Continuous maneuver of unmanned aerial vehicle using High Order Expansions method for optimal control problem

In this research, High Order Expansions method implementation in order to obtain an optimal solution for an unmanned aerial vehicle continuous maneuver problem is studied. The main goal of this research, is to describe a specific approach to solve nonlinear optimal control problems using series expansions and algebraic matrix Riccati equation in order to obtain solutions with better performance. Based on this, the state feedback control with different powers is used for optimal commands calculations. Clearly, the control command would be high order and closed-loop; it has been shown it results in a superior performance in smooth nonlinear problems. In this research, in addition to the implementation of High Order Expansions method and its usage, a different approach of dealing with optimal control problem based on this method has been given. Continuous maneuver of an unmanned aerial vehicle problem is solved for investigating the performance of the proposed method. In this example, the High Order Expansions up to and including the third order are used and two different flight scenarios are simulated. By investigating the result of the solution to this problem, the superior performance of the third order optimal command with respect to the first order is illustrated.