scholarly journals Analysis of an Iteration Method for the Algebraic Riccati Equation

2016 ◽  
Vol 37 (2) ◽  
pp. 624-648 ◽  
Author(s):  
Arash Massoudi ◽  
Mark R. Opmeer ◽  
Timo Reis
Keyword(s):  
Riccati Equation ◽  
Iteration Method ◽  
Algebraic Riccati Equation

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

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhikun Luo ◽  
Huafei Sun ◽  
Xiaomin Duan
Keyword(s):  
Riccati Equation ◽  
Iteration Method ◽  
Learning Algorithm ◽  
Positive Definite ◽  
Gradient Algorithm ◽  
Algebraic Riccati Equation ◽  
Symmetric Matrices ◽  
Algebraic Riccati Equations ◽  
Subspace Iteration ◽  
Hamiltonian Algorithm

We use a second-order learning algorithm for numerically solving a class of the algebraic Riccati 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.

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