项目名称: 非线性双曲系统的控制与优化
项目编号: No.11301387
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 尚培培
作者单位: 同济大学
项目金额: 22万元
中文摘要: 非线性双曲系统具有很强的应用背景,可广泛应用于物理、生物、力学以及工业生产。由此类系统支配的实际问题的分析与控制属于近代数学研究中一个十分活跃的前沿研究方向。关于非线性双曲系统的理论研究,虽已有很多结果,但由于实际问题的复杂性和多样性,研究相应的模型在理论上往往有较大的难度,在数学上是一个挑战,但如果能结合实际对模型进行深入透彻的研究,便可以更好地解释现象的本质,为实际问题提供理论依据。本课题主要研究非线性双曲系统在三个具有很强实际背景的新模型中的应用,研究其与实际问题紧密相关的控制以及优化问题。
中文关键词: 非线性;双曲方程;能控性;稳定性;最优化
英文摘要: Nonlinear hyperbolic equations are very popular due to its widely applications in physics, biology, mechanics and industry. The associated analysis and control problems are activated by practical requirements. There are already many classical results for general nonlinear hyperbolic equations. However, due to the complexity and variety in reality, it is a challenge to study theoretically the well-posedness, control and optimization problems for such equations. It would be very helpful if we could provide theoretical results and apply these results to reality. This proposal is mainly concerned with three new models arised from reality. We are mainly interested in related control and optimization problems.
英文关键词: Nonlinearity;Hyperbolic equations;Controllability;Stabilization;Optimization