Lipschitz regularity of controls and inversion mapping for a class of smooth extremization problems
From MaRDI portal
Publication:6419536
DOI10.1016/J.AUTOMATICA.2022.110794arXiv2212.02102MaRDI QIDQ6419536
Publication date: 5 December 2022
Abstract: In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between minima/maxima and extremals could break down. Commonly, this is due to a loss of convexity/concavity of the cost functional or to a presence of state constraints, in which further controllability assumptions are needed. For many science applications, this a trend is not required, as in energy saving problems. In the present paper, we deal with the set of a functional's extremals subject to end-point restrictions. We consider an affine control system and a cost functional associated to an autonomous Lagrangian. The dynamics is smooth, satisfying the Lie bracket condition, and the functional is assumed merely Fr'echet differentiable. Here we provide a regularity result for controls in the context of constrained extremization problems, under weaker conditions on Lagrangian than the not met classical ones. More precisely, we show a characterization for the Lipschitz regularity of controls associated with the extremal trajectories steering two fixed points, assuming the absence of singular controls. As main application, we construct a locally Lipschitz inversion mapping from the ambient space to the set of constrained extremals.
Fréchet and Gateaux differentiability in optimization (49J50) Existence of solutions for minimax problems (49J35)
This page was built for publication: Lipschitz regularity of controls and inversion mapping for a class of smooth extremization problems
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6419536)
