Title :
Computing the Positive Stabilizing Solution to Algebraic Riccati Equations With an Indefinite Quadratic Term via a Recursive Method
Author :
Lanzon, Alexander ; Feng, Yantao ; Anderson, Brian D O ; Rotkowitz, Michael
Author_Institution :
Control Syst. Center, Univ. of Manchester, Manchester
Abstract :
An iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.
Keywords :
Riccati equations; convergence of numerical methods; game theory; iterative methods; matrix algebra; stability; Hamiltonian matrices; algebraic Riccati equations; game theoretic interpretation; global convergence; indefinite quadratic term; iterative algorithm; recursive method; Australia Council; Computational efficiency; Control systems; Convergence; Game theory; Iterative algorithms; Iterative methods; Packaging; Riccati equations; Symmetric matrices; $H_{infty}$ Riccati equations; Algebraic Riccati equation (ARE); indefinite quadratic term; iterative algorithms;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.2006108
