Solving Impulsive Control Problems by Discrete-Time Dynamic Optimization Methods

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

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.




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

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia