A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations

DOI10.1016/j.laa.2004.10.010zbMath1151.93340OpenAlexW2002533862MaRDI QIDQ1763824

E. K.-W. Chu, Hung-Yuan Fan, Wen-Wei Lin

Publication date: 22 February 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2004.10.010

zbMATH Keywords

Cayley transformStructure preserving algorithms

Mathematics Subject Classification ID

Related Items (42)

A new class of complex nonsymmetric algebraic Riccati equations with its ω-comparison matrix being an irreducible singular M-matrix ⋮ A structure-preserving doubling algorithm for solving a class of quadratic matrix equation with \(M\)-matrix ⋮ Computational Experience with a Modified Newton Solver for Discrete-Time Algebraic Riccati Equations ⋮ Structure-Preserving Flows of Symplectic Matrix Pairs ⋮ Large-scale Stein and Lyapunov equations, Smith method, and applications ⋮ Symplectic method based on generating function for receding horizon control of linear time-varying systems ⋮ A subspace shift technique for nonsymmetric algebraic Riccati equations associated with an M-matrix ⋮ The structure-preserving doubling algorithm and convergence analysis for a nonlinear matrix equation ⋮ Lur'e equations and even matrix pencils ⋮ An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations ⋮ Low-rank updates and divide-and-conquer methods for quadratic matrix equations ⋮ Solving large-scale nonlinear matrix equations by doubling ⋮ A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems ⋮ Hermitian Polynomial Matrix Equations and Applications ⋮ Iterative and doubling algorithms for Riccati‐type matrix equations: A comparative introduction ⋮ The intrinsic Toeplitz structure and its applications in algebraic Riccati equations ⋮ Doubling algorithm for the discretized Bethe-Salpeter eigenvalue problem ⋮ Large-scale discrete-time algebraic Riccati equations -- doubling algorithm and error analysis ⋮ Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms ⋮ A generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations ⋮ A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems ⋮ An inverse eigenvalue problem and a matrix approximation problem for symmetric skew-Hamiltonian matrices ⋮ The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations ⋮ Using permuted graph bases in \(\mathcal{H}_\infty\) control ⋮ A factored variant of the Newton iteration for the solution of algebraic Riccati equations via the matrix sign function ⋮ Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation ⋮ A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations ⋮ A structure‐preserving doubling algorithm for Lur'e equations ⋮ Duality of matrix pencils, Wong chains and linearizations ⋮ A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation ⋮ Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control ⋮ Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations ⋮ Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations ⋮ The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case ⋮ Krylov subspace methods for discrete-time algebraic Riccati equations ⋮ A structure-preserving algorithm for the minimum H _∞ norm computation of finite-time state feedback control problem ⋮ Large-scale algebraic Riccati equations with high-rank constant terms ⋮ Homotopy for Rational Riccati Equations Arising in Stochastic Optimal Control ⋮ Solvability theory and iteration method for one self-adjoint polynomial matrix equation ⋮ The extended Hamiltonian algorithm for the solution of the algebraic Riccati equation ⋮ H∞ norm computation of linear continuous-time periodic systems by a structure-preserving algorithm ⋮ Calibrating linear continuous-time dynamical systems via perturbation analysis

Uses Software

• Matlab
• mctoolbox
• HQR3
• HQR3 EXCHNG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Hamiltonian and symplectic Hessenberg forms
• A Schur decomposition for Hamiltonian matrices
• Solving the algebraic Riccati equation with the matrix sign function
• On the numerical properties of the Schur approach for solving the matrix Riccati equation
• The autonomous linear quadratic control problem. Theory and numerical solution
• A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues
• The matrix sign function and computations in systems
• A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations
• On swapping diagonal blocks in real Schur form
• The sign matrix and the separation of matrix eigenvalues
• Asymptotic solutions to the matrix Riccati equation
• A new similarity transformation method for eigenvalues and eigenvectors
• A step toward a unified treatment of continuous and discrete time control problems
• A generalization of the matrix-sign-function solution for algebraic Riccati equations
• A Hamiltonian $QR$ Algorithm
• Convergence of the doubling algorithm for the discrete-time algebraic Riccati equation
• Defect correction method for the solution of algebraic Riccati equations
• Doubling algorithm for continuous-time algebraic Riccati equation
• A Schur method for solving algebraic Riccati equations
• Computer control algorithms for a tubular ammonia reactor
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other matrix equations
• A Chart of Numerical Methods for Structured Eigenvalue Problems
• Second-order convergent algorithms for the steady-state Riccati equation†
• The Matrix Sign Function Method and the Computation of Invariant Subspaces
• Using the Matrix Sign Function to Compute Invariant Subspaces
• On Newton's method for Riccati equation solution
• Structure-Preserving Algorithms for Periodic Discrete-Time Algebraic Riccati Equations
• Matlab code for sorting real Schur forms

This page was built for publication: A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations