Numerical solution of the symmetric riccati equation through riccati iteration

Abstract

AbstractThis paper presents a new method for solving the symmetric algebraic Riccati equation from optimal control. The new method employs ‘Riccati iteration’ as used for time‐scale decoupling in structural vibration problems. The rate of convergence of the algorithm is governed by the relative separation of small and large eigenvalues in the shifted Hamiltonian equations. If this ratio of eigenvalues is less than one, the algorithm is globally convergent. Riccati iteration is demonstrated for a set of 8th‐order linear‐quadratic regulator problems, and preliminary timing and accuracy comparisons are presented.