Search results for "Algebraic Riccati equation"

showing 4 items of 4 documents

Solving coupled Riccati matrix differential systems

1991

Abstract We start by noting that coupled Riccati matrix differential systems appearing in differential games may be considered as a single rectangular Riccati equation. An explicit solution of the coupled differential system in terms of a solution of the associated algebraic Riccati equation is given.

Applied MathematicsMathematical analysisMathematics::Optimization and ControlLinear-quadratic regulatorAlgebraic Riccati equationMatrix (mathematics)Nonlinear Sciences::Exactly Solvable and Integrable SystemsComputer Science::Systems and ControlOrdinary differential equationRiccati equationMathematics::Mathematical PhysicsUniversal differential equationDifferential (mathematics)MathematicsAlgebraic differential equationApplied Mathematics Letters
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Explicit solutions of Riccati equations appearing in differential games

1990

Abstract In this paper an explicit closed form solution of Riccati differential matrix equations appearing in games theory is given.

Computer Science::Computer Science and Game TheoryApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISLinear-quadratic regulatorAlgebraic Riccati equationMatrix (mathematics)ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONRiccati equationApplied mathematicsClosed-form expressionGame theoryDifferential (mathematics)MathematicsApplied Mathematics Letters
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Analytic solution for a class of discrete-time Riccati equations arising in Nash games

1990

Discrete mathematicsClass (set theory)Discrete time and continuous timeApplied MathematicsRiccati equationApplied mathematicsLinear-quadratic regulatorAnalytic solutionAlgebraic Riccati equationMathematicsNash gamesApplied Mathematics Letters
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Solution of coupled riccati equations occurring in nash games

2006

To obtain the open-loop Nash strategy for a linear-quadratic differential game, a set of coupled matrix Riccati equations has to be solved. It is shown that by means of algebraic transformations, the original problem can be reduced to another one to which the successive approximation method is applicable. This leads to a simple iterative algorithm with a predetermined approximation error. An example is given to illustrate the proposed method.

Matrix (mathematics)Simple (abstract algebra)Iterative methodApproximation errorComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONDifferential gameMatrix normRiccati equationApplied mathematicsMathematical economicsAlgebraic Riccati equationMathematics
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