A Symplectic Orthogonal Method for Single Input or Single Output Discrete Time Optimal Quadratic Control Problems

DOI10.1137/0609019zbMath0643.65032OpenAlexW2052968934MaRDI QIDQ3785831

Volker Mehrmann

Publication date: 1988

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0609019

zbMATH Keywords

eigenvaluesinvariant subspacessymplectic matricesdiscrete optimal control problemQZ-algorithmlinear quadratic controldiscrete algebraic Riccati equations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Discrete approximations in optimal control (49M25) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (18)

A new method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation ⋮ Backward error for the discrete-time algebraic Riccati equation ⋮ Fifty Three Matrix Factorizations: A Systematic Approach ⋮ An efficient and stable structure preserving algorithm for computing the eigenvalues of a Hamiltonian matrix ⋮ First order structure-preserving perturbation theory for eigenvalues of symplectic matrices. II ⋮ Iterative and doubling algorithms for Riccati‐type matrix equations: A comparative introduction ⋮ First Order Structure-Preserving Perturbation Theory for Eigenvalues of Symplectic Matrices ⋮ On the convergence of inexact Newton methods for discrete-time algebraic Riccati equations ⋮ Backward Error Analysis for Eigenproblems Involving Conjugate Symplectic Matrices ⋮ Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations ⋮ Unit Triangular Factorization of the Matrix Symplectic Group ⋮ An iterative algorithm for the solution of the discrete-time algebraic Riccati equation ⋮ On computing the eigenvalues of a symplectic pencil ⋮ How to decompose semi-definite discrete-time algebraic Riccati equations ⋮ On Hamiltonian and symplectic Hessenberg forms ⋮ Implicit QR algorithms for palindromic and even eigenvalue problems ⋮ A Core-Chasing Symplectic QR Algorithm ⋮ The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method

Uses Software

• HQR3

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