State Matrix Research Articles

Finite‐time distributed block‐decomposed information filter for nonlinear systems with colored measurement noise

AbstractThis paper considers the distributed filtering problem for discrete‐time nonlinear systems with colored measurement noise obeying a nonlinear autoregressive process in sensor networks. A novel block‐decomposed information‐type filter for such systems is proposed in a centralized fusion structure, by using the statistical linear regression to deal with model nonlinearities and the measurement difference approach to overcome the noise correlation caused by colored measurement noises. Meanwhile, with the help of block matrix inverse operation to realize the high‐dimensional block matrix decomposition, the information vector and information matrix of the original system state in the designed information filter is directly estimated recursively, so as to own good numerical stability. Then, the finite‐time distributed implementation of the proposed filter is put forward, where the final filtering estimate in each sensor node is consistent with the centralized filtering result, by ensuring that each sensor node directly obtains the average values of shared variables in the sensor network through finite iterations of average consensus. Finally, the posterior Cramér–Rao lower bound is derived to show the proposed filter reaches the optimal theoretical performance bound in the premise of statistical linear regression and Gaussian posterior probability density approximation. A target tracking example with colored measurement noise obeying a linear and a nonlinear autoregressive processes validates the proposed method.

Approximation and control of a class of distributed delay systems

Abstract In this paper, we show that a linear system with distributed state delay can be approximated by a linear delay-free system that has the same state dimension as the original system if a so-called smallness condition holds. The smallness condition is an inequality which the maximum lag and norms of the system matrices have to satisfy. The eigenvalues of the approximate system correspond to the dominant eigenvalues of the original system with distributed delay. We provide a numerically stable, iterative algorithm to compute the state matrix of the approximate system. Furthermore, we show that, based on the proposed approximation, the stabilisation, pole placement and setpoint tracking control problems of the addressed class of distributed delay systems can be performed using methods developed for delay-free systems. Simulation results are provided to show the applicability of the proposed approximation and control design method.

Genome-wide scan reveals important additive and non-additive genetic effects associated with resistance to Haemonchus contortus in Florida Native sheep

Florida Native sheep is among the sheep breeds best adapted to humid and hot climatic conditions such as those of Florida, USA, and have shown a superior ability to regulate nematode burdens. This is one of the oldest sheep breeds in North America and is an endangered species. To ensure genetic diversity and long-term survival of the breed, protection of the current genetic stock is critical and conservation efforts are required to promote its breeding and production. The objective of the present study was to investigate the importance of additive and non-additive genetic effects on resistance to natural Haemonchus contortus infections in Florida Native sheep using a whole genome scan. A total of 200 sheep were evaluated in the present study. Phenotypic records included faecal egg count (FEC, eggs/gram), FAMACHA® score, packed cell volume (PCV, %), body condition score and average daily gain (ADG, kg). Sheep were genotyped using the GGP Ovine 50K SNP chip and 45.2 k single nucleotide polymorphism (SNP) markers spanning the entire genome were available for quality control procedures. Mixed models were used to analyse the response variables and included the identity by state matrix to control for population structure. Bonferroni correction was used to control for multiple testing and a second arbitrary threshold (0.1 × 10−3) was used. Fifteen SNPs with additive and non-additive genetic effects and located in Ovis aries chromosome OAR1, 2, 3, 6, 8, 10, 11, 12, 13 and 21 were associated with FEC, FAMACHA® score, PCV and ADG. These SNPs could be potential genetic markers for resistance to natural H. contortus exposure in Florida Native sheep.

Rapid Initial Self-Alignment Method Using CMKF for SINS Under Marine Mooring Conditions

To address the initial self-alignment problem of strapdown inertial navigation system under marine mooring conditions, a rapid initial self-alignment method based on the constraint matrix Kalman filter (CMKF) is proposed in this paper. The novelties of this method are two-fold. First, based on the Lie group differential equation, a one-step direct self-alignment model without coarse alignment process is designed directly based on a special orthogonal group of rigid-body rotations. In addition, to improve the alignment accuracy, the sensor biases are augmented into the state matrix to be estimated and compensated during the alignment process. Second, because the state of the proposed model is a matrix containing a special orthogonal group, a CMKF is developed to ensure the estimated accuracy. And a Lagrange function is designed in the CMKF to maintain the orthogonality of the special orthogonal group during the filtering process. The simulation and experimental results demonstrate that the proposed method exhibits better performance than existing methods in alignment accuracy and time, which can achieve the self-alignment of SINS under marine mooring conditions.

Triangular finite element in a mixed formulation for a flate problem of elasticity theory

Annotation. The algorithm for obtaining the stress-strain state matrix of a triangular finite element in a mixed formulation for calculating elastic structures under flat stress and flat deformation is analyzed. The nodal unknowns are assumed to be displacements and stresses. Approximation of desired quantities through the nodal values was carried out pelenanie functions. The stress-strain state matrix is obtained on the basis of a functional that reflects the equality of the actual work of external and internal forces when replacing the actual work of internal forces with the difference between the total and additional work of these forces. The calculation example shows the specificity of the algorithm.

Sub/Super-Synchronous Oscillation Oriented Dominant Controller Parameters Stability Region Based on Gerschgorin Disk Theorem

Since the development of renewable power generation, Sub/Super-Synchronous Control Interac-tion (SSCI), has attracted wide attention. Sub/super-synchronous oscillation (SSO) belongs to the category of small signal stability, and its characteristics are closely related to the operation mode and controller parameters in power grid. The operation mode of renewable power system changes frequently, a method to construct controller parameter stability region (PSR) is proposed for online assessment of the matching degree of controller parameters in power grid under current operation mode. Based on Gerschgorin disk theorem (GDT), eigenvalue distribution range of the system state matrix is estimated, thus the feasible value set of the controller parameter is deduced through small signal stability criterion. The stability margin evaluation index is proposed for guiding the prevention and control of SSO. Specifically, the preconditions of the application of the GDT on the PSR construction are discussed, and a construction method of transition matrix is proposed for the PSR construction. Furthermore, to reduce the conservativeness of PSR, an extension method for PSR is given. Finally, the validity of the proposed method is verified by a realistic benchmark. The efficiency of the proposed method is highlighted by comparing with the point-wise eigenvalue calculation of the state matrix.

Multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond

Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications. Due to the spatial localization of the defect states, these deep defects can be considered as artificial atoms/molecules in a solid state matrix. Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers and correctly predict properties that single-particle treatments fail to obtain. We choose the negatively charged nitrogen-vacancy (NV$^-$) center in diamond as the prototype defect to study with these techniques due to its importance for quantum information applications and because its properties are well-known, which makes it an ideal benchmark system. By properly accounting for electron correlations and including spin-orbit coupling and dipolar spin-spin coupling in the quantum chemistry calculations, for the NV$^-$ center in diamond clusters, we are able to: (i) show the correct splitting of the ground (first-excited) triplet state into two levels (four levels), (ii) calculate zero-field splitting values of the ground and excited triplet states, in good agreement with experiment, and (iii) calculate the energy differences between ground and exited spin-triplet and spin-singlet states, as well as their ordering, which are also found to be in good agreement with recent experimental data. The numerical procedure we have developed is general and it can screen other color centers whose properties are not well known but promising for applications.

Quantised scaled consensus of linear multiagent systems on faulty networks

In this paper, the practical mean-square scaled-consensus problem of multiagent systems is studied. Higher-order general linear dynamics is investigated, where all agents are subject to faults or denial of service attacks (DoS). The considered network comprises agents taking quantised states under undirected communication channels. Different from the existing works, no strict conditions have been imposed on the eigenvalues of the agents' state matrix. First, we propose a distributed scaled-consensus protocol that utilises a probabilistic quantisation algorithm. Second, scaled-disagreement analysis is provided via mean-square stability methodology. Finally, sufficient conditions in terms of linear matrix inequalities are presented in order to obtain scaled-consensus gain for both leaderless and leader–follower cases. The presented theoretical results are examined through two simulation examples.

SoC-Based Droop Coefficients Stability Region Analysis of the Battery for Stand-Alone Supply Systems With Constant Power Loads

The droop control is an advantageous approach for stand-alone supply systems consisting of multiple batteries, allowing among various inverters without intercommunication. The droop coefficients of batteries always vary with their state-of-charge (SoC) and charge/discharge mode, resulting in small-signal instability. Nevertheless, the existing impedance-based approaches can only assess the droop coefficients stability point, but not the stability region. Therefore, this article proposes a droop coefficients stability region analysis approach. First, the charge/discharge SoC-based droop controlled battery, the P&Q controlled distributed generator and the constant power load are separately discussed. Meanwhile, the state matrix and return-ratio matrix are established, respectively. Furthermore, the novel forbidden region criterion based on the return-ratio matrix is constructed, which reduces conservatism compared with norm-based impedance criteria and partial forbidden region criteria. Such a forbidden region criterion is first switched to the Hurwitz identification problem regarding the equivalent return-ratio matrix. Combined the state matrix and the equivalent return-ratio matrix, the generalized incidence matrix is constructed to simultaneously identify subsystem stability and interactive stability. Based on the generalized incidence matrix, an adaptive step search strategy is proposed to obtain the droop coefficients coordinated stability region. Finally, the simulation and experimental results illustrate the validity of the proposed method.

Session Recommendation Model Based on Context-Aware and Gated Graph Neural Networks.

The graph neural network (GNN) based approach has been successfully applied to session-based recommendation tasks. However, in the face of complex and changing real-world situations, the existing session recommendation algorithms do not fully consider the context information in user decision-making; furthermore, the importance of context information for the behavior model has been widely recognized. Based on this, this paper presents a session recommendation model based on context-aware and gated graph neural networks (CA-GGNNs). First, this paper presents the session sequence as data of graph structure. Second, the embedding vector representation of each item in the session graph is obtained by using the gated graph neural network (GGNN). In this paper, the GRU in GGNN is expanded to replace the input matrix and the state matrix in the conventional GRU with input context captured in the session (e.g., time, location, and holiday) and interval context (representing the proportion of the total session time of each item in the session). Finally, a soft attention mechanism is used to capture users' interests and preferences, and a recommendation list is given. The CA-GGNN model combines session sequence information with context information at each time. The results on the open Yoochoose and Diginetica datasets show that the model has significantly improved compared with the latest session recommendation methods.

An Original Educational Algorithm Assessing the Behaviours of Angular Frequency Deviations of a Multimachine System in Small Signal Analysis

The paper presents a fully self-implementable algorithm that has demonstrated to be an effective tool for power education at the University of Padova-Department of Industrial Engineering. It deals with the small signal analysis of the electromechanical transients of a multimachine system. The algorithm allows analytically building both the state matrix and the input matrix. Moreover, by exploiting the matrix exponential, the angular frequency deviations of synchronous generators can be computed and plotted so to help students to evaluate transient stability. Besides the full exposition of the algorithm, the paper presents a comparison between a self-implemented linearized dynamic in Matlab environment and the dynamic simulation obtained by the commercial software DIgSILENT PowerFactory.

Quantum Error Mitigation for Quantum State Tomography

Quantum state tomography (QST) is the task of statistically constructing the density matrix of an unknown quantum state by measuring its several copies. The presence of noise in the QST setup can considerably degrade the fidelity between the constructed density matrix and the actual state. We consider a noisy QST setup with depolarizing noise and attempt to mitigate the effects of noise by quantum error mitigation (QEM). We compare the performance of different QEM methods with the same resources and find that the measurement error mitigation and zero noise extrapolation provide the best performance in terms of maximizing the fidelity between the state and its density matrix.

Improvement on Age of Information for Information Update Systems With HARQ Chase Combining and Sensor Harvesting-Transmitting Diversities

The age of information (AoI) has attracted increasing attentions as a new metric and tool to capture the timeliness of reception and freshness of data, which is different from the conventional metric such as outage, delay, and throughput. While most existing works focused on AoI analysis and optimizing method, the information update system design by utilizing diversity to reduce AoI is not fully exploited so far. Inspired by this fact, a novel information status update system is designed by jointing wireless energy harvesting diversity, status update transmitting diversity, and hybrid automatic repeat request (HARQ). Specially, the update system consists of two sensors that can be seen as an unified entity from the destination's perspective, and one destination. The two sensors, which have finite-size batteries and synchronously operate in half-duplex mode, harvest energy from a Bernoulli process source, and cooperatively deliver the status update to destination by sharing a common information source. To exploit the information of the unsuccessfully decoding update packet, the HARQ and chase combining (HARQ-CC) are jointly used at destination so that the HARQ-CC receiving diversity is also exploited. By using Bernoulli process energy arrival probability and sensor transmission probability, we first propose one novel sensor energy harvesting and update delivering model that can be represented by Markov Chain (MC) and develop one novel construction method of the transition matrix of sensor battery energy states. Considering the developed energy state transmission matrix column stochastic, irreducible, and aperiodic, we obtain the stationary distribution of sensor battery energy states so that the steady transmitting power is derived. Secondly, the average AoI of the dual-sensor status update system is derived in terms of a closed-form expression by accurately calculating the statistical descriptions of the maximum retransmission number (time) in HARQ-CC and the service time of one packet. The analytical results are validated by using the comparison from simulations. Moreover, compared with traditional single sensor system, the dual-sensor system not only harvests more energy, but also has smaller average AoI because of the joint exploitation of multi-diversity. Besides, the impact of the system parameters on harvested energy and average AoI is provided, which provides insights in terms of the optimal design of Internet of things system.

Теоретичне обґрунтування управління функціонуванням технічними та транспортними системами на основі методів системної теорії інформації

In the work from the theoretical point of view the management of functioning of transport and operation of technical systems on the basis of a method of the system theory of information is substantiated. The state vector and matrix on the basis of diagnostic information and sensitivity of influence of diagnostic parameters on a condition of transport or technical systems are offered. The properties of sensitivity (sensitivity) are reflected on the basis of classical and generalized information formulas of A. Kharkevich, K. Shannon, R. Hartley. The coefficients of quantum (emergence) of information according to the expressions of Shannon-Kharkevich and Hartley are used, the level of complexity of the changed states of the control system is taken into account. The scheme of connections of classical and generalized formulas which reflect functions of density of the diagnostic information on a condition of technical and transport systems is constructed. A universal numerical method and tools for it have been developed, which allows to perform information calculations on the basis of diagnostic data of the state of the studied objects. Numerical calculation refers to the sensitivity of the state (sensitivity factor) of technical and transport systems. The level of system organization of transport and technical systems and their management as active objects is considered. It is noted that the principle of correspondence is fulfilled, which is mandatory for a more general information theory. The system modification is implemented using the Hartley formula, and the modification in the classical case is the Kharkevich formula. It is determined that the semantic information model allows for small samples and comparison of partial criteria to well substantiate the interpretations of object state recognition, developed by the vectors of their classes. It is revealed that the semantic information model combines the advantages of meaningful and statistical models created for the implementation of the automated system of cognitive analysis of transport and technical systems. The behavior of systems is revealed when they are completely deterministic and completely random, which is important in predicting their state.

Математическая модель оценки вероятности коллизий преамбул при случайном доступе в сценарии массового межмашинного взаимодействия

The mass machine-to-machine communication (mMTC) scenario is one of the key ones in 5G cellular communication system. Tens of thousands of devices can operate simultaneously in one mMTC cell, sending data asynchronously to the data collection point. This is the reason for the occurrence of unavoidable collisions of preamble in the random access procedure. Mathematical models of traffic generation from a large number of devices within a cell are used to reliably estimate the probability of collisions. Most existing models are based on the approach of generating aggregated traffic from all devices and do not allow taking into account the current state of each individual device, which reduces the reliability of model studies. To solve this problem, we propose a mathematical model for generating traffic (preambles) in a random access channel, taking into account the transition state matrix of a discrete Markov chain. This approach allows to describe more reliably the synchronous and asynchronous transmission of preambles within a cell. The developed model is designed to estimate the collision probability of the random access procedure in the mMTC scenario, taking into account the synchronous and asynchronous transmission of preambles.

Sliding Mode Control for Singularly Perturbed Systems Using Accurate Reduced Model

In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.

A fractional approach to solve a mathematical model of HIV infection of CD4+T cells

A mathematical model that calculates susceptible CD4+T cells, infected CD4+T cells and virus particles has been examined here using the fractional differential transform method (FDTM) with stability analysis. A stability of the fractional nonlinear model with Hurwitz state matrix is examined using the Lyapunov direct method. A nonlinear mathematical model of differential equations has been put forward and analyzed by applying FDTM. An infinite series solution of the system of differential equation is computed by defining fixed components with different time intervals. Furthermore, the solution calculated through FDTM (integer order) is correlated with the solution calculated using DTM and LADM. The solution is analyzed numerically and graphically by using the software Python.

Ackermann’s Method: Revisited, Extended, and Generalized to Uncontrollabe Systems

The celebrated method of Ackermann for eigenvalue assignment of single-input controllable systems is revisited in this paper, contributing an elegant proof. The new proof facilitates a compact formula which consequently permits an extension of the method to what we call incomplete assignment of eigenvalues. The inability of Ackermann’s formula to deal with uncontrollable systems is considered a weakness inherent in the method. The notion of incomplete assignment leads to a straightforward generalization of our method to eigenvalue assignment of uncontrollable systems, thus mitigating such a drawback of a popular method. Further results concerning the incomplete assignment are stated, verified, and commented. Such results reveal the trace of the state matrix $A$ a worthy feature pertinent to an open loop system. Finally, four numerical examples are worked out to demonstrate cases of incomplete, and uncontrollable eigenvalues assignment. The examples consider a case where the structure of the feedback matrix can be easily simplified. The paper ends with a commentary brief concerning some commonly used MATLAB commands for eigenvalue assignment.

Entrainment matrix for BSk energy-density functionals

The entrainment matrix is an important parameter of superfluid hydrodynamics and is extensively used to model, e.g., neutron-star oscillations and glitches. Here we present a detailed step-by-step algorithm to calculate this matrix for a series of modern BSk energy-density functionals. Using it, both the entrainment matrix and equation of state can be determined self-consistently, within the same microscopic approach.

Flat-band ferromagnetism in twisted bilayer graphene

We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $\theta\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=\pm2$).