Control systems on Lie groups

Control Systems on Lie Groups

Integral Control on Lie Groups

In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of “integral action” for proportional(derivative)-controlled systems whose configuration evolves on a nonlinear space, where configuration errors cannot be simply added up to compute a definite integral. We then prove that the proposed integral...

Motion Control for Nonholonomic Systems on Matrix Lie Groups

Title of Dissertation: Motion Control for Nonholonomic Systems on Matrix Lie Groups Herbert Karl Struemper, Doctor of Philosophy, 1997 Dissertation directed by: Professor P. S. Krishnaprasad Department of Electrical Engineering In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coor...

Control Affine Systems on Solvable Three-dimensional Lie Groups, I

We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV , and V in the Bianchi-Behr classification.

The covering semigroup of invariant control systems on Lie groups