Convergence of Runge-Kutta Discretization for Optimal Control Problems
Appolinaire Nzali · Birkhäuser Basel eBooks · 2001
We present a discretization scheme for optimal control with an ordinary differential equation (ODE). It is based on Runge-Kutta methods for ODE and on a piecewise linear parameterization of the control. The order of convergence of the discrete solutions is obtained under regularity conditions and second order optimality conditions. Furthermore, an approach for the calculation of the gradients via the adjoint system is presented. Finally some numerical results are given and relations to the theoretical convergence results are discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.