On some iterations for optimal control of jump linear equations

Ivanov, Ivan Ganchev

doi:10.1016/j.na.2007.10.034

Cited by 23 publications

(41 citation statements)

References 12 publications

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“…We consider the Lyapunov iteration (13) as a special case of the Lyapunov iteration introduced and investigated by Ivanov [11]. Following the numerical experience in [11] we improve iteration (13) and introduce the improved Lyapunov iteration…”

Section: Proof the Algorithm Begins Withmentioning

confidence: 99%

“…Following the numerical experience in [11] we improve iteration (13) and introduce the improved Lyapunov iteration…”

Section: Proof the Algorithm Begins Withmentioning

confidence: 99%

“…Convergence properties of the matrix sequence defined by (14) are given with Theorem 2.1 [11]. Further on, we consider an alternative iteration process where one matrix sequence is constructed.…”

Section: Proof the Algorithm Begins Withmentioning

confidence: 99%

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H&#8734 Optimal Control Problems for Jump

Ivanov¹

2015

JMF

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We consider a set of continuous algebraic Riccati equations with indefinite quadratic parts that arise in H ∞ control problems. It is well known that the approach for solving such type of equations is proposed in the literature. Two matrix sequences are constructed. Three effective methods are described for computing the matrices of the second sequence, where each matrix is the stabilizing solution of the set of Riccati equations with definite quadratic parts. The acceleration modifications of the described methods are presented and applied. Computer realizations of the presented methods are numerically compared. In addition, a second iterative method is proposed. It constructs one matrix sequence which converges to the stabilizing solution to the given set of Riccati equations with indefinite quadratic parts. The convergence properties of the second method are commented. The iterative methods are numerically compared and investigated.

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Section: Proof the Algorithm Begins Withmentioning

confidence: 99%

“…Following the numerical experience in [11] we improve iteration (13) and introduce the improved Lyapunov iteration…”

Section: Proof the Algorithm Begins Withmentioning

confidence: 99%

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H&#8734 Optimal Control Problems for Jump

Ivanov¹

2015

JMF

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“…[19]. In the case when (48) admits a stabilizing solution, it coincides with the maximal solution, then the above algorithm described by (50)-(53) is a procedure to compute the stabilizing solution of (48).…”

Section: Several Procedural Issuesmentioning

confidence: 99%

“…For the reader's convenience we refer to [2,3,11,17] and the references therein, in the case of Riccati equations arising in the problem of linear quadratic regulator for systems modeled by Ito differential equations and to [1,4,16,19] in the case of Riccati equations arising in the linear quadratic problem and H 2 control problem for systems affected by Markov processes. To our knowledge, no reliable methods for numerical computation of the stabilizing solution of a game theoretic matrix Riccati equation exist in the stochastic framework.…”

Section: Introductionmentioning

confidence: 99%

Computation of the stabilizing solution of game theoretic Riccati equation arising in stochastic H ∞ control problems

Drăgan

Ivanov

2010

Numer Algor

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In this paper, the problem of the numerical computation of the stabilizing solution of the game theoretic algebraic Riccati equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the H ∞ control problem for a class of stochastic systems affected by state dependent and control dependent white noise. The stabilizing solution of the considered game theoretic Riccati equation is obtained as a limit of a sequence of approximations constructed based on stabilizing solutions of a sequence of algebraic Riccati equations of stochastic control with definite sign of the quadratic part. The efficiency of the proposed algorithm is demonstrated by several numerical experiments.

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Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

Liu,

Zhao,

Deng

2024

Asian Journal of Control

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This paper investigates the stochastic coupled algebraic Riccati equations (SCAREs) associated with linear stochastic Markovian jump systems. First, two existing algorithms utilized to solve the SCAREs are reviewed and discussed. Second, based on the analysis of these two algorithms, a modified Riccati iterative algorithm is proposed with a tuning parameter added. It is verified that the proposed algorithm with zero initial values converges to the unique positive definite solution of the SCAREs with fast speed. Furthermore, two numerical examples are given to verify the efficiency and superiority of the proposed algorithm.

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On some iterations for optimal control of jump linear equations

Cited by 23 publications

References 12 publications

<i>H</i><sub>&#8734</sub> Optimal Control Problems for Jump

<i>H</i><sub>&#8734</sub> Optimal Control Problems for Jump

Computation of the stabilizing solution of game theoretic Riccati equation arising in stochastic H ∞ control problems

Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

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On some iterations for optimal control of jump linear equations

Cited by 23 publications

References 12 publications

&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&amp;#8734&lt;/sub&gt; Optimal Control Problems for Jump

&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&amp;#8734&lt;/sub&gt; Optimal Control Problems for Jump

Computation of the stabilizing solution of game theoretic Riccati equation arising in stochastic H ∞ control problems

Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

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<i>H</i><sub>&#8734</sub> Optimal Control Problems for Jump

<i>H</i><sub>&#8734</sub> Optimal Control Problems for Jump