一类非线性脉冲发展方程的最优反馈控制

本文考虑受控系统为Banach空间中一类G0紧半群的非线性脉冲积微分方程的最优反馈控制问题。首先证明容许控制对的存在性,进一步对Lagrange问题给出了一个新的存在性定理。     

An exercise in structural congruence

Milner's structural congruence is decidable for the pi-calculus without restriction, in exponential space.     

Distributed control of nonlinear diffusion systems by input–output linearization

This paper addresses the distributed control by input–output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole–Hopf transformation. This framework helps to demonstrate the closed‐loop stability using some concepts from the powerful semigroup theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a nonlinear heat equation with Dirichlet boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

关于含乘积纯正断面的正则半群

介绍了乘积纯正断面的概念和性质,给出乘积纯正断面的等价条件,并给出含有乘积纯正断面的正则半群的结构定理.     

基于谱分解的中立型时滞系统观测器

针对线性中立型时滞系统, 利用线性算子半群的谱分解理论进行观测器设计. 在中立型项的范数小于一的条件下, 利用谱理论并结合投影算子, 将无穷维系统解的相空间分解为有限维不稳定广义特征子空间和无限维稳定广义特征子空间的直和. 进而利用线性算子半群的无穷小生成元得到具有积分微分形式的观测器方程, 并证明了观测器误差方程的渐近稳定性. 数值实验证实了所提设计方法的有效性.     

Recovering the initial state of an infinite-dimensional system using observers

Let A be the generator of a strongly continuous semigroup T on the Hilbert space X, and let C be a linear operator from D(A) to another Hilbert space Y (possibly unbounded with respect to X, not necessarily admissible). We consider the problem of estimating the initial state z₀∈D(A) (with respect to the norm of X) from the output function y(t)=CT_tz₀, given for all t in a bounded interval [0,τ]. We introduce the concepts of estimatability and backward estimatability for (A,C) (in a more general way than currently available in the literature), we introduce forward and backward observers, and we provide an iterative algorithm for estimating z₀ from y. This algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the Gramian. Our results lead also to a very general formulation of Russell’s principle, i.e., estimatability and backward estimatability imply exact observability. This general formulation of the principle does not require T to be invertible. We illustrate our estimation algorithms on systems described by wave and Schrödinger equations, and we provide results from numerical simulations.     

Intuitionistic fuzzy transformation semigroups

The idea of (faithful) intuitionistic fuzzy transformation semigroup, intuitionistic admissible relation, and intuitionistic (strong) homomorphism are introduced and their basic properties are examined.     

基于分布参数机械臂协调操作柔性负载双时标控制

基于分布参数系统理论,建立机械臂协调操作柔性负载系统的动力学模型.利用奇异摄动方法,对动力学模型进行双时标分解,得到一个表征系统大范围刚性运动的集中参数慢变子系统和表征系统弹性振动的分布参数快变子系统.分别设计了自适应模糊滑模慢变控制器和振动反馈快变控制器,并通过分析快变子系统主算子及其生成C_O半群的特性,证明了分布参数闭环子系统的渐近稳定性.最后,通过仿真实验验证了所提出方法的有效性.     

关于积分半群的两个结论

得到了生成元为闭算子的n次积分半群的表示定理，并根据积分半群的C半群的关系，进而得到了n次积分半群的谱映射定理。