Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term (Q1198463)
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scientific article; zbMATH DE number 92898
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term |
scientific article; zbMATH DE number 92898 |
Statements
Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term (English)
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16 January 1993
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The author gives necessary and sufficient conditions for existence of positive definite and negative definite solutions to algebraic Riccati equations. He gives examples of optimization problems in game and control theory giving rise to these equations. He gives explicit formulas for solutions and also a quadratically converging iterative algorithm. His methods include integral transforms and retranslating the problem into control theory.
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linear quadratic control problem
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two-person zero-sum differential game
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\(H^ \infty\)-optimization
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positive definite and negative definite solutions
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algebraic Riccati equations
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optimization problems
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iterative algorithm
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integral transforms
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