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Optimal control problems

The problem in optimal control is to determine the control variable u(t) and the control (or design) parameters p in order to minimize an objective of Mayer type


(with a real-valued function tex2html_wrap_inline1197 ). The final time tex2html_wrap_inline1267 may be givend or free.

In order to obtain an approximation of the optimal control a discretization of the control variable is applied. Hereby, a time grid tex2html_wrap_inline1269 consisting of NSGIT knots


is introduced. The control is approximated by a continuous, piecewise linear function over this time grid. The values of the control variables at these knots tex2html_wrap_inline1271 have to be determined in the optimization.

Also the inequality constraints (3) are discretized by the algorithm in a similiar way. They are satisfied at the times tex2html_wrap_inline1273 of the control discretization grid


The resulting nonlinearly constrained minimization problem is solved by a Sequential Quadratic Programming Method.

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