Approximate LQ Optimal Control Using High-Order Symplectic Partitioned Runge-Kutta Methods

Abstract

The formulation, numerical solution, and, eventually, the application of the solution of optimal control problems require discrete-time models of dynamical systems. These are usually computed by numerical integration schemes. Thus, minimising the approximation error is crucial for the performance of model-based control in real applications. For Hamiltonian systems, symplectic integrators are known to be beneficial in forward simulation and optimal feedforward control. Our focus is on linear Hamiltonian systems and linear-quadratic optimal control. We derive high-order feedback control along the lines of discrete-time Riccati equations. We investigate the numerical reconstruction to continuous-time equivalents. It is shown that the high-order symplectic control is particularly suitable for applications in which a near-exact solution is desired, but computation power is limited.