39 citations · 110 across the 14 of their papers we have counts for
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On the Noether Invariance Principle for Constrained Optimal Control Problems
Delfim F. M. Torres
We obtain a generalization of Noether's invariance principle for optimal control problems with equality and inequality state-input constraints. The result relates the invariance pr…
Newton's aerodynamic problem in media of chaotically moving particles
Alexander Yu. Plakhov, Delfim F. M. Torres
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particle…
Optimal Control of Newton-Type Problems of Minimal Resistance
Delfim F. M. Torres, Alexander Yu. Plakhov
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessar…
Two-Dimensional Problems of Minimal Resistance in a Medium of Positive Temperature
Alexander Yu. Plakhov, Delfim F. M. Torres
We study the Newton-like problem of minimal resistance for a two-dimensional body moving with constant velocity in a homogeneous rarefied medium of moving particles. The distributi…
On the Constancy of the Pontryagin Hamiltonian for Autonomous Problems
Delfim F. M. Torres
We provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respe…
Quasi-Invariant Optimal Control Problems
Delfim F. M. Torres
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryag…