基于有限区域量化的系统稳定性分析与设计

针对基于输出反馈和具有有限区域信号量化的离散时间系统,进行了系统稳定性分析与量化参数设计的研究.首先,分别对状态观测误差系统和对象系统在有限区域对数量化作用下的系统渐近稳定性进行了分析,得到了相应的稳定性条件,接着针对对数型量化器,给出了两个系统稳定性之间的内在关联,同时得到了各有限区域量化器的量化区间上界值.在此基础上,得到了保证各子系统稳定的系统通信速率比值.最后,给出了在时变量化作用下基于状态观测的控制策略和仿真例子.     

不可分解模的参量化

本文的主要结果是给出了有限群的不可分解模的一种参量化, 它相对于Puig 和Thévenaz 给出的参量化更加自然. 同时我们说明了用这两种不同的方式给出的参量化是一致的.     

有限维P-框架的冗余函数

最近,Hilbert空间里有限维框架的冗余度性质已被证明.本文把Hilbert空间里有限维框架量化冗余度的概念推广到Banach空间里有限维p-框架,研究定义在Banach空间球面上的冗余函数的最大值和最小值,并给出上冗余度和下冗余度的性质.     

基于∑△量化的多智能体系统的量化一致性

用量化控制分析多智能体的一致性问题.不同于以往的静态量化器,例如均匀量化或者对数量化,文章运用动态Sigma-Delta(Σ△)量化器提出新的多智能体量化一致性协议,利用有限比特数使系统达到渐进一致,且渐进收敛到初值的平均值,并且给出系统达到渐进一致的充分条件.与静态的非对称和对称量化器相比,∑△量化器克服了静态量化器无记忆并且不能消除稳态误差及需要无限比特的量化信息的缺点,体现了它的优越性.     

具有观测器的多自主体系统有限通信数据率一致性研究

有限通信数据率是网络通信中的重要约束条件.基于Luenberger观测器,主要研究了带有有限通信数据率的多自主体系统的一致性问题,分别考虑了通信带宽无限和有限两种情况.同时也给出了使得系统满足一致性条件的观测器和量化器的设计方法.最后给出数值仿真验证理论结果.     

考虑时间相关性的DSMC方法统计误差分析

过去的半个世纪,DSMC方法已经成为求解稀薄气体流动最有力的数值工具,它的精度问题得到了许多研究者的关注.DSMC方法的误差可以分为两类,一类是统计误差,另一类是数值误差.在DSMC方法中,宏观流动性质是通过对微观分布信息的抽样平均而得到的,因此模拟结果本质上是符合概率统计的,需要对由于有限的抽样步数而导致的统计误差进行仔细地量化考察.统计误差在DSMC方法中占有重要的地位,但是直到今天仍没有被完全研究清楚.尽管前人做了一些研究,但是通常都假设抽样结果是相互独立的,对于获得精确结果所需的最小抽样步数,还没有清晰统一的认识.时间相关性会增加统计误差理论分析的难度,因此在已有的工作中很少被考虑到.使用统计学中的自相关函数以及修正的中心极限定理,可以量化抽样结果中的时间相关性.在考虑抽样结果时间相关性的基础上,研究了DSMC方法中的统计误差,考核算例为一维的Couette流动问题.量化的结果显示,时间相关性对统计误差的影响很大.时间相关性可增大随机变量抽样序列的方差.     

考虑时间相关性的DSMC方法统计误差分析（英文）

过去的半个世纪,DSMC方法已经成为求解稀薄气体流动最有力的数值工具.它的精度问题得到了许多研究者的关注.DSMC方法的误差可以分为两类,一类是统计误差,另一类是数值误差.在DSMC方法中,宏观流动性质是通过对微观分布信息的抽样平均而得到的,因此模拟结果本质上是符合概率统计的,需要对由于有限的抽样步数而导致的统计误差进行仔细地量化考察.统计误差在DSMC方法中占有重要的地位,但是直到今天仍没有被完全研究清楚.尽管前人做了一些研究,但是通常都假设抽样结果是相互独立的,对于获得精确结果所需的最小抽样步数,还没有清晰统一的认识.时间相关性会增加统计误差理论分析的难度,因此在已有的工作中很少被考虑到.使用统计学中的自相关函数以及修正的中心极限定理,可以量化抽样结果中的时间相关性.在考虑抽样结果时间相关性的基础上,研究了DSMC方法中的统计误差,考核算例为一维的Couette流动问题.量化的结果显示,时间相关性对统计误差的影响很大.时间相关性可增大随机变量抽样序列的方差.     

不确定分数阶Qi系统有限时间同步控制

基于有限时间同步理论研究分数阶不确定Qi系统的有限时间同步,能够使系统误差有限时间收敛到原点.获得驱动响应系统有限时间同步充分条件,研究表明:一定条件下,分数阶不确定Qi系统的主从系统是有限时间同步的.     

一类高阶非线性系统停息时间可调的有限时间镇定

研究了一类高阶非线性系统停息时间可调的有限时间稳定性分析与控制器设计问题.利用有限时间Lyapunov定理的反步构造法,设计状态反馈有限时间控制器,并实现停息时间的适当调整.     

不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.     

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

This paper is concerned with the finite-time quantized H_∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H_∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.     

Quasi-projective and finite-time synchronization of delayed fractional-order BAM neural networks via quantized control

This paper deals with the problems of quasi-projective synchronization (QPS) and finite-time synchronization (FTS) for a kind of delayed fractional-order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite-time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols.     

Semi-global finite-time output feedback stabilization for a class of large-scale uncertain nonlinear systems

This paper addresses the problem of semi-global finite-time decentralized output feedback control for large-scale systems with both higher-order and lower-order terms. A new design scheme is developed by coupling the finite-time output feedback stabilization method with the homogeneous domination approach. Specifically, we first design a homogeneous observer and an output feedback control law for each nominal subsystem without the nonlinearities. Then, based on the homogeneous domination approach, we relax the linear growth condition to a polynomial one and construct decentralized controllers to render the nonlinear system semi-globally finite-time stable.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H_∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H_∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.     

Finite-time structure identification and synchronization of drive-response systems with uncertain parameter

This paper proposes an approach of finite-time synchronization to identify the topological structure and unknown parameters simultaneously for under general complex dynamical networks. Based on the finite-time stability theory, an effective control input and a feedback control with an updated law are designed to realize finite-time synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously. Since finite-time topology identification means the suboptimum in identified time, the results of this paper are important. Several useful criteria for finite-time synchronization are given. Finally, two examples simulations for supporting the theoretical results are also provided.     

Finite-Time Synchronization of Coupled Neutral-Type Neural Networks With Stochastic Disturbances and Uncertainties北大核心CSCD

The finite⁃time synchronization problems were solved for coupled neutral⁃type neural networks with stochastic disturbances and uncertainties. Based on the Lyapunov stability theory and the inequality techniques, the finite⁃time synchronization criterion was proposed for this system. Then the finite⁃time synchronization was realized for the master⁃slave system through the construction of an appropriate state feedback controller. At last, a numerical simulation was given to verify the effectiveness of the proposed theory. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Observer-based finite-time control of time-delayed jump systems

This paper provides the observer-based finite-time control problem of time-delayed Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time H_∞ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches.     

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.     

Finite-time control of discrete-time systems with time-varying exogenous disturbance

This paper deals with some finite-time control problems for uncertain discrete-time linear systems subject to exogenous disturbance. Sufficient conditions are presented for finite-time stabilization via state feedback. These conditions can be reduced to feasibility problems involving linear matrix inequality (LMI). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example illustrates the proposed methodology.     

Global finite-time stabilization of a class of nonlinear system based on a dynamic gain approach

In this paper, finite-time control problem of a class of nonlinear systems is considered. By using a dynamic gain-based backstepping approach, a state feedback controller involving the dynamic gains is constructed with the help of appropriate Lyapunov function, which guarantees the closed-loop system to be globally finite-time stabilization. A simulation example is provided to illustrate the effectiveness of the proposed control scheme.