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

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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.