A contact covariant approach to optimal control with applications to sub-Riemannian geometry

DOI10.1007/s00498-016-0176-3zbMath1350.49022arXiv1509.01628OpenAlexW3098037937WikidataQ59468898 ScholiaQ59468898MaRDI QIDQ329116

Witold Respondek, Michał Jóźwikowski

Publication date: 21 October 2016

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.01628

zbMATH Keywords

optimal controlPontryagin's maximum principlesub-Riemannian geometrycontact geometryabnormal extremalcontact vector field

Mathematics Subject Classification ID

Contact manifolds (general theory) (53D10) Optimality conditions for problems involving ordinary differential equations (49K15) Sub-Riemannian geometry (53C17) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (4)

Why are normal sub-Riemannian extremals locally minimizing? ⋮ Thermodynamics and evolutionary biology through optimal control ⋮ Optimal control, contact dynamics and Herglotz variational problem ⋮ Contact variational integrators

Cites Work

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• Graded contact manifolds and contact Courant algebroids
• Fundamental form and the Cartan tensor of \((2,5)\)-distributions coincide
• Characteristic vector fields of generic distributions of corank 2
• Contact geometry of the Pontryagin maximum principle
• Control theory from the geometric viewpoint.
• On geometry of curves of flags of constant type
• Rigid and abnormal line subdistributions of \(2\)-distributions
• Characterizations of Hamiltonian geodesics in sub-Riemannian geometry
• Remarks on contact and Jacobi geometry
• Time-Varying Vector Fields and Their Flows
• Pontryagin Maximum Principle on Almost Lie Algebroids
• Shortest paths for sub-Riemannian metrics on rank-two distributions
• Orbits of Families of Vector Fields and Integrability of Distributions

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