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动态系统建模和控制领域中的某些问题。所考虑的两个领域是包含刚性和柔性部件的机械系统的分析和控制，以及从数据集中识别静态和动态系统。要分析的一类机械系统可以建模为在有限维或无限维流形上发展的拉格朗日系统或哈密顿系统。使用为分析这种数学类型的系统而发展起来的理论，首席研究员将研究这些力学系统的性质，如平衡点的存在性、稳定性以及守恒积分和对称性的存在性。此外，他将推广非线性有限维系统控制理论的各个方面，以涵盖对这些更复杂的无限维系统的控制。在识别领域，首席调查员将分析所有变量都有误差的系统--“变量中的误差”系统。他的目标是在这一领域最新工作的基础上，发展一种令人满意的动态误差变量系统理论。将使用频域技术以及随机实现理论中的技术。本文从理论上分析的问题对于航空、机器人等领域的许多实际应用也具有重要意义。

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.