of the optimal sample length during measurements.

Multi-dimensional Security Range Query for Industrial IoT

The Internet of Things (IoT) has allowed for significant advancements in applications not only in the home, business, and environment, but also in factory automation. Industrial Internet of Things (IIoT) brings all of the benefits of the IoT to industrial contexts, allowing for a wide range of applications ranging from remote sensing and actuation to decentralization and autonomy. The expansion of the IoT has been set by serious security threats and obstacles, and one of the most pressing security concerns is the secure exchange of IoT data and fine-grained access control. A privacy-preserving multi-dimensional secure query technique for fog-enhanced IIoT was proposed in light of the fact that most existing range query schemes for fog-enhanced IoT cannot provide both multi-dimensional query and privacy protection. The query matrix was then decomposed using auxiliary vectors, and the auxiliary vector was then processed using BGN homomorphic encryption to create a query trapdoor. Finally, the query trapdoor may be matched to its sensor data using the homomorphic computation used by an IoT device terminal. With the application of particular auxiliary vectors, the spatial complexity might be efficiently decreased. The homomorphic encryption property might ensure the security of sensor data and safeguard the privacy of the user's inquiry mode. The results of the experiments reveal that the computing and communication expenses are modest.

Composed Resource Optimization for Multitarget Tracking in Active and Passive Radar Network

In this article, a composed resource optimization (CRO) scheme is developed for an active and passive radar network engaged in multiple target tracking (MTT). The motivation of the CRO scheme is to collaboratively optimize the transmit resources of active radars, as well as the receiving processing resources of passive radars, to improve the overall MTT performance. We utilize the predicted conditional Cramér–Rao lower bound to evaluate the impact of allocation strategies on tracking performance and formulate the CRO as a mixed-integer nonlinear program problem since the adaptable parameters w.r.t. the target selection process are in binary form. To solve the problem, we propose an alternating direction method of multiplier-based algorithm. This algorithm transforms the original problem into an equality constrained problem by introducing two auxiliary vectors. In such a case, the CRO problem can be tackled by alternately solving several simple subproblems. Specifically, the subproblem w.r.t. the resource vector is convex, and the subproblems w.r.t. the auxiliary vectors are separable. Simulation results demonstrate that the proposed CRO scheme outperforms the traditional allocation schemes in terms of MTT performance. In addition, the performance of the CRO scheme is close to the optimal performance provided by the exhaustive method, but the computation load of the CRO scheme is lower than that of the exhaustive method. Finally, physical interpretations are presented to support our conclusions.

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

ОСОБЕННОСТИ МОДЕЛИРОВАНИЯ В РАЗЛИЧНЫХ ТИПАХ НЕЙРОСЕТЕЙ

Currently, the IT market uses the term "machine learning" as a direction of scientific engineering, closely related to the development of algorithms for training artificial neural networks based on data from various sensors or databases. The main principle of machine learning is selftraining of a neural network to patterns and making reasonable decisions by analyzing the data obtained. Consequently, machine learning is closely related to areas such as statistics, data mining, pattern recognition, and artificial intelligence. Neural networks are a popular platform for machine learning, but there are many other machine learning methods, such as logistic regression and auxiliary vector machines.

Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory

We show that the equation of motion of scalar-tensor theory acquires thermodynamic identity when projected on a generic null surface. The relevant projection is given by $E_{ab}l^ak^b$, where $E_{ab} =8\pi T_{ab}^{(m)}$ represents the equation motion for gravitational field in presence of external matter, $l^a$ is the generator of the null surface and $k^a$ is the corresponding auxiliary null vector. Our analysis is done completely in a covariant way. Therefore all the thermodynamic quantities are in covariant form and hence can be used for any specific form of metric adapted to a null surface. We show this both in Einstein and Jordan frames and find that these two frames provide equivalent thermodynamic quantities. This is consistent with the previous findings for a Killing horizon. Also, a concrete proof of the zeroth law in scalar-tensor theory is provided when the null surface is defined by a Killing vector.

Dynamics of magnetic collective modes in square- and triangular-lattice Mott insulators at finite temperature

We study the equilibrium dynamics of magnetic moments in the Mott insulating phase of the Hubbard model on the square and triangular lattice. We rewrite the Hubbard interaction in terms of an auxiliary vector field and use a recently developed Langevin scheme to study its dynamics. A thermal noise, derivable approximately from the Keldysh formalism, allows us to study the effect of finite temperature. At strong coupling, $U\ensuremath{\gg}t$, where $U$ is the local repulsion and $t$ the nearest-neighbor hopping, our results reproduce the well known dynamics of the nearest-neighbor Heisenberg model with exchange $J\ensuremath{\sim}\mathcal{O}({t}^{2}/U)$. These include crossover from weakly damped dispersive modes at temperature $T\ensuremath{\ll}J$ to strong damping at $T\ensuremath{\sim}\mathcal{O}(J)$, and diffusive dynamics at $T\ensuremath{\gg}J$. The crossover temperatures are naturally proportional to $J$. To highlight the progressive deviation from Heisenberg physics as $U/t$ reduces we compute an effective exchange scale ${J}_{\mathrm{eff}}(U)$ from the low-temperature spin-wave velocity. We discover two features in the dynamical behavior with decreasing $U/t$: (i) the low-temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii) the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/{J}_{\mathrm{eff}}$. We relate this to enhanced mode coupling, in particular to thermal amplitude fluctuations, at weaker $U/t$. A comparison of the square and triangular lattice reveals the additional effect of geometric frustration on damping.

Admissibility analysis of Takagi–Sugeno fuzzy descriptor systems with time-varying delay via nonorthogonal free-matrix-based inequality

This paper studies the admissibility of Takagi–Sugeno (T-S) fuzzy descriptor systems with time-varying delay. To analyze the admissibility, various free-matrix-based inequalities (FMIs) are used in the existing works, since they directly produce bounds for integral terms without time-varying delay in denominator. However, the slack matrices in these inequalities are incomplete with some zero components, which may lead to incomplete coupling system information. In this case, conservatism is unavoidable. To remove the issue, a nonorthogonal FMI (NFMI) is proposed by constructing nonorthogonal polynomials with auxiliary scalars and auxiliary vectors, which includes some existing FMIs as its special cases. Based on the NFMI, a less conservative admissibility criterion is obtained for T-S fuzzy descriptor system. Two examples are illustrated to demonstrate the effectiveness of the obtained results.

Heat Kernels Estimates for Hermitian Line Bundles on Manifolds of Bounded Geometry

We consider a family of semiclassically scaled second-order elliptic differential operators on high tensor powers of a Hermitian line bundle (possibly, twisted by an auxiliary Hermitian vector bundle of arbitrary rank) on a Riemannian manifold of bounded geometry. We establish an off-diagonal Gaussian upper bound for the associated heat kernel. The proof is based on some tools from the theory of operator semigroups in a Hilbert space, results on Sobolev spaces adapted to the current setting, and weighted estimates with appropriate exponential weights.

Vector Gaussian Successive Refinement With Degraded Side Information

We investigate the problem of the successive refinement for Wyner-Ziv coding with degraded side information and obtain a complete characterization of the rate region for the quadratic vector Gaussian case. The achievability part is based on the evaluation of the Tian-Diggavi inner bound that involves Gaussian auxiliary random vectors. For the converse part, a matching outer bound is obtained with the aid of a new extremal inequality. Herein, the proof of this extremal inequality depends on the integration of the monotone path argument and the doubling trick as well as information-estimation relations.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Analytic tadpole coefficients of one-loop integrals

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators over an auxiliary vector R. Using differential operators, we establish the corresponding differential equations for tadpole coefficients at the first step. Then using the tensor structure of tadpole coefficients, we transform the differential equations to the recurrence relations for undetermined tensor coefficients. These recurrence relations can be solved easily by iteration and we can obtain analytic expressions of tadpole coefficients for arbitrary one-loop integrals.

Fault Tolerant Control of Sensor Faults in Microgrid Inverter Control System

Aiming at sensor drift fault, the design problem of active fault tolerant controller for island-AC microgrid inverter system is studied. The controller has good ability to suppress external finite energy disturbance. Firstly, a closed-loop system state space model is constructed for an isolated AC microgrid inverter system with external finite energy disturbance. Then, when the sensor fault occurs in the control system, the fault information is taken as an auxiliary state vector, and the estimated value of the sensor fault and the system state variable is obtained simultaneously through the proposed extended observer. A fault tolerant controller is designed based on the idea of fault compensation. Finally, the correctness and effectiveness of this method are verified by programming simulation in MATLAB.

Event-triggered synchronization for semi-Markov jump complex dynamic networks with time-varying delay

This paper investigates the event-triggered synchronization of complex dynamic networks (CDNs) with semi-Markov switching and time-varying delay. First, by proposing auxiliary vectors with a few nonorthogonal polynomials, two slack-matrix-based integral inequalities are formulated, which encompass some existing ones as special cases. Second, a triple-integral-based delay-product-type (TIDPT) Lyapunov-Krasovskii functional (LKF) is formulated, which fully utilizes the information of time delay. After designing a controller via the event- triggered scheme, some sufficient conditions are proposed to achieve the global stochastic synchronization by utilizing the reciprocally convex matrix inequality (RCMI) and the founded inequalities to evaluate the derivative of the established LKF. A numerical example is employed to show the effectiveness and practicability of the proposed method.

A Novel Strategy of Control Performance Improvement for Six-Phase Permanent Magnet Synchronous Hub Motor Drives of EVs Under New European Driving Cycle

This paper proposes a model predictive current control (MPCC) method of six-phase permanent magnet synchronous hub motor (PMSHM) using auxiliary voltage vectors. First of all, 26 voltage vectors can be obtained from the switching states of six inverters, and 24 auxiliary voltage vectors can be generated by combining them. Second, four virtual voltage vectors can be found through the required locations, and the two vectors with the lowest cost will be selected by cost function. Then, additional current error correction module can better track the current. Finally, the proposed method is compared with the conventional MPCC method and another method with virtual voltage vectors. The innovation of this paper is that the recombination of vectors can better track and predict the current. A current error compensation module is added to reduce the error between the actual current and the predicted current. And the experimental results show that the proposed method has better performance such as smaller torque ripple and current THD both in steady and dynamic states. Finally, the strategy proposed in this paper was applied to the vehicle model through HIL test platform. The possibility of applying the strategy proposed in this paper to pure electric vehicles was verified under New European Driving Cycle (NEDC).

Performance-based Bi-objective optimization of structural systems subject to stochastic wind excitation

This paper outlines the development of a stochastic simulation-based design optimization approach for dynamic wind excited structures in which correlations between component damages and losses are explicitly treated. The proposed approach integrates a bi-objective design optimization scheme with a probabilistic performance-based wind engineering methodology which systematically accounts for the various sources of uncertainties involved in system loss estimation. Through the ∊-constraint technique, the bi-objective optimization problem is transformed into a series of single-objective stochastic optimization problems. To solve each ∊-constraint optimization problem, a pseudo-simulation scheme is proposed that allows for the formulation of an approximate sub-problem that can be solved sequentially to identify solutions that define a set of Pareto optimal designs. In the proposed scheme, samples of engineering demands are approximated in terms of auxiliary variable vectors, which are by-products of an augmented simulation carried out in a fixed design point. Analytical expressions are derived that relate the engineering demand samples to the second-order statistics of wind-induced losses based on the concept of fragility. Potential correlations between the component capacities and component losses are explicitly treated. The effectiveness of the proposed approach and its scalability to high-dimensional problems are illustrated through optimal designs of moment-resisting frames subject to stochastic wind loads.