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Survey on the three time grids

Three time grids may appear (which do not depend on each other):

The measurement grid
of a parameter identification problem consists of the times tex2html_wrap_inline1239 of the measurements.

The control grid
of a discretized optimal control problem consists of the times tex2html_wrap_inline1273 where a piecewise linear approximation of the control variable u(t) is given by the values tex2html_wrap_inline1271 .

Also, any inequality constraint tex2html_wrap_inline1289 of an optimal control problem will only be satisfied at the times of the control discretization grid.

The multiple shooting grid
is an optional grid consisting of the multiple shooting nodes  tex2html_wrap_inline1291 . Its purpose is to split up the whole integration interval tex2html_wrap_inline1293 into a sequence of smaller ones tex2html_wrap_inline1295 , j=1,2,....

Please note that the multiple shooting grid and (if tex2html_wrap_inline1299 ) also the control discretization grid (in optimal control problems) always must contain at least two grid points, namely initial time tex2html_wrap_inline1301 and final time tex2html_wrap_inline1267 .

Oskar von Stryk
Tue Feb 1 13:50:42 CET 2000