Review of "On some new phenomena in state-constrained optimal control if ODEs as well as PDEs are

COSTANZA, V

Mathematical Reviews

American Mathematical Society

Lugar: Providence; Año: 2012 p. 1 - 2

0025-5629

In this paper a nonstandard optimization problem is presented, which is then reformulated analytically, and treated numerically. The case study involves finite-dimensional states (those associated with the linear control system known as “the double integrator”, modeled by two first-order ODEs), together with an infinite-dimensional state (the spatial temperature profile in the interior of a moving object). The dynamics of the temperature profile is governed by the heat equation plus a source term that depends on the kinetic energy of the object. The cost for minimizing has an equally unusual formulation: it is the sum of the time duration of the process on one side, and the total control energy on the other. These two partial objectives appear frequently in the optimal control literature, but hardly ever together. In addition, both the control and the temperature are constrained, and the final position and velocity are inflexible, fixed at the origin of R2.R2.