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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，首席研究员研究了一阶和二阶非线性发展方程描述的分布参数系统的最优控制问题和辨识问题，并基于有限元方法进行了数值分析。在Lions的变分框架下，我们在Ha，ElGamal，Vanualailai和Wang等人的帮助下，构造了系统的最优控制和辨识问题的一般理论。一般理论可以涵盖一大类非线性分布参数系统，如单Sine-Gordon方程等。在此理论和方法的基础上，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Sine-Gordon方程、非线性梁方程和Klein-Gordon方程。由于方程的强非线性，我们不能直接应用我们的一般理论来处理这些方程。这些方程具有适当的非线性结构，需要对其解进行专门的分析。为了解决这些问题，我们需要对解决方案作出微妙和适当的估计。在有问题意识的情况下，我们成功地得到了上述方程问题的基本结果。在此基础上，研究了抛物型线性时滞分布参数系统的可镇定性和极点可配置性。其他研究者的研究成果如下。研究员Nambu研究了线性抛物系统镇定问题的算法方面。研究人员塔巴塔提出并研究了新的社会动力学模型方程。研究者Naito研究了非线性椭圆型方程，建立了正径向解存在和不存在的新条件。所有调查人员的结果都发表在下面给出的期刊上。