FBSM Solution of Optimal Control Problems Using Hybrid Runge-Kutta Based Methods

Solving optimal control problems (OCP) with analytical methods has usually been difficult or not cost-effective. Therefore, solving these problems requires numerical methods. There are, of course, many ways to solve these problems. One of the methods available to solve OCP is a forward-backward sweep method (FBSM). In this method, the state variable is solved in a forward and co-state variable by a backward method where an explicit Runge–Kutta method (ERK) is often used to solve differential equations arising from OCP. In this paper, instead of the ERK method, three hybrid methods based on ERK method of order 3 and 4 are proposed for the numerical approximation of the OCP. Truncation errors and stability analysis of the presented methods are illustrated. Finally, numerical results of the four optimal control problems obtained by new methods, which shows that new methods give us more detailed results, are compared with those of ERK approaches of orders 3 and 4 for solving OCP.