Skip to main content

Optimal Control of Systems Governed By Hemivariational Inequalities

  • Chapter
Mathematical Models for Phase Change Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 88))

Abstract

The present paper deals with the following optimal control problem: Minimize J(y, u) where (y, u) are related by the hemivariational inequality

$$y \in V,\left( {A\left( u \right)y,y* - y} \right) + \int {_{\Omega '}} {j^0}\left( {y,y* - y} \right)d\Omega \geqslant \left( {f + Bu,y* - y} \right)\forall y* \in V.$$

.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Panagiotopoulos, P.D. — Non-convex superpotentials in the sense of F.H. Clarke and applications, Mech. Res. Comm. 8 (1981), 335–340.

    Google Scholar 

  2. Panagiotopoulos, P.D. — Inequality Problems in Mechanics and Applications. Convex and Non-convex Energy Functions, Birkhäuser Verlag, Basel, Boston, Stuttgart 1985 (Russian Transl. MIR Publ. Moscow 1988).

    Google Scholar 

  3. Moreau, J. J., Panagiotopoulos, P.D., Strang, G. — Topics in Nonsmooth Mechanics, Birkhäuser Verlag, Boston, Basel 1988.

    Google Scholar 

  4. Moreau, J.J., Panagiotopoulos, P.D. (eds.) — Nonsmooth Mechanics and Applications, CISM Lect. Notes Vol. 302, Springer Verlag, Wien, N. York 1988.

    Google Scholar 

  5. Moreau, J.J. — La notion de sur-potential et les liaisons unilaterales en élastostatique, CR. Acad. Sc. Paris 267A (1968), 954–957.

    Google Scholar 

  6. Clarke, F.H. — Nonsmooth analysis and optimization, J. Wiley, New York 1984.

    Google Scholar 

  7. Yvon, J.P. — Etude de quelques problèmes de controle pour des systemes distribués, These de Doet or at d’Etat, Université Paris VI, 1973.

    Google Scholar 

  8. Lions, J.L. — Optimal control of systems governed by partial differential equations, Springer-Verlag 1971.

    Google Scholar 

  9. Panagiotopoulos, P.D. — Optimal control in the Unilateral Thin Plate Theory, Archives of Mechanics 29 (1977), 25–39.

    Google Scholar 

  10. Mignot, F. - Controle dans les inequations variationnelles elliptiques, J. Funct. Anal., 22 (1976) 130–185.

    Article  Google Scholar 

  11. Mignot, F., Puel, J.P. — Optimal control in some variational inequalities, SIAM Journal on Control and Optimization 22 (1984), 466–476.

    Article  Google Scholar 

  12. Shuzhong Shi — Optimal control of Strongly Monotone Variational Inequalities, SIAM Journal on Control and Optimization 26 (1988), 274–290.

    Article  Google Scholar 

  13. Haslinger, J., Neittaanmäki, P., Tiihonen, T. — Shape Optimization on Contact Problems Based on Penalization of the State Inequality, Aplikace Matematiky 31 (1986), 1–88.

    Google Scholar 

  14. Haslinger, J., Neittaanmäki, P. — On Optimal Shape Design of Systems Governed by Mixed Dirichlet-Signorini Boundary Value Problems, Math. Meth. in the Appl. Sei. 8 (1986), 157–181.

    Article  Google Scholar 

  15. Panagiotopoulos, P.D. — Nonconvex Problems of Semipermeable Media and Related Topics, ZAMM 65 (1985), 29–36.

    Article  Google Scholar 

  16. Stavroulakis, G., Panagiotopoulos, P.D. — Laminated orthotropic plates under Subdifferential Boundary Conditions. A Variational-Hemivariation-al Inequality Approach, ZAMM 68 (1988), 213–224.

    Article  Google Scholar 

  17. 17Chang, K.C. — Variational methods for non-differentiate Junctionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102–129.

    Article  Google Scholar 

  18. Ekelahd, I., Temam, R. — Convex Analysis and Variational Problems, North-Holland, Amsterdam and Americal Elsevier, N. York 1976.

    Google Scholar 

  19. Rauch, J. — Discontinuous semilinear differential equations and multiple valued maps, Proc. A.M.S. 64 (1977), 277–282.

    Article  Google Scholar 

  20. Panagiotopoulos, P.D. — Inequations Hémivariationnelles semi-coercives dans la théorie des plaques de von Karman, CR. Acad. Sc. Paris 307 Serie I (1988), 735–738.

    Google Scholar 

  21. Panagiotopoulos, P.D. — Semicoercive Hemivariational Inequalities. On the Delamination of Composite Plates, Quart. J. of Appl. Mathematics (to appear).

    Google Scholar 

  22. Panagiotopoulos, P.D., Haslinger, J. — Optimal Control for systems governed by hemivariational inequalities, SIAM J. of a Control and Optimization (to appear).

    Google Scholar 

  23. Baniotopoulos, C.C., Panagiotopoulos, P.D. — A Hemivariational Inequality Approach to the Analysis of Composite Material Structures, In Eng. Applic. of New Composites ed. by S.A. Paipetis, G.C. Papanicolaou, Omega Scientific, England 1988, p. 162–172.

    Google Scholar 

  24. Panagiotopoulos, P.D. — Optimal Control of Structures with convex and nonconvex energy densities and variational and hemivariational inequalities, Eng. Struct. 6 (1984), 12–18.

    Article  Google Scholar 

  25. Panagiotopoulos, P.D. — Property Control and Identification of Composite Materials via Hemivariational Inequalities, In “Phase Interaction of Composites” ed. by S.A. Paipetis, G.C. Papanicolaou, Omega Scientific, England 1989 (to appear).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Panagiotopoulos, P.D., Haslinger, J. (1989). Optimal Control of Systems Governed By Hemivariational Inequalities. In: Rodrigues, J.F. (eds) Mathematical Models for Phase Change Problems. International Series of Numerical Mathematics, vol 88. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9148-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-9148-6_16

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9926-0

  • Online ISBN: 978-3-0348-9148-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics