A Toolbox for Optimal Control Based on Symmetry Analysis with Applications to Aircraft Maximum Endurance and Maximum Range

Solutions of optimal control problems are the solutions of the Hamilton-Jacobi-Bellman equation. The main contribution of this paper is to propose a symmetry analysis approach to find solutions of the Hamilton-Jacobi-Bellman equation and to introduce a Toolbox to automate the procedure. Several examples will be presented illustrating the effectiveness of the procedure including the maximum endurance and maximum range of an aircraft.