Solving Impulsive Control Problems by Discrete-Time Dynamic Optimization Methods

Authors

  • R.T.N. Cardoso
  • R.H.C. Takahashi

DOI:

https://doi.org/10.5540/tema.2008.09.01.0021

Abstract

This work presents an open-loop discrete-time dynamic optimization scheme for continuous-variable impulsive control problems. This methodology can be more useful than the classical optimal control in several contexts, since it delivers control actions just in discrete times, which introduce discontinuities in the system state variables. Two case studies are presented: the biological control of pests incrops using a prey-predator model and the optimal vaccination in epidemics control using an SIR model.

References

[1] D.P. Bertsekas, “Dynamic Programming and Optimal Control”, Athena Scientific, 1995.

M.S. Branicky, “Studies in Hybrid Systems: Modeling, Analysis, and Control”, Phd dissertation, Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, USA, 1995.

R.T.N. Cardoso, R.H.C. Takahashi, Algoritmos para programação dinâmica baseados em famílias invariantes [in portuguese], Simpósio Brasileiro de Pesquisa Operacional, 2005.

A.C. Chiang, “Elements of Dynamic Optimization”, Mc Graw Hill, 1992.

A.R. da Cruz, R.T.N. Cardoso, E.F. Wanner, R.H.C. Takahashi, A multiobjective non-linear dynamic programming approach for optimal biological control

in soy farming via NSGA-II, IEEE Congress on Evolutionary Computation, 2007.

A.N. Dar’in, A.B. Kurzhanskii, A.V. Selesznev, The dynamic programming method in impulsive control synthesis, Ordinary Differential Equations, 41, No. 11 (2005), 1491–1500.

A. d’Onofrio, On pulse vaccination strategy in the SIR epidemic model with vertical transmission, Applied Mathematics Letters, 18, No. 7 (2005), 729–732.

C.C. Feltrin, M. Rafikov, Aplicação da função de Lyapunov num problema de controle ótimo de pragas [in portuguese], in “Seleta do XXIV CNMAC” (E.X.L. de Andrade et al., eds.), TEMA - Tendências em Matemática Aplicada e Computacional, Vol. 3, No.2, pp. 83–92, SBMAC, 2002.

H.W. Hetchcote, The mathematics of infectious diseases, SIAM Review, 42, No. 4 (2000), 599–653.

V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, “Theory of Impulsive Differential Equations”, Series in Modern Applied Mathematics, World Scientific, Singapore, 1989.

B. Liu, Z. Teng, L. Chen, Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy, Journal of Computational and Applied Mathematics, 193, No. 2 (2006), 347–362.

E.G. Nepomuceno, “Dinãmica, Modelagem e Controle de Epidemias”, Tese de doutorado [in portuguese], Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, Brasil, 2005.

J.T. Sun, Y.P. Zhang, Stability analysis of impulsive control systems, IEE Proceedings in Control Theory and Applications, 150, No. 4 (2003), 331–334.

T. Yang, Impulsive control, IEEE Transactions on Automatic Control, 44, No. 5 (1999), 1081–1083.

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Published

2008-06-01

How to Cite

Cardoso, R., & Takahashi, R. (2008). Solving Impulsive Control Problems by Discrete-Time Dynamic Optimization Methods. Trends in Computational and Applied Mathematics, 9(1), 21–30. https://doi.org/10.5540/tema.2008.09.01.0021

Issue

Vol. 9 No. 1 (2008)

Section

Original Article

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