scientific article

zbMath1146.22001MaRDI QIDQ3511194

Yuri L. Sachkov

Publication date: 8 July 2008

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

symmetrycontrollabilityhomogeneous spacesLie groupsinvariant systems

Mathematics Subject Classification ID

Controllability (93B05) Research exposition (monographs, survey articles) pertaining to systems and control theory (93-02) Control of mechanical systems (70Q05) Algebraic methods (93B25) Analysis on real and complex Lie groups (22E30) Control/observation systems governed by ordinary differential equations (93C15) Optimality conditions for problems involving ordinary differential equations (49K15) Motion of a rigid body in contact with a solid surface (70E18) Sub-Riemannian geometry (53C17) Harmonic analysis on general compact groups (43A77)

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Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ Control of a mobile robot with a trailer based on nilpotent approximation ⋮ The normal sub-Riemannian geodesic flow on E(2) generated by a left-invariant metric and a right-invariant distribution ⋮ Extremal paths in the nilpotent sub-Riemannian problem on the Engel group (subcritical case of pendulum oscillations) ⋮ Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group \(\mathrm{SOLV}^-\)

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