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Numerical methods for the minimal non‐negative solution of the non‐symmetric coupled algebraic Riccati equation
Author(s) -
Zhang Juan,
Tan Fangyuan
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2205
Subject(s) - algebraic riccati equation , riccati equation , mathematics , convergence (economics) , algebraic equation , linear quadratic regulator , algebraic solution , algebraic number , order (exchange) , mathematical analysis , optimal control , differential equation , mathematical optimization , nonlinear system , differential algebraic equation , ordinary differential equation , physics , finance , quantum mechanics , economics , economic growth
In this paper, base on the theory of the non‐symmetric algebraic Riccati equation and the coupled Riccati equation, we give the general form of the non‐symmetric coupled algebraic Riccati equation (NCARE). In order to effectively solve the minimal non‐negative solution of the NCARE, two numerical iteration methods are improved: inexact Newton method (INewton) and alternate linear implicit method (ALI). Further, we give the convergence theory of the two iteration methods. Finally, we offer numerical examples to show the effectiveness of the derived methods.