Application of the principle of the Pontryagin maximum in the solution of a problem of minimum time

Authors

  • José Luis Ponte Bejarano Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú.
  • Juan Carlos Ponte Bejarano Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú.
  • Alexis Rodríguez Carranza Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú.
  • Nelson Omar Aragones Salazar Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú.

DOI:

https://doi.org/10.17268/sel.mat.2021.02.10

Keywords:

Optimal control, ordinary differential equations

Abstract

In the present work, necessary and sufficient optimality conditions are presented for the solution to a mínimum time problem. These conditions are established by the principle of the Pontryagin maximum, as a necessary and sufficient condition. In addition, the principle of the Pontryagin maximum is used in the search for the solution to an optimal control problem of mechanical origin.

References

Intriligator DM. Mathematical optimization and economic theory. University of California. Prentice Hall. 2002. Pages 398-430.

Kirk ED. Optimal control theory: An introduction. New York, Mineola. Prentice Hall. 2004. Pages 240-308.

Hull GD. Optimal control theory for applications. New York. Springer Velag. 2003. Pages 89-91.

Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mischenko EF. The mathematical theory of optimal processes . Rusia. Interscience Publishers. 1962. Pages 115-188.

Pontryagin LS. Optimal Control Processes. Selected Research Papers. 1959. Vol 1, pp 511-532.

Cerdá TE. Optimización dinámica. España, Madrid. Prentice Hall. 2001. Pages 100-153.

Published

2021-12-27

How to Cite

Ponte Bejarano, J. L., Ponte Bejarano, J. C., Rodríguez Carranza, A., & Aragones Salazar, N. O. (2021). Application of the principle of the Pontryagin maximum in the solution of a problem of minimum time. Selecciones Matemáticas, 8(02), 333-347. https://doi.org/10.17268/sel.mat.2021.02.10