Consider the following Bolza problem: min integral h(x, u)dt, x = F(x) + uG(x), \u\ less-than-or-equal-to 1, x is-an-element-of OMEGA subset-of R2, x(0) = x0, x(1) = x1. We show that, under suitable assumptions on F, G, h, all optimal trajectories are bang-bang. The proof relies on a geometrical approach that works for every smooth two-dimensional manifold. As a corollary, we obtain existence results for nonconvex optimization problems.
Bang-Bang Property for Bolza Problems in Two Dimensions / Crasta, G., B., P.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 83:1(1994), pp. 155-165. [10.1007/bf02191766]
Bang-Bang Property for Bolza Problems in Two Dimensions
CRASTA, Graziano;
1994
Abstract
Consider the following Bolza problem: min integral h(x, u)dt, x = F(x) + uG(x), \u\ less-than-or-equal-to 1, x is-an-element-of OMEGA subset-of R2, x(0) = x0, x(1) = x1. We show that, under suitable assumptions on F, G, h, all optimal trajectories are bang-bang. The proof relies on a geometrical approach that works for every smooth two-dimensional manifold. As a corollary, we obtain existence results for nonconvex optimization problems.File allegati a questo prodotto
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