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Optimal control discrete-time systems

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System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 113))

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References

  1. Canon M. D., Cullum C. D., Polak E.: Theory of Optimal Control and Mathematical Programming. McGraw-Hill, New York 1970.

    Google Scholar 

  2. Blaquiere A., Gerard F., Leitmann G.: Quantitative and Qualitative Games. Academic Press, New York 1969.

    Google Scholar 

  3. Propoi A. I.: Elements of Optimal Discrete Processes. Nauka. Moscow 1973. In Russian.

    Google Scholar 

  4. Boltjanskij V. G.: Optimal Control of Discrete Systems, Nauka, Moscow 1973. In Russian.

    Google Scholar 

  5. Dolezal J.: Necessary optimality conditions for discrete systems with state-dependent control region. Kybernetika 11 (1975), 423–450.

    Google Scholar 

  6. Dolezal J.: Necessary condition for discrete dynamical systems with delays and general constraints. Kybernetika 17 (1981), 425–432.

    Google Scholar 

  7. Dolezal J.: Optimal control of discrete systems involving delays. JOTA 39 (1983). 59–66.

    Google Scholar 

  8. Dolezal J.: Discrete optimal control problems with isoperimetric constraints and discrete multiobjective optimization. Preprints of the 2nd IFAC Symposium on Optimization Methods, Varna 1979, 7–13.

    Google Scholar 

  9. Dolezal J.: Optimal control of discrete systems: periodic systems and systems with delays. Proceedings of the 5th Symposium Computer in Chemical Engineering, High Tatras 1977, 831–834.

    Google Scholar 

  10. Dolezal J.: Existence of optimal solutions in general discrete systems. Kybernetika 11 (1975), 301–312.

    Google Scholar 

  11. Dolezal J.: Optimal control existence results for general discrete systems. Appl. Math. Optimiz. 3 (1976), 51–63.

    Google Scholar 

  12. Hautus M. L. J.: Necessary conditions for multiple constraint optimization problems. SIAM J. Control 11 (1973), 653–669.

    Google Scholar 

  13. Pontrjagin L. S., Bltjanskij V. G., Gamkrelidze R. V., Mishchenko E. F.: The Mathematical Theory of Optimal Processes. Interscience, New York 1962.

    Google Scholar 

  14. Holtzman J. M., Halkin H.: Directional convexity and the maximum principle for discrete systems. SIAM J. Control 4 (1966), 265–275.

    Google Scholar 

  15. Gabasov R., Kirillova F.: On discrete maximum principle. Math. Operationsforsch. Statist., Ser. Optimization 10 (1979), 543–553.

    Google Scholar 

  16. Nahorski Z., Ravn H. F., Vidal R. V. V.: The discrete-time maximum principle: a survey and some new results. Int. J. Control 40 (1984), 533–554.

    Google Scholar 

  17. Dolezal J.: On the sufficient optimality conditions for difference inclusions. Systems Science 5 (1979), 187–198.

    Google Scholar 

  18. Rockafellar R. T., Wets R. J.-B.: Deterministic and stochastic optimization problems of Bolza type in discrete time. Working Paper WP-81-69, IIASA, Laxenburg 1981.

    Google Scholar 

  19. Clarke F. H.: Generalized gradients and applications. Trans. Amer. Math. Soc. 205 (1975), 247–262.

    Google Scholar 

  20. Dolezal J.: Non-smooth and non-convex problems in discrete optimal control. Int. J. Systems Sci. 13 (1982), 969–978.

    Google Scholar 

  21. Dolezal J.: Necessary conditions for Lipschitz continous discrete control problems. In "Mathematical Control Theory", J. Zabczyk (Ed.), Banach Center Publications, Vol. 14, Polish Scientific Publishers, Warsaw 1985, 171–179.

    Google Scholar 

  22. Mordukhovich B. Sh.: On necessary conditions for an extremum in nonsmooth optimization. Soviet Math. Dokl. 32 (1985), 215–219.

    Google Scholar 

  23. Dolezal J.: Hierarchical solution concept for static and multistage decision problems with two objectives. Kybernetika 12 (1976), 363–385.

    Google Scholar 

  24. DaCunha N. O., Polak E.: Constrained minimization under vector-valued criteria in finite dimensional spaces. J. Math. Anal. Appl. 19 (1976), 103–124.

    Google Scholar 

  25. Dolezal J.: Necessary optimality conditions for discrete systems with state-dependent control region and vector-valued objective function. Systems Science 3 (1977), 171–184.

    Google Scholar 

  26. Goffin J. L., Haurie A.: Pareto optimality with nondifferentiable cost functions. In "Multiple Criteria Decision Making", H. Thiriez, S. Zionts (Eds.), Springer-Verlag, Berlin 1976, 232–246.

    Google Scholar 

  27. Kanniappan P.: Necessary conditions for optimality of nondifferentiable convex multiobjective programming. JOTA 40 (1983), 167–174.

    Google Scholar 

  28. Dolezal J.: Necessary conditions for Pareto optimality in nondifferentiable problems. Problem of Control Theory 14 (1985), 131–141.

    Google Scholar 

  29. Dolezal J.: Necessary optimality conditions for N-player nonzero-sum multistage games. Kybernetika 12 (1976), 268–295.

    Google Scholar 

  30. Kleindorfer P. R., Sertel M. R.: Equilibrium existence results for simple dynamic games. JOTA 14 (1974), 613–631.

    Google Scholar 

  31. Dolezal J.: Stackelberg solution concept for general multistage games. Kybernetika 14 (1978), 369–380.

    Google Scholar 

  32. Aubin J.-P.: Locally Lipschitz cooperative games. J. Math. Economics 8 (1981), 241–262.

    Google Scholar 

  33. Polak E.: Computational Methods in Optimization: Unified Approach. Academic Press, New York 1971.

    Google Scholar 

  34. Dolezal J.: On a certain type of discrete two-point boundary-value problem arising in discrete optimal control. Kybernetika 15 (1979), 215–221.

    Google Scholar 

  35. Ritch P. S.: Discrete optimal control with multiple constraints I: Constraint separation and transformation technique. Automatica 9 (1973), 415–429.

    Google Scholar 

  36. Dolezal J.: Gradient method for discrete-time optimal control. In "5th Symp. on Algorithms", Part Algorithms, High Tatras 1981, 249–270. In Czech.

    Google Scholar 

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Masao Iri Keiji Yajima

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© 1988 International Federation for Information Processing

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Dolezal, J. (1988). Optimal control discrete-time systems. In: Iri, M., Yajima, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042771

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  • DOI: https://doi.org/10.1007/BFb0042771

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19238-1

  • Online ISBN: 978-3-540-39164-7

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