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2021•Selecciones MatemáticasOpen access

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

Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú, José Luis Ponte Bejarano, 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

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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.

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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.

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Available 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.

Key concepts: Pontryagin's minimum principle, Maximum principle, Mathematics, Optimal control, Work (physics), Hamiltonian (control theory), Applied mathematics, Mathematical optimization

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