Title page for ETD etd-10242005-124120

Type of Document Dissertation
Author Huang, Wei
URN etd-10242005-124120
Title Compensator design for a system of two connected beams
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Cliff, Eugene M. Committee Member
Gunzburger, Max D. Committee Member
Hannsgen, Kenneth B. Committee Member
Herdman, Terry L. Committee Member
  • Approximation theory
  • Flexible structures Automatic control
  • Control theory
Date of Defense 1994-08-05
Availability restricted

The goal of this paper is to study the LQG problem for a class of infinite dimensional systems. We investigate the convergence of compensator gains for such systems when standard finite element schemes are used to discretize the problem. We are particularly interested in the analysis of the uniformly exponential stability of the corresponding closed - loop systems resulting from the finite dimensional compensators. A specific multiple component flexible structure is used to focus the analysis and to test problem in numerical simulations. An abstract framework for analysis and approximation of the corresponding dynamics system is developed and used to design finite - dimensional compensators. Linear semigroup theory is used to establish that the systems are well posed and to prove the convergence of generic approximation schemes. Approximate solutions of the optimal regulator and optimal observer are constructed via Galerkin - type approximations. Convergence of the scheme is established and numerical results are presented to illustrate the method

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