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 ). The final time 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 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 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 of the control discretization grid
The resulting nonlinearly constrained minimization problem is solved by a Sequential Quadratic Programming Method.