Iterations for solving a rational Riccati equation arising in stochastic control

DOI10.1016/j.camwa.2006.12.009zbMath1127.65025OpenAlexW2083209678MaRDI QIDQ2458700

Ivan Ganchev Ivanov

Publication date: 2 November 2007

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.12.009

zbMATH Keywords

algorithmsconvergenceLyapunov equationiterative methodsNewton methodnonlinear matrix equationHermitian solutionspositive semidefinite solutionrational matrix functionpseudo-inverse matrixstochastic matrix Riccati equations

Mathematics Subject Classification ID

Related Items (11)

On the solution of the linear matrix equation \(X = Af(X) B + C\) ⋮ On some iterations for optimal control of jump linear equations ⋮ A quadratic bilinear equation arising from the quadratic dynamical system ⋮ Perturbation Theory for Linearly Perturbed Algebraic Riccati Equations ⋮ Stochastic Algebraic Riccati Equations Are Almost as Easy as Deterministic Ones Theoretically ⋮ Weight splitting iteration methods to solve quadratic nonlinear matrix equation \(MY^2+NY+P=0\) ⋮ An adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problems ⋮ On the convergence of the accelerated Riccati iteration method ⋮ Convergence analysis of some iterative methods for a nonlinear matrix equation ⋮ Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control ⋮ Homotopy for Rational Riccati Equations Arising in Stochastic Optimal Control

Cites Work

• On a class of rational matrix differential equations arising in stochastic control.
• Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon
• Properties of the solutions of rational matrix difference equations
• Iterative solution of two matrix equations
• Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation
• Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
• Newton's method for a rational matrix equation occurring in stochastic control
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