Design of switched linear systems in the presence of actuator saturation and L-infinity disturbances

This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and L-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the L-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and L-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the L-infinity norm of the system output or by the system’s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.     

LMI Condition of Quadratic D-stability for a Class of Uncertain Linear Systems

A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology.Finally,the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.     

H_∞ Control with Multiple Delays in Measurements

Based on an innovation analysis method in the Krein space,a sufficient and necessary condition is given for the existence of the solution of H_∞control problem for a linear continuous- time system with multiple delays.By introducing a re-organized innovation sequence,the H_∞control problem with delayed measurements is converted into a linear quadratic(LQ)problem and a delay- free H_2 estimation problem in the Krein space.The controller is given in terms of two forward Riccati equations and a backward Riccati equation.     

多步观测时滞的控制

Based on an innovation analysis method in the Krein space, a sufficient and necessary condition is given for the existence of the solution of H1 control problem for a linear continuous-time system with multiple delays. By introducing a re-organized innovation sequence, the H1 control problem with delayed measurements is converted into a linear quadratic (LQ) problem and a delay-free H2 estimation problem in the Krein space. The controller is given in terms of two forward Riccati equations and a backward Riccati equation.     

Robust H ∞ filter design for time-delay systems with saturation

This paper investigates the H∞ filtering problem for a class of linear continuous-time systems with both time delay and saturation. Such systems have time delay in their state equations and saturation in their output equations, and their process and measurement noises have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the linear matrix inequalities (LMIs) technique, a generalized dynamic filter architecture is proposed, and a filter design method is developed. The linear H∞ filter designed by the method can guarantee the H∞ performance. The parameters of the designed filter can be obtained by solving a kind of LMI. An illustrative example shows that the design method proposed in this paper is very effective.     

Design of high performance linear feedback laws for operation that extends into the nonlinear region of AMB systems

Existing active magnetic bearings (AMBs) operate in the linear region of the magnetic material flux density, which limits the utilization of the bearing capacity. In order to increase the utilization of the bearing capacity and enhance the performance of the AMB system, this paper develops a method for designing high performance linear feedback laws. The resulting feedback laws allow the AMB to operate in its nonlinear region and hence improve the closed-loop performance. We first establish an approximate nonlinear AMB current force response model, and place this nonlinear curve inside a sector formed by two piecewise linear lines. Based on the linear line segments in these two piecewise linear lines, we determine the maximum disturbance that can be tolerated by solving an optimization problem with linear matrix inequality (LMI) constraints. For a given level of disturbance under the maximum tolerable disturbance, we formulate and solve the problem of designing the linear feedback that achieves the highest level of disturbance rejection as another LMI problem. Both $L_2$ disturbances and $L_\infty$ disturbances are considered. Finally, we illustrate our design by both simulation and experimental results.     

New application methods for word-oriented cryptographic primitives

Modern software oriented symmetric ciphers have become a key feature in utilizing word-oriented cryptographic primitives.Using the output sequence,in the order of its generation,of a word-oriented cryptographic primitive in the same way as traditional bit-oriented primitives,we can expose the intrinsic weakness of these primitives,especially for word-oriented linear feedback shift registers,T-functions,and so on.Two new methods for using word-oriented cryptographic primitives are presented in this paper,that is,the extracted state method and cascading extracted coordinate method.Using a T-function as an example,we research the different cryptographic properties of the output sequences of the original method and the two proposed methods,focusing mainly on period,linear complexity,and k-error linear complexity.Our conclusions show that the proposed methods could enhance at low cost the cryptographic properties of the output sequence.As a result,since the new methods are simple and easy to implement,they could be used to design new word-oriented cryptographic primitives.     

Frequency-domain $L_2$-stability conditions for time-varying linear and nonlinear MIMO systems

The paper deals with the g2-stability analysis of multi-input-multi-output （MIMO） systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin- earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain. These conditions have the following features： i） They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block, ii） For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.     

Robust power control method for wireless sensor networks with static output feedback

This paper proposed distributed strategies for the joint control of power and data rates in a wireless sensor network. By adapting a linear state-space model to describe the network dynamics, the power controller with static output feedback is designed in the case that the transmission signal are not always available and the estimation of the unmeasured states constitutes a crucial task in the network. The existence of the power controller is formulated as the feasibility of the convex optimization problem, which can be solved via a linear matrix inequality (LMI) approach. The proposed algorithm also caters to the uncertainties in the network dynamics. Numerical examples are given to illustrate the effectiveness of the proposed methods.     

非线性模型下的摄像机自标定

摄像机标定是从二维图像获取三维信息必不可少的步骤，线性（小孔）模型摄像机自标定，目前已成为计算机视觉领域的研究热点之一，对于非线性模型下摄像机的自标定，目前还未见到相关的研究报道，用于线性模型一般不能准确地描述真实像机的几何成像关系，因此对非线性模型摄像机自标定的研究具有十分重要的实际意义，该文主要探索非线性模型摄像机的自标定方法，基本原理是将非线性模型视为线性模型和畸变项的叠加，然后利用线性模型的基本矩阵或单应矩阵，给出非线性模型参数的约束方程，从而实现非线性模型摄像机的自标定，模拟和真实图像实验均表明该文所给的方法是可行的，具有一定的实用价值。     

直线电机的发展及应用概况

介绍了直线电机的分类及特点,直线电机是一种将电能直接转换成直线运动,而不需要通过任何中间转换机构的新颖电机.阐述了直线电机理论分析和优化设计的研究手段和最新研究成果,分析了直线电机核心控制部件、外围输出通道、控制理论和控制技术发展状况,简要叙述了直线电机在工业、办公设备、交通、家庭自动化、军事装备等领域的的应用现状和动态.根据直线电机应用研究的发展趋势,指出在利用计算机提高直线电机的控制精度和依据新原理研制新型直线电机的新技术推动下,直线电机具有广阔的应用和发展前景.     

Linear control of nonlinear systems based on nonlinearity measures

In reality, virtually every process is a nonlinear system. Nevertheless, linear controller design methods have proved to be adequate in many applications. In practice, the linear controller design is usually done disregarding a possible nonlinear plant/linear model mismatch. In this work we introduce a general framework for the development of linear controllers for nonlinear systems based on nonlinearity measures. Nonlinearity measures are tools to assess the extent of a system’s inherent nonlinearity instead of just recognizing a system as being linear or nonlinear. Recent work shows that nonlinearity measures characterize the magnitude of the modeling error when an optimal linear model is used for the nonlinear system. The best linear model can then be used to design a linear controller that robustly stabilizes the linear system in presence of the nonlinear modeling error. A crucial point is that both, the best linear model and the modeling error, are determined for a specified region of operation, thus significantly increasing the class of applicable nonlinear systems. Examples demonstrate the (necessity and) effectiveness of the proposed approach.     

若干二元周期序列的紧错线性复杂度

综合线性复杂度,k错线性复杂度、k错线性复杂度曲线和最小错误minerror(S)的概念,提出m紧错线性复杂度的概念.序列S的m紧错线性复杂度是一个二元组(km,LCm).序列S的k错线性复杂度曲线的第m个跃变点对应的km值和对应km错线性复杂度LCm,称为序列S的m紧错线性复杂度.通过使用简洁的cost二维结构,给出...     

城市线性景观的构建与发展——以北方地区线性景观为例

城市线性景观是景观设计学中的一个综合概念,可以理解为人类活动与生态环境相互叠加形成的具有线性特征的复合生态系统。文章以城市线性景观为主要研究对象,结合北方地区的实际情况,对如何构建城市线性景观进行探索研究,总结线性景观对于景观设计学的影响,并在线性景观构建的基础上探讨其在城市中的发展方向与趋势。     

一种SPN线性层的设计方法

提出了线性码理论用于SPN分组密码线性层（或称扩散层）设计，并给出了过线性码设计最优扩散线性层的方法，从而为密码结构中的线性变换的没计提供了理论基础。利用该方法进行了实例设计与分析，并对其扩散特性进行了仿真。     

各向同性线性系统理论研究综述

各向同性线性系统作为一类特殊的线性系统,不仅具有广泛的应用背景,还具备许多一般线性系统不具有的特殊性质.鉴于此,系统地归纳总结各向同性线性系统的特点,特别是这类系统与其对应的复系数线性系统之间的关联;此外,讨论对各向同性线性系统设计各向同性反馈的必要性,并以航天器姿态控制系统为例介绍各向同性线性系统的具体应用实例;结合几类常见的可用各向同性线性系统描述的工程控制系统,对现有的相关结果进行归纳和介绍;最后对各向同性线性系统进一步的研究方向进行简单的展望.     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

Semi-global stabilization of partially linear composite systems via feedback of the state of the linear part

We consider the problem of semi-global stabilization of a class of partially linear composite systems. We show, by explicit construction of the control laws, that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi-globally stabilizable by a dynamic feedback of the state of the linear subsystem if (a) the linear subsystem is right invertible and has all its invariant zeros in the closed left half s-plane, and (b) the only linear variables entering the nonlinear subsystem are the output of the linear subsystem. Our work generalizes previous results by C.I. Byrnes and A. Isidori (1991), H.J. Sussmann and P.V. Kokotovic (1991), and A.R. Teel (1992).     

Polyhedral representation of fuzzy linear bases

 In [15], we introduced the concepts of fuzzy bases, fuzzy linear interpolation and fuzzy polygon of four-component fuzzy linear bases. In [16], these concepts were used in the maximal profile of the set of polygons generated from a set of break points for each variable dimension. Theconcept was operationalized in a fuzzy linear basis algorithm (FLBA) for nonlinear separable programming problems involving no more than a finite number of discontinuities. The FLBA provides a powerful platform forparallel processing of the fuzzy linear sub-problems included in the finite FLB-chain. In this paper we extend the theory of fuzzy linear bases from the set of polygons toapolyhedral representation of four-component fuzzy linear bases defined on a closed subset of the real line.