Title page for ETD etd-0711102-152933

Type of Document Dissertation
Author Cardetti, Fabiana
Author's Email Address fcardet@lsu.edu
URN etd-0711102-152933
Title On Properties of Linear Control Systems on Lie Groups
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Guillermo Ferreyra Committee Chair
Gestur Olafsson Committee Member
Jimmie Lawson Committee Member
Robert Perlis Committee Member
William Adkins Committee Member
Young Hak Chun Dean's Representative
  • geometric control theory
Date of Defense 2002-07-10
Availability unrestricted
In this work we study controllability properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system Σ Lie group G is defined by

x' = X(x) + Σkj=1 ujYj(x),

where the drift vector field X is an infinitesimal automorphism, uj are piecewise constant functions, and the control vectors Yj are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by Σ are presented in Chapter 3. Under a condition similar to the Kalman condition which is needed for controllability of linear control systems on Rn, Ayala and Tirao showed local controllability of the system Σ at the group identity e. An alternate proof of this result is obtained using the Lie theory of semigroups. More importantly, an extension of this result is proved. These results are contained in Chapter 4. Finally, in Chapter 5 an example on the Heisenberg Lie group is presented and its properties are proved using the theory developed.

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