Skip to Main content Skip to Navigation
Journal articles

Singular trajectories of control-affine systems

Abstract : When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the underlying optimal control problem. In this article, we provide characterizations for singular trajectories of control-affine systems. We prove that, under generic assumptions, such trajectories share nice properties, related to computational aspects; more precisely, we show that, for a generic system -- with respect to the Whitney topology --, all nontrivial singular trajectories are of minimal order and of corank one. These results, established both for driftless and for control-affine systems, extend previous results. As a consequence, for generic systems having more than two vector fields, and for a fixed cost, there do not exist minimizing singular trajectories. We also prove that, given a control system satisfying the LARC, singular trajectories are strictly abnormal, generically with respect to the cost. We then show how these results can be used to derive regularity results for the value function and in the theory of Hamilton-Jacobi equations, which in turn have applications for stabilization and motion planning, both from the theoretical and implementation issues.
Document type :
Journal articles
Complete list of metadata

Cited literature [31 references]  Display  Hide  Download
Contributor : Emmanuel Trélat Connect in order to contact the contributor
Submitted on : Tuesday, July 18, 2006 - 6:52:44 PM
Last modification on : Friday, December 3, 2021 - 11:34:08 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 12:15:33 AM



Yacine Chitour, Frédéric Jean, Emmanuel Trélat. Singular trajectories of control-affine systems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (2), pp.1078--1095. ⟨10.1137/060663003⟩. ⟨hal-00086397⟩



Record views


Files downloads