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Numerical solution of the symmetric riccati equation through riccati iteration
Author(s) -
Anderson Leonard R.,
Brewer Dennis W.,
Baykan A. Rasim
Publication year - 1983
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660040305
Subject(s) - algebraic riccati equation , linear quadratic regulator , riccati equation , mathematics , eigenvalues and eigenvectors , rate of convergence , optimal control , convergence (economics) , mathematical analysis , mathematical optimization , differential equation , computer science , channel (broadcasting) , computer network , physics , quantum mechanics , economic growth , economics
This paper presents a new method for solving the symmetric algebraic Riccati equation from optimal control. The new method employs ‘Riccati iteration’ as used for time‐scale decoupling in structural vibration problems. The rate of convergence of the algorithm is governed by the relative separation of small and large eigenvalues in the shifted Hamiltonian equations. If this ratio of eigenvalues is less than one, the algorithm is globally convergent. Riccati iteration is demonstrated for a set of 8th‐order linear‐quadratic regulator problems, and preliminary timing and accuracy comparisons are presented.