Mathematical Sciences: Analysis and Control of Mechanical and Flexible Systems and Identification of Dynamic Errors-in-Variables Models

首席研究员将使用各种理论 技术来分析建模领域的某些问题， 动力系统的控制 考虑的两个领域是分析和控制 包含刚性和柔性部件的机械系统， 从数据集识别静态和动态系统。 要分析的机械系统的类别可以建模为 拉格朗日或哈密顿系统在有限或无限- 维流形 利用已经发展起来的理论， 分析这种数学类型的系统，主要 调查人员将调查财产，如是否存在 平衡，稳定性，以及守恒积分的存在性， 这些力学系统的对称性。 此外，他还将 非线性有限维控制理论的若干方面 系统，包括控制这些更复杂的无限- 维度系统 在身份识别方面，主要调查员将 分析所有变量都会出现错误的系统--“错误”-- “不变量”系统 他的目标是在这一领域最近工作的基础上 发展一个令人满意的理论的动态误差变量系统。 频域技术以及随机技术 将使用实现理论。 这里从理论角度分析的问题是 这对于航空学中的许多实际应用也是非常重要的， 机器人和其他领域。

The principal investigator will use a variety of theoretical techniques to analyse certain problems in the field of modeling and control of dynamical systems. The two areas considered are the analysis and control of mechanical systems which contain rigid and flexible components, and the identification of static and dynamic systems from sets of data. The class of mechanical systems to be analyzed can be modeled as Lagrangian or Hamiltonian systems evolving on finite-or infinite- dimensional manifolds. Using the theory that has been developed for analysing systems of this mathematical type, the principal investigator will investigate properties such as the existence of equilibria, stability, and the existence of conserved integrals and symmetries for these mechanical systems. Further, he will generalize aspects of the theory of control of nonlinear finite-dimensional systems to encompass control of these more complex infinite- dimensional systems. In the area of identification, the principal investigator will analyse systems where all variables are subject to error- the "errors- in-variables" systems. His aim is to build on recent work in this area to develop a satisfactory theory of dynamic error-in variables systems. Frequency domain techniques as well as techniques from stochastic realization theory will be used. The problems analysed here from a theoretical perspective are also of great importance for many practical applications in aeronautics, robotics and other areas.