Skip to main content
SpringerLink
Log in
Book cover

International Conference on Mathematical Optimization Theory and Operations Research

MOTOR 2019: Mathematical Optimization Theory and Operations Research pp 474–488Cite as

Optimality Conditions and Numerical Algorithms for Hybrid Control Systems

  • Conference paper
  • First Online:

  • 866 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

For an optimal control problem with intermediate state constraints, we construct an iterative descent algorithm and prove a related necessary optimality condition. Finally, we show how these results can be applied to measure-driven multiprocesses.

Partially supported by the Russian Foundation for Basic Research, projects nos 18-31-20030, 18-31-00425, 18-01-00026, 17-01-00733.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
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

Learn about institutional subscriptions

References

  1. Ashepkov, L.T.: Optimal Control of Discontinuous Systems. Nauka, Novosibirsk (1987)

    Google Scholar 

  2. Baturin, V.A., Maltugueva, N.S.: Second-order improvement method to solve problems of optimal control of the logic-dynamic systems. Autom. Remote Control 72(4), 808–817 (2011)

    Article  MathSciNet  Google Scholar 

  3. Betounes, D.: Differential Equations: Theory and Applications, 2nd edn. Springer, New York (2010). https://doi.org/10.1007/978-1-4419-1163-6

    Book  MATH  Google Scholar 

  4. Buss, M., Von Stryk, O., Bulirsch, R., Schmidt, G.: Towards hybrid optimal control. at - Automatisierungstechnik 48(9), 448–459 (2000). https://doi.org/10.1524/auto.2000.48.9.448

  5. Clarke, F.H., Vinter, R.B.: Applications of optimal multiprocesses. SIAM J. Control Optim. 27(5), 1048–1071 (1989)

    Article  MathSciNet  Google Scholar 

  6. Clarke, F.H., Vinter, R.B.: Optimal multiprocesses. SIAM J. Control Optim. 27(5), 1072–1091 (1989)

    Article  MathSciNet  Google Scholar 

  7. Clarke, F.H.: Functional Analysis, Calculus of Variations and Optimal Control, Graduate Texts in Mathematics, vol. 264. Springer, London (2013). https://doi.org/10.1007/978-1-4471-4820-3

    Book  Google Scholar 

  8. Dmitruk, A.V., Kaganovich, A.M.: The hybrid maximum principle is a consequence of Pontryagin maximum principle. Syst. Control. Lett. 57(11), 964–970 (2009)

    Article  MathSciNet  Google Scholar 

  9. Dykhta, V.A.: Variational necessary optimality conditions with feedback descent controls for optimal control problems. Dokl. Math. 91(3), 394–396 (2015)

    Article  MathSciNet  Google Scholar 

  10. Dykhta, V.A., Samsonyuk, O.N.: Maximum principle for nonsmooth optimal control problems with multipoint state constraints. Russ. Math. (Izvestiya VUZ. Matematika) 45(2), 16–29 (2001)

    Google Scholar 

  11. Dykhta, V.A., Samsonyuk, O.N.: A maximum principle for smooth optimal impulsive control problems with multipoint state constraints. Comput. Math. Math. Phys. 49, 942–957 (2009)

    Article  MathSciNet  Google Scholar 

  12. Gurman, V.I., Baturin, V.A., Danilina, E.V., et al.: New methods for the improvement of control processes. (Novye metody uluchsheniya upravlyaemykh protsessov). Nauka, Novosibirsk. 184 p. R. 1.80 (TIB: FM 1097) (1987)

    Google Scholar 

  13. Miller, B.M.: The generalized solutions of nonlinear optimization problems with impulse control. SIAM J. Control Optim. 34, 1420–1440 (1996)

    Article  MathSciNet  Google Scholar 

  14. Miller, B.M., Rubinovich, E.Y.: Impulsive Control in Continuous and Discrete-continuous Systems. Kluwer Academic/Plenum Publishers, New York (2003). https://doi.org/10.1007/978-1-4615-0095-7

    Book  MATH  Google Scholar 

  15. Miller, B.M., Rubinovich, E.Y.: Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations. Autom. Remote Control 74, 1969–2006 (2013)

    Article  MathSciNet  Google Scholar 

  16. Motta, M., Rampazzo, F.: Space-time trajectories of nonlinear systems driven by ordinary and impulsive controls. Differ. Integr. Equ. 8(2), 269–288 (1995)

    MathSciNet  MATH  Google Scholar 

  17. Poliquin, R.A., Rockafellar, R.T., Thibault, L.: Local differentiability of distance functions. Trans. Am. Math. Soc. 352(11), 5231–5249 (2000)

    Article  MathSciNet  Google Scholar 

  18. Rasina, I.V.: Iterative optimization algorithms for discrete-continuous processes. Autom. Remote Control 73(10), 1591–1603 (2012). https://doi.org/10.1134/S0005117912100013

    Article  MathSciNet  MATH  Google Scholar 

  19. Samsonyuk, O.N.: Invariant sets for nonlinear impulsive control systems. Autom. Remote Control 76(3), 405–418 (2015)

    Article  MathSciNet  Google Scholar 

  20. Srochko, V.A.: Iterative Methods for Solving Optimal Control Problems. Fizmatlit, Moscow (2000)

    Google Scholar 

  21. von Stryk, O., Bulirsch, R.: Direct and indirect methods for trajectory optimization. Ann. Oper. Res. 37(1–4), 357–373 (1992)

    Article  MathSciNet  Google Scholar 

  22. Wei, S., Uthaichana, K., Žefran, M., Decarlo, R.A., Bengea, S.: Applications of numerical optimal control to nonlinear hybrid systems. Nonlinear Anal. Hybrid Syst. 1(2), 264–279 (2007)

    Article  MathSciNet  Google Scholar 

  23. Zavalishchin, S.T., Sesekin, A.N.: Dynamic Impulse Systems, Mathematics and Its Applications, vol. 394. Kluwer Academic Publishers Group, Dordrecht (1997). https://doi.org/10.1007/978-94-015-8893-5

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, 664033, Russia

    Nadezhda Maltugueva, Nikolay Pogodaev & Olga Samsonyuk

Authors
  1. Nadezhda Maltugueva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolay Pogodaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olga Samsonyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nadezhda Maltugueva .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Maltugueva, N., Pogodaev, N., Samsonyuk, O. (2019). Optimality Conditions and Numerical Algorithms for Hybrid Control Systems. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22629-9_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation