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Partial conjugate gradient methods for a class of optimal control problems

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1 Author(s)
Bertsekas, D.P. ; University of Illinois, Urbana, ILL, USA

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 ofs+1conjugate 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 exhibitss+1- step superlinear convergence rate. Furthermore, it solves a linear-quadratic problem ins+1steps as compared with them.Nsteps (m= control space dimension,N= number of stages) required by the ordinary conjugate gradient method.

Published in:

Automatic Control, IEEE Transactions on  (Volume:19 ,  Issue: 3 )

Date of Publication:

Jun 1974

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