Short-term turning in presence of wind as a trajectory optimization problem

In this paper, we concentrate on formulating a short-term-turn of an aircraft as an optimal control problem. Our main aim will be to analyze the problem by investigating the optimal turn at minimum time in existence of given path constraints. In this problem formulation, heading angle becomes a state variable and therefore cannot be used as a control action. On the other hand, with the assumption that `bank angle changes could occur instantaneously´, it is possible to convert bank angle into a control variable, together with thrust. Thus, in our problem formulation, optimal control problem becomes a `minimum time´ problem. Correspondingly, solution strategies are provided in the paper. for this purpose method of collocation will be used to analyze the problem numerically. Solution strategies are limited to 2D problems in x-y axis. Moreover, a 2D-wind model has been defined to demonstrate the effects of the wind in (constrained) trajectory optimization. Obtained results show that better minimum time solution(s) in existence of wind conditions could be obtained and solution(s) could provide unique insights into the trajectory optimization problem in existence of wind.