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Journal of Mathematical Sciences

, Volume 126, Issue 6, pp 1561–1573 | Cite as

Regularity properties of optimal trajectories of single-input control systems in dimension three

  • M. Sigalotti
Article

Abstract

Let \(\dot q = f(q) + ug(q)\) be a smooth control system on a three-dimensional manifold. Given a point q0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories.

Keywords

Manifold Switching Time Optimal Trajectory Regularity Property Independence Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. Sigalotti
    • 1
  1. 1.SISSA-ISASTriesteItaly

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