求解 ℳ张量多线性系统的一种新预处理Richardson迭代法

Richardson迭代法是求解ℳ张量多线性系统的一种有效方法。为了进一步加快其收敛速度,本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后,通过数值例子验证该方法的有效性和可行性。The Richardson iterative method is an effective method for solving multi-linear systems with ℳ-tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ-tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.

基于预处理分裂迭代算法求解Mz张量方程组

偶数阶张量的正定性和半定性由于在谱超图理论、自动控制、多项式理论、随机过程、磁共振成像等众多领域均有着广泛的应用,近年来得到了深入而广泛的研究。研究表明,M张量、B张量、H张量、希尔伯特张量以及随机张量在特定条件下可以是正定的。然而,仍有许多正定张量无法通过上述准则来确定。在本文中,我们提出了一类全新的正定张量,其非对角项相对于强M张量可以为正,我们将其称为强Mz张量。这类强Mz张量可从离散微分方程中产生,原因在于它是基于Z特征值而非传统的H特征值。由于Z特征值定义中涉及的非齐次性通常比H特征值更难处理相应的问题,因此Z特征值的计算结果远远小于h本征值的计算结果。定义在Z特征值基础上的Mz张量在结构上比已被广泛研究的M张量更复杂。对Mz张量的研究几乎是一片空白。到目前为止,还没有人提出求解强Mz方程的算法。作为本文的动机之一,我们创新性地利用张量迭代给出了求解系数张量为Mz张量的多线性系统的张量分裂迭代算法。其次,给出了相应的预处理分裂迭代算法以及理论分析。最后,通过数值算例说明了所提算法的有效性。这在图像处理以及物理领域等多维信息分析方面,乃至高阶非线性系统的稳定性研究等领域均具有广泛的应用前景。The positive definiteness and semi-definiteness of even-order tensors have received extensive and in-depth research in recent years due to their wide applications in various fields such as spectral hypergraph theory, automatic control, polynomial theory, stochastic processes, and magnetic resonance imaging. Studies have shown that M-tensors, B-tensors, H-tensors, Hilbert tensors, and random tensors can be positive definite under specific conditions. However, there are still many positive definite tensors that cannot be determined by the above criteria. In this paper, we propose a new class of positive definite tensors whose off-diagonal terms can be positive relative to strong M-tensors. We call them strong Mz-tensor. This kind of strong Mz-tensor can be generated from discrete differential equations because it is based on Z-eigenvalues rather than the traditional H-eigenvalues. Due to the non-homogeneity involved in the definition of Z-eigenvalues, which is usually more difficult to handle corresponding problems than H-eigenvalues, the computational results of Z-eigenvalues are much smaller than those of h-eigenvalues. The Mz-tensor defined on the basis of Z-eigenvalues is structurally more complex than the widely studied M-tensor. The research on Mz-tensor is almost a blank. So far, no one has proposed an algorithm for solving strong Mz equations. As one of the motivations of this paper, we innovatively use tensor iteration to give a tensor splitting iterative algorithm for solving multilinear systems with coefficient tensors being Mz-tensor. Secondly, the corresponding preconditioned splitting iterative algorithm and theoretical analysis are given. Finally, numerical examples illustrate the effectiveness of the proposed algorithm. This has broad application prospects in multi-dimensional information analysis such as image processing and the physical field, and even in the stability research of high-order nonlinear systems.

A New Method for Constructing the Inversion of Multivariable Linear Systems

A new algorithm for constructing an inverse of a multivariable linear system is presented. This algorithm makes the constructing an inverse of the higher order matrices into searching for the equivalent normal form of the lower order matrices. Consequently, the calculation is more simple efficient and programmed than previous methods. Another result of the paper is that the lower reduced inverse system is obtained, by selecting special bases of the observable space of the original systems, it reveals the effect of the observability of the original systems on the order of the inverse systems.

在Einstein积上关于张量-矩阵形式的一个注释

利用Einstein积研究了矩阵和张量之间的关系。得到了保持爱因斯坦积的张量空间和矩阵空间之间是线性同构的。研究结果推广了Brazell等([1]中(2.5)式)给出的变换。

STABILITY ANALYSIS AND COOPERATIVE CONTROL OF DISTRIBUTED MULTI-AGENT SYSTEM WITH SAMPLED COMMUNICATION

The cooperative control and stability analysis problems for the multi-agent system with sampled com- munication are investigated. Distributed state feedback controllers are adopted for the cooperation of networked agents. A theorem in the form of linear matrix inequalities（LMI） is derived to analyze the system stability. An- other theorem in the form of optimization problem subject to LMI constraints is proposed to design the controller, and then the algorithm is presented. The simulation results verify the validity and the effectiveness of the pro- posed approach.

Stability analysis of time-varying systems via parameter-dependent homogeneous Lyapunov functions

This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.

Performance of the geometric approach to fault detection and isolation in SISO,MISO,SIMO and MIMO systems

In this paper, a geometric approach to fault detection and isolation （FDI） is applied to a Multiple-Input Multipie-Output （MIMO） model of a frame and the FDI results are compared to the ones obtained in the Single-Input Single-Output （SISO）, Multiple-Input Single-Output （MISO）, and Single-Input Multiple-Output （SIMO） cases. A proper distance function based on parameters obtained from parametric system identification method is used in the geometric approach. ARX （Auto Regressive with exogenous input） and VARX （Vector ARX） models with 12 parameters are used in all of the above-mentioned models. The obtained results reveal that by increasing the number of inputs, the classification errors reduce, even in the case of applying only one of the inputs in the computations. Furthermore, increasing the number of measured outputs in the FDI scheme results in decreasing classification errors. Also, it is shown that by using probabilistic space in the distance function, fault diagnosis scheme has better performance in comparison with the deterministic one.

Adaptive predictive functional control based on Takagi-Sugeno model and its application to pH process

In order to obtain accurate prediction model and compensate for the influence of model mismatch on the control performance of the system and avoid solving nonlinear programming problem,an adaptive fuzzy predictive functional control(AFPFC) scheme for multivariable nonlinear systems was proposed.Firstly,multivariable nonlinear systems were described based on Takagi-Sugeno(T-S) fuzzy models;assuming that the antecedent parameters of T-S models were kept,the consequent parameters were identified on-line by using the weighted recursive least square(WRLS) method.Secondly,the identified T-S models were linearized to be time-varying state space model at each sampling instant.Finally,by using linear predictive control technique the analysis solution of the optimal control law of AFPFC was established.The application results for pH neutralization process show that the absolute error between the identified T-S model output and the process output is smaller than 0.015;the tracking ability of the proposed AFPFC is superior to that of non-AFPFC(NAFPFC) for pH process without disturbances,the overshoot of the effluent pH value of AFPFC with disturbances is decreased by 50% compared with that of NAFPFC;when the process parameters of AFPFC vary with time the integrated absolute error(IAE) performance index still retains to be less than 200 compared with that of NAFPFC.

Diversity and Bioactivity of Actinomycetes from Marine Sediments of the Yellow Sea

Among the 116 actinomycetes collected from marine sediments of the Yellow Sea,56 grew slowly and appeared after 2?3 weeks of incubation.Among the 56 strains,only 3 required seawater(SW) for growth,and 21 grew well in the medium prepared with SW rather than distilled water(DW),while the remaining 32 grew well either with SW or with DW.Six representatives with different morphological characteristics,including 1 SW-requiring strain and 5 well-growing with SW strains,were selected for phy-logenetic analysis based on 16S rRNA gene.Two strains belong to Micrococcaceae and Nocardiopsaceae respectively.The other 4 strains belong to the family of Streptomycetaceae.In the analyzed 6 strains,one was related to Nocardiopsis spp.and the other three were related to Streptomyces spp.,representing new taxa.Bioactivity testing of fermentation products from 3 SW-requiring strains and 21 well-growing with SW strains revealed that 17 strains possessed remarkable activities against gram-positive pathogen or/and tumor cells,suggesting that they were prolific resources for natural drug discovery.

A simple rectification method for linear multi-baseline stereovision system

The linear multi-baseline stereo system introduced by the CMU-RI group has been proven to be a very effective and robust stereovision system. However, most traditional stereo rectification algorithms are all designed for binocular stereovision system, and so, cannot be applied to a linear multi-baseline system. This paper presents a simple and intuitional method that can simultaneously rectify all the cameras in a linear multi-baseline system. Instead of using the general 8-parameter homography transform, a two-step virtual rotation method is applied for rectification, which results in a more specific transform that has only 3 parameters, and more stability. Experimental results for real stereo images showed the presented method is efficient.

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control(NMPC) approach based on support vector machine(SVM) and genetic algorithm(GA) for multiple-input multiple-output(MIMO) nonlinear systems.Individual SVM is used to approximate each output of the controlled plant Then the model is used in MPC control scheme to predict the outputs of the controlled plant.The optimal control sequence is calculated using GA with elite preserve strategy.Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.

Total Variation and Multisymplectic Structure for CNLS System

The relation between the toal variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schroedinger system are obtained directly from the variational principle.

An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Web-based supplier relationship framework using agent systems

In order to enable both manufacturers and suppliers to be profitable on today’s highly competitive markets, manufacturers and suppliers must be quick in selecting best partners establishing strategic relationship, and collaborating with each other so that they can satisfy the changing competitive manufacturing requirements. A web-based supplier relationships (SR) framework is therfore proposed using multi-agent systems and linear programming technique to reduce supply cost, increase flexibility and shorten response time. Web-based SR approach is an ideal platform for information exchange that helps buyers and suppliers to maintain the availability of materials in the right quantity, at the right place, and at the right time, and keep the customer-supplier relationship more transparent. A multi-agent system prototype was implemented by simulation, which shows the feasibility of the proposed architecture.

LINEAR-DISPERSION DIVISION MULTIPLE-ACCESS FOR MIMO SYSTEMS

Comprehensive study on novel Linear-Dispersion Division Multiple-Access(LDDMA) for multi-user uplink Multiple-Input Multiple-Output(MIMO)systems is proposed.In the new multi-plexing scheme,each user’s information symbol is dispersed by a User-Specific Matrix(USM)both inspace and time domain and linearly combined at base-station side.And a simple random search al-gorithm,based on capacity maximization criteria,is developed to generate a bank of USMs.Simulationresults are presented to demonstrate the advantages of LDDMA.When the Bit Error Rate(BER)reaches 10–3,the performance gains are 3dB and 5dB,compared with Time-Division Linear DispersionCodes(TD-LDC)and BLAST,respectively.

The Structure and Stabilization Decom position of Linear Interconnected ControlSystem swith Multidelays

This paper gives a structural concept for linear interconnected control systems with multidelays,which is based on equivalence method of lyapunovs frequency area, a sufficient \{criteria\} is obtained for the interconnected stabilization of linear constant control system with multidelays,at the same time,the estimation of bound both time delays and parametric perturbation are given.

Large Deflection Dynamic Response Analysis of Flexible Hull Beams by the Multibody System Method

In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.

Modeling and Control of Nonlinear Discrete-time Systems Based on Compound Neural Networks

An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the nonlinear system and a recurrent neural network to minimize the difference between the linear model and the real nonlinear system. Because the current control input is not included in the input vector of recurrent neural network (RNN), the inverse control law can be calculated directly. This scheme can be used in real-time nonlinear single-input single-output (SISO) and multi-input multi-output (MIMO) system control with less computation work. Simulation studies have shown that this scheme is simple and affects good control accuracy and robustness.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Trajectory tracking and formation control based on consensus in high-dimensional multi-agent systems

This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.