A Game Theoretic Algorithm to Solve Riccati and Hamilton—Jacobi—Bellman—Isaacs (HJBI) Equations in H ∞ Control

Brian D. O. Anderson (), Yantao Feng () and Weitian Chen ()
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Brian D. O. Anderson: the Australian National University
Yantao Feng: the Australian National University
Weitian Chen: the Australian National University

A chapter in Optimization and Optimal Control, 2010, pp 277-308 from Springer

Abstract: Summary In this chapter, we propose a new algorithm to solve Riccati equations and certain Hamilton—Jacobi—Bellman—Isaacs (HJBI) equations arising in $$H_{\infty}$$ control. The need for the algorithm is motivated by the existence of $$H_{\infty}$$ 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 $$H_{\infty}$$ Riccati equations or HJBI equations by the problem of solving a sequence of H 2 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: Riccati; HJBI; iterative; game theoretic; convergence (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-89496-6_15

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DOI: 10.1007/978-0-387-89496-6_15

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