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Parametric approach to optimal control

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Abstract

We consider the optimal control problem from view point of parametric aspects. We have examined two cases of the parameterized problems. First case describes the situation when the objective functional contains time t as a parameter. We also show how to apply the parametric optimization techniques, such as pathfollowing methods, for finding a nominal optimal control path.

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References

  1. Clarke F.H., Hiriart-Urruty J.-B., Ledyaev Yu.S.: On global optimality conditions for nonlinear optimal control problems. J. Glob. Optim. 13(2), 109–122 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dentcheva, D., Guddat, J., Rückmann, J.-J., Wendler, K.: Pathfollowing methods in nonlinear optimization. III. Lagrange multiplier embedding. ZOR—Math. Methods Oper. Res. 41(2), 127–152 (1995) (parametric optimization)

  3. Guddat J., Guerra Vazquez F., Jongen H.Th.: Parametric optimization: singularities, pathfollowing and jumps. B. G. Teubner, Stuttgart (1990)

    MATH  Google Scholar 

  4. Guddat, J., Jongen, H.Th., Kummer, B., Nožička, F.: (eds.) Parametric optimization and related topics. III, Approximation & Optimization, vol. 3. Peter Lang, Frankfurt am Main (1993) (Papers from the Third Conference held in Güstrow, August 30–September 5 (1991))

  5. Gollmer, R., Kausmann, U., Nowack, D., Wendler, K., Bacallao Estrada, J.: Program package pafo. Software development report, Humboldt University, Berlin (1995–2007)

  6. Guddat, J., Rückmann, J.-J.: One-parametric optimization: jumps in the set of generalized critical points. Control Cybern. 23(1–2), 139–151 (1994) (parametric optimization)

    Google Scholar 

  7. Jongen H.Th., Jonker P., Twilt F.: Critical sets in parametric optimization. Math. Program. 34(3), 333–353 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nakayama H.: Trade-off analysis using parametric optimization techniques. Eur. J. Oper. Res. 60(1), 87–98 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The mathematical theory of optimal processes. Interscience Publishers John Wiley & Sons, Inc., New York (1962) (translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt)

  10. Pinch E.R.: Optimal control and the calculus of variations. Oxford Science Publications. The Clarendon Press Oxford University Press, New York (1993)

    MATH  Google Scholar 

  11. Rohde A., Stavroulakis G.E.: Path-following energy optimization in unilateral contact problems. J. Glob. Optim. 6(4), 347–365 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Vasiliev, O.V.: Optimization methods. Advanced Series in Mathematical Science and Engineering, vol. 5. World Federation Publishers Company, Atlanta, GA (1996) (translated from the Russian)

  13. Vasilieva O.: Successive approximations technique for optimal control problem with boundary conditions. J. Mong. Math. Soc. 5(1), 70–85 (2001)

    MathSciNet  MATH  Google Scholar 

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Correspondence to A. Radwan.

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Radwan, A., Vasilieva, O., Enkhbat, R. et al. Parametric approach to optimal control. Optim Lett 6, 1303–1316 (2012). https://doi.org/10.1007/s11590-011-0377-0

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