DocumentCode :
822783
Title :
Approximations to Riccati equations having slow and fast modes
Author :
Womble, M. Edward ; Potter, James E. ; Speyer, Jason L.
Author_Institution :
United States Air Force School of Aerospace Medicine, Brooks Air Force Base, TX, USA
Volume :
21
Issue :
6
fYear :
1976
fDate :
12/1/1976 12:00:00 AM
Firstpage :
846
Lastpage :
855
Abstract :
Problems associated with the optimal linear regulator when one control is penalized much less than the others, and the optimal linear estimator when one measurement is of a much higher quality than the others are considered. Both situations cause the Riccati equation´s solution to have transients with radically different speeds. In order to generate solutions with radically different transient speeds, a large number of small numerical integration time steps must be used-small to capture the rapid transient and a large number to generate the slow transient. Approximations are derived to the solutions to these Riccati equations. Although the number of scalar numerical integrations required is reduced by only one, a closed-form approximation is derived for the rapidly varying part of the transient. This allows the use of large numerical integration time steps and results in a considerable decrease in computation time. Measures are derived of both the errors in the approximations and how they affect the resulting regulators and estimators. A numerical example is given comparing the solution of the Riccati equation to its approximation.
Keywords :
Differential Riccati equations; Kalman filtering; Linear systems, time-invariant continuous-time; Numerical integration; Optimal regulators; Riccati equations, differential; State estimation; Automatic control; Control system synthesis; Eigenvalues and eigenfunctions; Riccati equations; Robustness; Sections; Stability; State feedback; Sufficient conditions; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1976.1101372
Filename :
1101372
Link To Document :
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