Numerical Solution of the Symmetric Riccati Equation through Riccati Iteration

This research paper presents a new numerical method for solving the symmetric algebraic Riccati equation from optimal control. This algorithm employs the "Riccati iteration" which has been successully used to solve time-scale decoupling problems in structural vibrations. The algorithm is related to the subspace iteration method, and the rate of convergence to the solution is governed by the relative separation between the stable and unstable eigenvalues in the Hamiltonian system of equations. Provided there is adequate eigenvalue separation the algorithm is globally convergent to the desired Riccati solution. The method is demonstrated for a set of the 8th order random examples. Preliminary accuracy and timing comparisons with other standard methods of solving the symmetric Riccati equations are presented.