A New Relaxative Algorithm for Coupled Riccati Matrix Equations

In this paper, an iterative algorithm for solving coupled algebraic Riccati equations is proposed that has the ad-vantage of fast convergence. Firstly, the importance and related theories of solving the Riccati equation in the control problem of Markovian jumping are introduced, and then mathematica...

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Veröffentlicht in:Chinese Control Conference S. 227 - 232
Hauptverfasser: Du, Yi-Xiao, Wu, Yu-Yao, Wang, Ping, Sun, Hui-Jie, Liu, Wanquan
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: Technical Committee on Control Theory, Chinese Association of Automation 24.07.2023
Schlagworte:
Convergence
iterative algorithm
Iterative algorithms
Iterative methods
Markovian jump
Mathematical models
Numerical simulation
Riccati equation
Riccati equations
ISSN:1934-1768
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Abstract In this paper, an iterative algorithm for solving coupled algebraic Riccati equations is proposed that has the ad-vantage of fast convergence. Firstly, the importance and related theories of solving the Riccati equation in the control problem of Markovian jumping are introduced, and then mathematical induction is used to prove the mono-tonicity and bounded properties of iterative algorithms, and the method of obtaining the initial matrix of iterative algorithms is given. Also, numerical simulation verifies that the convergence speed of the algorithm is faster than some current algorithms.
AbstractList In this paper, an iterative algorithm for solving coupled algebraic Riccati equations is proposed that has the ad-vantage of fast convergence. Firstly, the importance and related theories of solving the Riccati equation in the control problem of Markovian jumping are introduced, and then mathematical induction is used to prove the mono-tonicity and bounded properties of iterative algorithms, and the method of obtaining the initial matrix of iterative algorithms is given. Also, numerical simulation verifies that the convergence speed of the algorithm is faster than some current algorithms.
Author Liu, Wanquan
Du, Yi-Xiao
Wu, Yu-Yao
Wang, Ping
Sun, Hui-Jie
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  givenname: Yu-Yao
  surname: Wu
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  givenname: Hui-Jie
  surname: Sun
  fullname: Sun, Hui-Jie
  email: sunhj6@mail.sysu.edu.cn
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  givenname: Wanquan
  surname: Liu
  fullname: Liu, Wanquan
  organization: Shenzhen Campus of Sun Yat-sen University,Shenzhen,PR China,518107
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Snippet In this paper, an iterative algorithm for solving coupled algebraic Riccati equations is proposed that has the ad-vantage of fast convergence. Firstly, the...
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StartPage 227
SubjectTerms Convergence
iterative algorithm
Iterative algorithms
Iterative methods
Markovian jump
Mathematical models
Numerical simulation
Riccati equation
Riccati equations
Title A New Relaxative Algorithm for Coupled Riccati Matrix Equations
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