The Extended Hamiltonian Algorithm for the Solution of the Algebraic Riccati Equation

摘要

We use a second-order learning algorithmfor numerically solving a class of the algebraicRiccati equations. Specifically, the extended Hamiltonian algorithm based on manifold of positive definite symmetric matrices is provided. Furthermore, this algorithm is compared with the Euclidean gradient algorithm, the Riemannian gradient algorithm, and the new subspace iteration method. Simulation examples show that the convergence speed of the extended Hamiltonian algorithm is the fastest one among these algorithms.