@inbook{464d30fb6fbb441abd314cf34da08038,
title = "A game theoretic algorithm to solve riccati and hamilton-jacobi-bellman-isaacs (HJBI) equations in H∞ control",
abstract = "In this chapter, we propose a new algorithm to solve Riccati equations and certain Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations arising in H∞ control. The need for the algorithm is motivated by the existence of H∞ problems for which standard Riccati solvers break down, but which can be handled by the algorithm. By using our algorithm, we replace the problem of solving H∞ Riccati equations or HJBI equations by the problem of solving a sequence of H2 Riccati equations or Hamilton-Jacobi-Bellman (HJB) equations. The algorithms have some advantages such as a simple initialization, local quadratic rate of convergence, and a natural game theoretic interpretation. Some numerical examples are given to demonstrate advantages of our algorithm.",
keywords = "Convergence, Game theoretic, HJBI, Iterative, Riccati",
author = "Anderson, {Brian D.O.} and Yantao Feng and Weitian Chen",
note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media, LLC 2010.",
year = "2010",
doi = "10.1007/978-0-387-89496-6_15",
language = "English",
series = "Springer Optimization and Its Applications",
publisher = "Springer International Publishing Switzerland",
pages = "277--308",
booktitle = "Springer Optimization and Its Applications",
address = "Switzerland",
}