Asymptotic behaviour of optimal solutions of control problems governed by inclusions

Maciej Smołka

doi:10.3934/dcds.1998.4.641

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1998, Volume 4, Issue 4: 641-652. Doi: 10.3934/dcds.1998.4.641

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Asymptotic behaviour of optimal solutions of control problems governed by inclusions

Maciej Smołka^1,

1.
Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków

Received: October 31, 1997

Published: September 1998

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Abstract

We study the convergence (as $h \rightarrow \infty$) of solutions of control problems $(CP_h)$ governed by inclusions $A_h(y) \in B_h(u)$, where the sequence of abstract operators $A_h$ is $G$-convergent. We are especially interested in finding an explicit form of the limit problem for $(CP_h)$. This is done by means of the theory of $\Gamma$-convergence.

Keywords:

Multivalued input operators,
asymptotics of optimal solutions,
$G$-convergence of abstract operators,
$\Gamma$-convergence of cost functionals.

Mathematics Subject Classification: 49J24, 49J45.

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