Skip to main content
Log in

Relaxation methods in control theory

  • Published:
Applied Mathematics and Optimization Aims and scope Submit manuscript

Abstract

Two different “relaxed problems” associated with a problem of optimal control theory, governed by an ODE, are considered: the first is obtained by Young's methods and the second by semicontinuity arguments. A formula which relates the two relaxed functionals to each other is given.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Buttazzo, Some relaxation problems in optimal control theory, J. Math. Anal. Appl., 125 (1987), 272–287.

    Google Scholar 

  2. G. Buttazzo, G. Dal Maso, Integral representation and relaxation of local functionals, Nonlinear Anal., 9 (1985), 515–532.

    Google Scholar 

  3. G. Buttazzo, G. Dal Maso, Γ-convergence and optimal control problems, J. Optim. Theory Appl., 38 (1983), 385–407.

    Google Scholar 

  4. I. Capuzzo Dolcetta, On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming, Appl. Math. Optim., 10 (1983), 367–377.

    Google Scholar 

  5. I. Capuzzo Dolcetta, H. Ishii, Approximate solution of the Bellman equation of deterministic control theory, Appl. Math. Optim., 11 (1984), 161–181.

    Google Scholar 

  6. F. Clarke, Admissible relaxation in variational and control problems, J. Math. Anal. Appl., 51 (1975), 557–576.

    Google Scholar 

  7. E. De Giorgi, Some Semicontinuity and Relaxation Problems, Proc. Colloque E. de Giorgi, Paris, Research Notes in Mathematics, Pitman, London (1983).

    Google Scholar 

  8. R. E. Edwards, Functional Analysis Theory and Applications, Holt Rinehart and Winston, New York (1965).

    Google Scholar 

  9. J. Ekeland, R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam (1976).

    Google Scholar 

  10. A. D. Joffe, V. Tihomirov, Extension of variational problems, Trans. Moscow Math. Soc., 18 (1968), 207–273.

    Google Scholar 

  11. E. B. Lee, L. Markus, Foundations of Optimal Control Theory, Wiley, New York (1976).

    Google Scholar 

  12. F. Murat, L. Tartar, Calculus of variations, Collection de la Direction des Etudes et Recherches d'Electricite de France, Eyrolles, Paris (1984).

    Google Scholar 

  13. L. Tartar, Compensated compactness and applications to partial differential equations, in: R. J. Knops (ed.), Heriot-Watt Symposium, vol. 4, Pitman, London (1979).

    Google Scholar 

  14. J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York (1972).

    Google Scholar 

  15. L. C. Young, Lectures on the Calculus of Variations and Optimal Control, Saunders, Philadelphia (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mascolo, E., Migliaccio, L. Relaxation methods in control theory. Appl Math Optim 20, 97–103 (1989). https://doi.org/10.1007/BF01447649

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01447649

Keywords

Navigation