DocumentCode :
814591
Title :
Partial conjugate gradient methods for a class of optimal control problems
Author :
Bertsekas, Dimitri P.
Author_Institution :
University of Illinois, Urbana, ILL, USA
Volume :
19
Issue :
3
fYear :
1974
fDate :
6/1/1974 12:00:00 AM
Firstpage :
209
Lastpage :
217
Abstract :
In this paper, we examine the computational aspects of a certain class of discrete-time optimal control problems. We propose and analyze two partial conjugate gradient algorithms which operate in cycles of s+1 conjugate gradient steps ( s \\leq n = state space dimension). The algorithms are motivated by the special form of the Hessian matrix of the cost functional. The first algorithm exhibits a linear convergence rate and offers some advantages over steepest descent in certain cases such as when the system is unstable. The second algorithm requires second-order information with respect to the control variables at the beginning of each cycle and exhibits s+1 - step superlinear convergence rate. Furthermore, it solves a linear-quadratic problem in s+1 steps as compared with the m.N steps ( m = control space dimension, N = number of stages) required by the ordinary conjugate gradient method.
Keywords :
Gradient methods; Linear systems, time-varying discrete-time; Optimal control; Convergence; Cost function; Gradient methods; Minimization methods; Optimal control; Positron emission tomography; Riccati equations; State-space methods; Terrorism;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1974.1100556
Filename :
1100556
Link To Document :
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