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HIV Infection Control: A Constructive Algorithm for a State-based Switching Control

  • Paolo Di Giamberardino
  • Daniela Iacoviello
Technical Notes and Correspondence
  • 17 Downloads

Abstract

The control of the HIV infection is considered in the framework of the optimal control theory within the problem of resource allocation. A control action, changing the intervention strategy on the basis of the updated situations, is proposed. The switching instants are not fixed in advance but are determined along with the final control time. A constructive algorithm to compute iteratively the switching control is outlined. The solutions obtained provide interesting and promising results.

Keywords

Epidemic models HIV model piece-wise constant control state-based switching cost function 

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References

  1. [1]
    P. Di Giamberardino, L. Compagnucci, C. De Giorgi, and D. Iacoviello, “A new model of the HIV/AIDS infection diffusion and analysis of the intervention effects,” Proc. of 25th IEEE Mediterranean Conference on Control and Automation, pp. 291–296, 2017.Google Scholar
  2. [2]
    C. Xiong, Y. Zhou, C. Yu, and H. Mei, “Control model of the HIV/AIDS epidemic based on kinetic equation, ” World Journal of AIDS, vol. 3, pp. 79–84, 2013. [click]CrossRefGoogle Scholar
  3. [3]
    D. Wodarz, “Helper-dependent vs. helper-independent CTL responses in HIV infection: implications for drug therapy and resistance,” Journal Theor. Biol., vol. 213, pp. 447–459, 2001. [click]CrossRefGoogle Scholar
  4. [4]
    H. Chang and A. Astolfi, “Control of HIV infection dynamics,” IEEE Control Systems, vol. 28, no. 2, pp. 28–39, 2009.Google Scholar
  5. [5]
    H. T. Banks, H. D. Kwon, J. A. Toivanen, and H. T. Tran, “A state-dependent Riccati equation-based estimator approach for HIV feedback control,” Opt. Control Applications and Methods, vol. 27, pp. 93–121, 2006.MathSciNetCrossRefGoogle Scholar
  6. [6]
    H. R. Joshi, “Optimal control of an HIV immunology model,” Opt. Control Applications and Methods, vol. 23, 199–213, 2002.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Y. Zhou, K. Yang, K. Zhou, and C. Wang, “Optimal treatment strategies for HIV with antibody response,” Journal of Applied Mathematics, vol. 52, pp. 1–13, 2014MathSciNetGoogle Scholar
  8. [8]
    E. A. H. Vargas, P. Colaneri, and R. H. Middleton, “Switching strategies to mitigate HIV mutation,” IEEE Trans. on Control System Technology, vol. 22, no. 4, pp. 1623–1628, 2014. [click]CrossRefGoogle Scholar
  9. [9]
    S. K. Kim, D. Kim, and T.W. Yoon, “Adaptive observer for estimating the parameters of an HIV model with mutants,” International Journal of Control, Automation and Systems, vol. 13, no. 1, pp. 126–137, 2015. [click]CrossRefGoogle Scholar
  10. [10]
    Y. Ding, Z. Wang, and H. Ye, “Optimal control of a fractional-order HIV-immune system with memory,” IEEE Trans. on Control System Technology, vol. 30, no. 3, pp. 763–769, 2012.CrossRefGoogle Scholar
  11. [11]
    E. C. Yuan, D. L. Alderson, S. Stromberg, and J. M. Carlson, “Optimal vaccination in a stochastic epidemic model of two non-interacting populations,” PLOS ONE, pp. 1–25, 2015.Google Scholar
  12. [12]
    H. Shim, S. J. Han, C. C. Chung, S.W. Nam, and J. H. Seo, “Optimal scheduling of drug treatment for HIV infection: continuous dose control and receding horizon control,” International Journal of Control, Automation, and Systems, vol. 1, no. 3, pp. 282–288, 2003.Google Scholar
  13. [13]
    R. F. Hartl, S. P. Sethi, and R. G. Vickson, “A survey of the maximum principles for optimal control problems with state constraints,” Society for Industrial and Applied Mathematics, vol. 37, pp. 181–218, 1995. [click]MathSciNetzbMATHGoogle Scholar
  14. [14]
    C. Li, X. Yu, Z. Liu, and T. Huang, “Asynchronous impulsive containment controlling switched multi-agent systems,” Information Sciences, vol. 370, pp. 667–679, 2016.CrossRefGoogle Scholar
  15. [15]
    X. Ding and X. Liu, “Stability analysis for switched positive linear systems under state dependent switching,” International Journal of Control, Automations and Systems, vol.15, pp. 481–488, 2017. [click]CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer, Control and Management Engineering Antonio RubertiSapienza University of RomeRomeItaly

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