分布参数控制系统逼近能达集对非线性扰动的不变性

一、引言非线性分布参数控制系统的能控性问题,在近二十年的研究中已经有了很多结果,但由于该问题难度较大,因而所得结论还比较零散,如,文[2,4,5,6]分别讨论了各类非线性分布参数控制系统的能控性.本文将在以上工作的基础上进一步讨论线性分布参数控制系统的逼近能达集对非线性扰动的不变性.对非线性扰动,我们给出了较弱的限制条件,由此可以得到一类非线性系统的逼近能控性,所得结论推广了很多已知的结果.     

含有一个控制的拟线性抛物系统的能控性

该文讨论了一类拟线性抛物系统的全局零能控性和逼近能控性. 文中首先给出并证明了相应的线性系统的Carleman不等式,再由Carleman不等式去证明观测不等式, 最后利用Kakutani不动点定理证明非线性系统的全局零能控性和逼近能控性.     

非线性年龄等级结构种群系统的近似能控性

研究一类基于年龄的等级结构种群模型的近似能控性,状态系统由具有全局反馈边界条件的非线性偏微分-积分方程描述,控制手段为迁移(投放或移除).以线性系统的能控性为基础,借助冻结系数法和集值映射的Ky Fan-Glicksberg不动点定理,确立了非线性系统的近似能控性.     

不变流形方法与非线性控制系统的能控制性

在Kovalev方法基础上运用不变流形研究非线性系统的能控制性问题,得出了一类仿射非线性系统能控的必要条件,讨论了必要条件的实现问题,研究了带有两个陀螺的刚体运动,证明了它满足能控性的必要条件.     

非线性年龄等级结构种群系统的边界控制问题

探究一类具有年龄等级结构的种群模型的边界调控问题,包括系统的能控性和最优控制.应用特征线方法和Gronwall不等式建立状态分布关于控制变量的连续依赖性;基于线性系统的能控性与集值映射不动点方法获得了非线性种群系统的近似能控性;运用Ekeland变分原理证明了最优策略的存在唯一性,构造适当的共轭系统和法向量对最优策略作出精细刻画.数值模拟结果展示了控制策略的可行性.     

非线性中立型控制系统函数能控性

本文讨论形如的非线性中立型控制系统函数能控性．给出该类系统的函数能控性和零函数能控性的判定定理．所得结果在实际系统的设计、分析等方面是非常实用的．     

带极大单调图的半线性抛物型方程的零能控性(英文)

本文讨论非线性项带一个极大单调图的半线性抛物型方程系统的零能控性.文中利用Kakutani不动点定理和线性抛物型方程的能控性得到该系统是零能控的,如果控制作用在内部区域上.由此,还得到该系统是零能控的,如果控制施加在一部分边界上.     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

非线性开关控制系统的能控性

本文研究了一类具有不同控制器的非线性开关控制系统的能控性问题.利用了几何控制的方法和Kalman秩条件,获得了这类控制系统的能控性结果,推广了E.Zuazua在参考文献[7]中的结论.     

球面、柱面、锥面与非线性控制系统

我们首先从整体化的观点定义了一种建立在三维欧氏空间的二维曲面上的非线性控制系统,并给出了在曲面的局部坐标系下非线性系统状态方程的表达式,研究了非线性系统的平衡态与曲面的测地线之间的关系.刻划了球面、柱面、锥面的特殊曲面几何结构和奇异结构与非线性控制系统之间的内在联系.进一步,讨论了建立在球面、柱面和锥面上的非线性控制系统的局部和整体能控性与能观测性.     

Controllability of nonlinear fractional order integrodifferential system with input delay

This paper addressed the controllability of nonlinear fractional order integrodifferential systems with input delay. Firstly, the Caputo fractional derivatives and the Mittag‐Leffler functions are employed. Thereafter, we establish a set of sufficient and necessary conditions for the controllability of the linear fractional system. Furtherly, controllability conditions of the nonlinear integrodifferential fractional order system with input delay are acquired by utilizing Arzela‐Ascoli theorem and Schauder's fixed‐point theorem. Finally, an example is presented to demonstrate our main results.     

Null controllability for a parabolic-elliptic coupled system

In this paper, we prove the null controllability of some parabolic-elliptic systems. The control is distributed, locally supported in space and appears only in one PDE. The arguments rely on fixed-point reformulation and suitable Carleman estimates for the solutions to the adjoint system. Under appropriate assumptions, we also prove that the solution can be obtained as the asymptotic limit of some similar parabolic systems.     

Controllability of a Reaction-Diffusion System Describing Predator–Prey Model

This article establishes the controllability to the trajectories of a reaction-diffusion-advection system describing predator–prey model by using distributed controls acting on a single equation with the no-flux boundary conditions. We first prove the exact null controllability of an associated linearized problem by establishing an observability estimate, derived from a global Carleman type inequality, for the adjoint system. The proof of the nonlinear problem relies on the suitable regularity of the control and Kakutani's fixed point theorem.     

Controllability of Second-Order Systems with Nonlocal Conditions in Banach Spaces

In this article, exact controllability of second-order semilinear differential system with nonlocal conditions in Banach spaces is studied. To establish sufficient conditions for exact controllability, Sadovskii's fixed point theorem together with the theory of strongly continuous cosine family is been used. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. An example is given to illustrate the developed theory.     

非线性抛物椭圆方程组的正则解和奇异解

该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间L^{n/2,∞ ₍}Rⁿ), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性.     

On the existence of periodic solutions in the thermistor problem with degenerate thermal conductivity

Abstract This paper deals with the existence of weak periodic solutions for a parabolic-elliptic system proposed as a model for a time dependent thermistor with degenerate thermal conductivity. Applying the maximal monotone mappings theory, we prove an existence result for weak periodic solutions. Keywords: Nonlinear parabolic-elliptic system of degenerate type, Periodic solutions, Thermistor problem Mathematics Subject Classification (2000): 35B10, 35J60, 35K65     

A controllability minimum principle

A controllability minimum principle and two associated transversality conditions are presented, dealing with the controllability of nonlinear systems. The theorems represent necessary conditions for a control function to generate a system path which lies in the boundary of the set of points that are controllable to a target. The theorems presented here are controllability counterparts to Pontryagin's maximum principle, and undoubtedly these results will seem familiar or may have occurred to other researchers in the area of optimal control. The purpose of this paper is to make the distinction explicit and to establish the validity of these controllability theorems on their own merits. The theorems are demonstrated using a simple example and the principal result (a controllability minimum principle) is shown to be equivalent to the Kalman controllability criterion for linear systems.     

具有趋化性的非线性系统的解的爆破性态分析

讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.     

Local controllability for autonomous nonlinear systems

This paper is concerned with the study of local controllability for nonlinear, analytic, autonomous, control systems. To this aim, we consider the control system as a set-valued differential system, and we show that the convexification of the set of velocities does not change the local controllability properties. Given a finite family of vector fields, we also give a necessary condition for local controllability at timet, for everyt.This work was performed under the auspices of the National Research Council of Italy (CNR).     

Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions

We consider two simple conservative systems of parabolic-elliptic and parabolic-degenerate type arising in modeling chemotaxis and angiogenesis. Both systems share the same property that when the norm of initial data is small enough, where d 2 is the space dimension, then there is a global (in time) weak solution that stays in all the L^p spaces with max This result is already known for the parabolic-elliptic system of chemotaxis, moreover blow-up can occur in finite time for large initial data and Dirac concentrations can occur. For the parabolic-degenerate system of angiogenesis in two dimensions, we also prove that weak solutions (which are equi-integrable in L¹) exist even for large initial data. But break-down of regularity or propagation of smoothness is an open problem.Lecture by B. Perthame held at the Presentation of MJM, Milano, October 18, 2002Received: March, 2003