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

Solving optimal control problems (OCP) with analytical methods has usually been diffcult or not cost-effective. Therefore, solv- ing 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 pa- per, 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 opti- mal 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