American Institute of Mathematical Sciences

Advanced
October  1998, 4(4): 641-652. doi: 10.3934/dcds.1998.4.641

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, Poland

Received  November 1997 Published  July 1998

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: $\Gamma$-convergence of cost functionals., Multivalued input operators, asymptotics of optimal solutions, $G$-convergence of abstract operators.
Mathematics Subject Classification: 49J24, 49J4.
Citation: Maciej Smołka. Asymptotic behaviour of optimal solutions of control problems governed by inclusions. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 641-652. doi: 10.3934/dcds.1998.4.641
[1]

Harun Karsli, Purshottam Narain Agrawal. Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation. Mathematical Foundations of Computing, 2022  doi: 10.3934/mfc.2022002
[2]

Lorenza D'Elia. $ \Gamma $-convergence of quadratic functionals with non uniformly elliptic conductivity matrices. Networks and Heterogeneous Media, 2022, 17 (1) : 15-45. doi: 10.3934/nhm.2021022
[3]

Giuseppe Buttazzo, Lorenzo Freddi. Optimal control problems with weakly converging input operators. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 401-420. doi: 10.3934/dcds.1995.1.401
[4]

Teresa Alberico, Costantino Capozzoli, Luigi D'Onofrio, Roberta Schiattarella. $G$-convergence for non-divergence elliptic operators with VMO coefficients in $\mathbb R^3$. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 129-137. doi: 10.3934/dcdss.2019009
[5]

Jean Louis Woukeng. $\sum $-convergence and reiterated homogenization of nonlinear parabolic operators. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1753-1789. doi: 10.3934/cpaa.2010.9.1753
[6]

Benzion Shklyar. Exact null-controllability of interconnected abstract evolution equations with unbounded input operators. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 463-479. doi: 10.3934/dcds.2021124
[7]

Kenji Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the same space. Communications on Pure and Applied Analysis, 2002, 1 (2) : 237-252. doi: 10.3934/cpaa.2002.1.237
[8]

Purshottam N. Agrawal, Thakur Ashok K. Sinha, Avinash Sharma. Convergence of derivative of Szász type operators involving Charlier polynomials. Mathematical Foundations of Computing, 2022, 5 (1) : 1-15. doi: 10.3934/mfc.2021016
[9]

Svetlana Pastukhova, Valeria Chiadò Piat. Homogenization of multivalued monotone operators with variable growth exponent. Networks and Heterogeneous Media, 2020, 15 (2) : 281-305. doi: 10.3934/nhm.2020013
[10]

Julián Fernández Bonder, Analía Silva, Juan F. Spedaletti. Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2125-2140. doi: 10.3934/dcds.2020355
[11]

Gianni Dal Maso. Ennio De Giorgi and $\mathbf\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1017-1021. doi: 10.3934/dcds.2011.31.1017
[12]

Alexander Mielke. Deriving amplitude equations via evolutionary $\Gamma$-convergence. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2679-2700. doi: 10.3934/dcds.2015.35.2679
[13]

Francesca Papalini. Strongly nonlinear multivalued systems involving singular $\Phi$-Laplacian operators. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1025-1040. doi: 10.3934/cpaa.2010.9.1025
[14]

Jacson Simsen, Mariza Stefanello Simsen, José Valero. Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2347-2368. doi: 10.3934/cpaa.2020102
[15]

Mohd Qasim, Mohd Shanawaz Mansoori, Asif Khan, Zaheer Abbas, Mohammad Mursaleen. Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters. Mathematical Foundations of Computing, 2022, 5 (3) : 187-196. doi: 10.3934/mfc.2021027
[16]

José C. Bellido, Pablo Pedregal. Explicit quasiconvexification for some cost functionals depending on derivatives of the state in optimal designing. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 967-982. doi: 10.3934/dcds.2002.8.967
[17]

Sylvia Serfaty. Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1427-1451. doi: 10.3934/dcds.2011.31.1427
[18]

Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure and Applied Analysis, 2021, 20 (5) : 2101-2116. doi: 10.3934/cpaa.2021059
[19]

Guangcun Lu. Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1243-1316. doi: 10.3934/dcds.2021154
[20]

Thaís Jordão, Xingping Sun. General types of spherical mean operators and $K$-functionals of fractional orders. Communications on Pure and Applied Analysis, 2015, 14 (3) : 743-757. doi: 10.3934/cpaa.2015.14.743

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (53)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy