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Topics in Time Delay Systems pp 255–265Cite as

Time Optimal and Optimal Impulsive Control for Coupled Differential Difference Point Delay Systems with an Application in Forestry

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 388))

Summary

In this paper we consider the optimal timing and impulsive control for a class of systems described by coupled differential and continuous time difference equations. The necessary conditions for optimality follow the approach for a single time-optimal impulse control, which is derived in full detail, using a streamlined approach with appropriately defined Hamiltonian. An example in regeneration of a deforested area is reported.

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References

  1. Freedman, H.I., Kuang, Y.: Stability switches in linear scalar neutral delay equations. Funkcialaj Ekvacioj 34, 187–209 (1991)

    MATH  MathSciNet  Google Scholar 

  2. Kuang, Y.: Delay differential equations with applications in population dynamics. Academic Press, San Diego (1993)

    MATH  Google Scholar 

  3. Gopalsamy, K., Zhang, B.G.: On a neutral delay-logistic equation. Dynamics and Stability of Systems 2, 183–195 (1988)

    MathSciNet  Google Scholar 

  4. Hadeler, K.P., Müller, J.: Optimal harvesting and optimal vaccination. Mathematical Biosciences 206, 249–272 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hale, J.K., Verduyn Lunel, S.M.: Introduction to functional differential equations. Applied Math. Sciences Series. Springer, New York (1993)

    MATH  Google Scholar 

  6. Pepe, P., Verriest, E.I.: On the stability of coupled delay differential and continuous time difference equations. IEEE Transactions on Automatic Control 48(8), 1422–1427 (2003)

    Article  MathSciNet  Google Scholar 

  7. Pielou, E.C.: Mathematical Ecology. Wiley Interscience, New York (1977)

    Google Scholar 

  8. Rǎsvan, V.: Functional differential equations of lossless propoagation and almost linear behavior. In: Proc. 6th IFAC Workshop on Time Delay Systems, l’Aquila, Italy (2006)

    Google Scholar 

  9. Verriest, E.I., Yeung, D.: Parity in LQ control: the infinite time limit for terminal control. In: Proc. 2006 American Control Conference, Minneapolis, USA, pp. 1706–1711 (2006)

    Google Scholar 

  10. Verriest, E.I., Delmotte, F., Egerstedt, M.: Optimal impulsive control for point delay systems with refractory period. In: Proc. 5th IFAC Workshop on Time Delay Systems, Leuven, Belgium (2004)

    Google Scholar 

  11. Verriest, E.I., Delmotte, F.: Optimal control for switched point delay systems with refractory period. In: Proc. 16th IFAC World Congress, Prague, Czeck Republic (2005)

    Google Scholar 

  12. Verriest, E.I.: Optimal control for switched distributed delay systems with refractory period. In: Proc. IEEE Conference on Decision and Control, Sevilla, Spain, pp. 1421–1426 (2005)

    Google Scholar 

  13. Verriest, E.I., Delmotte, F., Egerstedt, M.: Control of epidemics by vaccination. In: Proc. 2005 American Control Conference, Portland, USA, pp. 985–990 (2005)

    Google Scholar 

  14. Xiao, Y., Cheng, D., Qin, H.: Optimal impulsive control in periodic ecosystems. Systems & Control Letters 55, 558–565 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0250, USA

    Erik I. Verriest

  2. Dipartimento di Ingegneria Elettrica, Università degli Studi dell’Aquila, 67040, L’Aquila, Italy

    Pierdomenico Pepe

Authors
  1. Erik I. Verriest
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  2. Pierdomenico Pepe
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Editor information

Editors and Affiliations

  1. Ecole Centrale de Nantes, Nantes, France

    Jean Jacques Loiseau

  2. Katholieke Universiteit, Leuven, Heverlee, Belgium

    Wim Michiels

  3. CNRSSupélec, Gif-sur-Yvette, France

    Silviu-Iulian Niculescu

  4. Northeastern University, Boston, MA, USA

    Rifat Sipahi

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© 2009 Springer-Verlag Berlin Heidelberg

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Verriest, E.I., Pepe, P. (2009). Time Optimal and Optimal Impulsive Control for Coupled Differential Difference Point Delay Systems with an Application in Forestry. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_22

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  • DOI: https://doi.org/10.1007/978-3-642-02897-7_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02896-0

  • Online ISBN: 978-3-642-02897-7

  • eBook Packages: EngineeringEngineering (R0)

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