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On the local structure of optimal trajectories in R3

TitleOn the local structure of optimal trajectories in R3
Publication TypeJournal Article
Year of Publication2003
AuthorsAgrachev, AA, Sigalotti, M
JournalSIAM J. Control Optim. 42 (2003) 513-531
Abstract

We analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.

URLhttp://hdl.handle.net/1963/1612
DOI10.1137/S0363012902409246

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