View source for Optimal Control of Affine Connection Control Systems: A Variational Approach

{{HTDB paper
| authors = Alex Fax and Richard Murray
| title = Optimal Control of Affine Connection Control Systems: A Variational Approach
| source = 2000 Conference on Decision and Control
| year = 2000
| type =  Conference 
  Submission 
| funding = AFOSR
| url = http://www.cds.caltech.edu/~murray/preprints/fm00b-cdc.pdf
| abstract = 
In this paper we investigate the optimal control of affine connection
control systems. The formalism of the affine connection can be used to
describe geometrically the dynamics of me chanical systems, including those
with nonholonomic constraints. In the standard variational approach to such
problems, one converts an n dimensional second order system into a 2n
dimensional first order system, and uses these equations as constraints on
the optimization.  An alternative approach, which we develop in this paper,
is to include the system dynamics as second order constraints of the
optimization, and optimize relative to variations in the configuration
space. Using the affine connection, its associated tensors, and the notion
of covariant differentiation, we show how variations in the configuration
space induce variations in the tangent space. In this setting, we derive
second order equations have a geometric formulation parallel to that of the
system dynamics. They also specialize to results found in the literature.

| flags = 
| tag = fm00-cdc
| id = 2000b
}}