Discretization and Integration Schemes for Hybrid Optimal Control Problems

The practical problems of interest will seldom have an analytical solution and numerical integration is the only way to obtain information about the trajectory. In this chapter, the famous Runge–Kutta discretizations process is introduced. The determination of the Runge–Kutta order is briefly discussed and conditions up to the fourth order are given including the additional conditions for solving optimal control problems. Regarding optimal control problems only explicit and implicit Runge–Kutta discretizations which satisfy additional conditions for the adjoint differential equation are discussed.