ABSTRACT
The optimal control theory and methods are considered very important parts of modern control theory and practice. A big part of optimal control is developed in continuous time domain. In fact, the advent of the optimal control principles and approaches themselves, are where from the modern control theory came to be known as such. The optimal includes, in its definition, either a maximum or a minimum of the so-called cost function. It is well-known that one can incorporate a constraint, say of the dynamics of the system, into the cost function for optimization by using the LM. As such, this artifice does not alter the cost function, since the additional term is anyway zero. Some optimal control problems need different terminal conditions: the terminal time is free, i.e. to traverse in a minimum time; the state variables at the final time are either fixed or restricted to lay on a smooth manifold.
