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On approximation theorems for controllability of non-linear parabolic problems

DSpace at IIT Bombay

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Title On approximation theorems for controllability of non-linear parabolic problems
 
Creator KUMAR, A
JOSHI, MC
PANI, AK
 
Subject generalized hammerstein equations
existence theorems
integral-equation
controllability
optimal control
non-linear parabolic system
penalty function
nemytskii operator
c-0-semigroup
lipschitz continuity
generalized hammerstein equation
 
Description In this paper, we consider the following control system governed by the non-linear parabolic differential equation of the form: partial derivative(t)/partial derivative t +Ay(t)=f(t,y(t))+u(t), t epsilon[0, T], y(0) =y0, where A is a linear operator with dense domain and f (t, y) is a non-linear function. We have proved that under Lipschitz continuity assumption on the non-linear function f (t, y), the set of admissible controls is non-empty. The optimal pair (u*, y*) is then obtained as the limit of the optimal pair sequence {(u(n)*, y(n)*)}, where u(n)* is a minimizer of the unconstrained problem involving a penalty function aris. n n ing from the controllability constraint and y(n)* is the solution of the parabolic non-linear system defined n above. Subsequently, we give approximation theorems which guarantee the convergence of the numerical schemes to optimal pair sequence. We also present numerical experiment which shows the applicability of our result.
 
Publisher OXFORD UNIV PRESS
 
Date 2011-08-22T06:43:17Z
2011-12-26T12:56:14Z
2011-12-27T05:44:37Z
2011-08-22T06:43:17Z
2011-12-26T12:56:14Z
2011-12-27T05:44:37Z
2007
 
Type Article
 
Identifier IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 24(1), 115-136
0265-0754
http://dx.doi.org/10.1093/imamci/dnl012
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10349
http://hdl.handle.net/10054/10349
 
Language en