Theoretical and Numerical Research of Control Theory and Identification Problems for nonlinear parabolic and Hyperbolic Distributed parameter System

非线性抛物型和双曲分布参数系统控制理论与辨识问题的理论与数值研究

基本信息

批准号：
11640201
负责人：
NAKAGIRI Shin-ichi
金额：
$ 1.73万
依托单位：
KOBE UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

According to the research plan, the head investigator studied the optimal control problems and the identification problems for distributed parameter systems described by nonlinear first and second order evolution equations, and studied their numerical analysis based on the finite element method. In the variational framework due to Lions, we have constructed the general theory of optimal control and identification problems for the systems with the help of Drs Ha, Elgamal, Vanualailai and Wang. The general theory can cover a wide class of nonlinear distributed parameter systems such as single sine-Gordon equations and others. Based on the theory and the method we have started to study the more physically important equations such as Cahn-Hilliard equations, Hopfield-type neural network equations, coupled sine-Gordon equation, nonlinear beam equations and Klein-Gordon equations. We can not apply directly our general theory these equations because of the hard nonlinearities of equations. These equations have own proper nonlinear structures and the special analysis of solutions is needed. In order to solve the problems we are required to have the delicate and proper estimates of solutions. Under the conscious of problems, we have succeeded in obtaining the fundamental results of problems for the above equations. Further the head investigator studied the stabilizability and pole assignability for the linear retarded distributed parameter systems of parabolic types. The researches of other investigators are as follows. The investigator Nambu studied the algbraic aspect of stabilization problems for linear parabolic systems. The investigator Tabata proposed and ivestigated new model equations for sociodynamics. The investigator Naito studied nonlinear elliptic equations and established new conditions for the existence and nonexistence of positive radial solutions. The results of the all investigators were published in the journals given below.

根据研究计划，课题组组长研究了非线性一阶、二阶演化方程描述的分布参数系统的最优控制问题和辨识问题，并基于有限元方法研究了它们的数值分析。在Lions的变分框架中，我们在Ha、Elgamal、Vanualailai和Wang博士的帮助下构建了系统最优控制和识别问题的一般理论。一般理论可以涵盖广泛的非线性分布参数系统，例如单正弦戈登方程等。基于该理论和方法，我们开始研究物理上更重要的方程，如Cahn-Hilliard方程、Hopfield型神经网络方程、耦合正弦-Gordon方程、非线性梁方程和Klein-Gordon方程。由于方程的硬非线性，我们不能直接应用我们的一般理论这些方程。这些方程有其固有的非线性结构，需要对其解进行专门的分析。为了解决问题，我们需要对解决方案有细致而正确的估计。在问题意识下，我们成功地得到了上述方程问题的基本结果。首席研究员进一步研究了抛物型线性延迟分布参数系统的稳定性和极点可分配性。其他研究者的研究如下。研究员 Nambu 研究了线性抛物线系统稳定性问题的代数方面。研究者 Tabata 提出并研究了社会动力学的新模型方程。研究者内藤研究了非线性椭圆方程，并建立了正径向解存在和不存在的新条件。所有研究人员的结果均发表在以下期刊上。