Optimal control laws for aircraft tracking

The aim of this research is to find the most satisfactorily method of controlling the trajectory of an aircraft that passes through a set of designated points at specific times in two dimensional space. Generally, optimal control theory yield controls which are minimal with respect to a cost function and the aircraft is controlled using this minimizing control law. Some of the more widely used cost functions are /Q V? dt and J^ (u') dt where u{t) is the desired control. In this thesis we will define a parameterized cost function which is a linear combination of the above two cost functions and show that for particular values of the parameter, the new cost function yield smoother paths and requires control functions of lesser magnitude. Several numerical and curve-fitting examples are given to illustrate advantages of this new cost function. Finally, this cost function will be applied to two very special cases to analyze the the advantages over the minimal energy cost function.