On the curvature of two-dimensional optimal control systems and Zermelo's navigation problem

DOI10.1007/s10958-006-0153-3zbMath1244.93070OpenAlexW1967914268WikidataQ124866392 ScholiaQ124866392MaRDI QIDQ443181

Ulysse Serres

Publication date: 6 August 2012

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-006-0153-3

zbMATH Keywords

Zermelo's navigation problemoptimal control system

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Sub-Riemannian geometry (53C17) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items

On Zermelo-like problems: Gauss-Bonnet inequality and E. Hopf theorem ⋮ Coverage maximization with autonomous agents in fast flow environments ⋮ Time-optimal control of a self-propelled particle in a spatiotemporal flow field ⋮ On curvature and feedback classification of two-dimensional optimal control systems ⋮ Optimal partitioning for spatiotemporal coverage in a drift field

Cites Work

• Control theory from the geometric viewpoint.
• Feedback-invariant optimal control theory and differential geometry. I: Regular extremals
• THE EXPONENTIAL REPRESENTATION OF FLOWS AND THE CHRONOLOGICAL CALCULUS
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