IDEAS home Printed from
   My bibliography  Save this paper

Optimal Control Synthesis in Grid Approximation Schemes


  • A.M. Tarasyev


Grid approximation schemes for constructing value functions and optimal feedbacks in problems of guaranteed control are proposed via a theory of generalized (minimax, viscosity) solutions of Hamilton-Jacobi equations. Value functions in optimal control problems are usually nondifferentiable and corresponding feedbacks have the discontinuing switching character. Therefore, constructions of generalized gradients for local hulls of different types are used in finite difference operators which approximate value functions. Optimal feedbacks are synthesized by external shift in the direction of the generalized gradients. Both problems of constructing the value function and control synthesis are solved simultaneously in the unique grid scheme. The interpolation problem is analyzed for grid values of optimal feedbacks. Questions of correlating spatial and temporal meshes are examined. Significance of quasiconvexity properties is clarified for the linear dependence of space-time grids. The proposed grid schemes for solving optimal guaranteed control problems can be applied for models arising in mechanics, mathematical economics, differential and evolutionary games.

Suggested Citation

  • A.M. Tarasyev, 1997. "Optimal Control Synthesis in Grid Approximation Schemes," Working Papers ir97012, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir97012

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. David J. TEECE, 2008. "Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy," World Scientific Book Chapters,in: The Transfer And Licensing Of Know-How And Intellectual Property Understanding the Multinational Enterprise in the Modern World, chapter 5, pages 67-87 World Scientific Publishing Co. Pte. Ltd..
    2. Geroski, Paul A & Jacquemin, Alexis, 1988. "The Persistence of Profits: A European Comparison," Economic Journal, Royal Economic Society, vol. 98(391), pages 375-389, June.
    3. Henderson, Rebecca., 1994. "The evolution of integrative capability : innovation in cardiovascular drug discovery," Working papers 3711-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Baldwin, John R. & Johnson, Joanne, 1996. "Business strategies in more- and less-innovative firms in Canada," Research Policy, Elsevier, vol. 25(5), pages 785-804, August.
    5. Paul Geroski & Steve Machin & John Van Reenen, 1993. "The Profitability of Innovating Firms," RAND Journal of Economics, The RAND Corporation, vol. 24(2), pages 198-211, Summer.
    6. Mueller,Dennis C., 2009. "Profits in the Long Run," Cambridge Books, Cambridge University Press, number 9780521101592, March.
    7. Klepper, Steven, 1996. "Entry, Exit, Growth, and Innovation over the Product Life Cycle," American Economic Review, American Economic Association, vol. 86(3), pages 562-583, June.
    8. Cohen, Wesley M & Levinthal, Daniel A, 1989. "Innovation and Learning: The Two Faces of R&D," Economic Journal, Royal Economic Society, vol. 99(397), pages 569-596, September.
    9. Pavitt, Keith, 1984. "Sectoral patterns of technical change: Towards a taxonomy and a theory," Research Policy, Elsevier, vol. 13(6), pages 343-373, December.
    10. Schmalensee, Richard, 1989. "Inter-industry studies of structure and performance," Handbook of Industrial Organization,in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 2, chapter 16, pages 951-1009 Elsevier.
    11. Bartel, Ann P & Lichtenberg, Frank R, 1987. "The Comparative Advantage of Educated Workers in Implementing New Technology," The Review of Economics and Statistics, MIT Press, vol. 69(1), pages 1-11, February.
    12. Arrow, Kenneth J., 1973. "Higher education as a filter," Journal of Public Economics, Elsevier, vol. 2(3), pages 193-216, July.
    13. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
    14. Richard C. Levin & Alvin K. Klevorick & Richard R. Nelson & Sidney G. Winter, 1988. "Appropriating the Returns from Industrial R&D," Cowles Foundation Discussion Papers 862, Cowles Foundation for Research in Economics, Yale University.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:iasawp:ir97012. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.