Symplectic Partitioned Runge‐Kutta Methods for High‐Order Approximation in Linear‐Quadratic Optimal Control of Hamiltonian Systems

Abstract

Symplectic partitioned Runge-Kutta (SPRK) methods are known to be a good choice in forward simulations of Hamiltonian systems due to their structure-preserving properties. Recent works study the application of SPRK methods to nonlinear and linear-quadratic optimal control problems howing various advantages of these methods compared to standard non-symplectic integration schemes. Now, our focus is on extending the comparison to SPRK and RK methods of higher orders. For linear-quadratic optimal control problems, we consider the discrete-time Riccati feedback as well as the feedforward control implementation. For applications in which computational power or computation time is limited, low sampling rates are of particular interest. Hence we study this case for the n-fold harmonic oscillator.