Systems governed by ordinary differential equations arise in many applications as, e. g., in astronautics, aeronautics, robotics, and economics. The task of optimizing these systems leads to the optimal control problems investigated in this paper.
The aim is to find a control vector 
and the final time 
that minimize the functional
subject to a system of 
nonlinear differential equations
boundary conditions
and 
inequality constraints
Here, the 
vector of control variables is denoted by 
and the 
vector of state variables is denoted by 
.
The functions 
, and 
are assumed to be continuously differentiable.
The controls 
are assumed to be bounded and measureable and 
may be fixed or free.
