Geometry of neighborhoods of singular trajectories in problems with multidimensional control

DOI10.1134/S0081543812040062zbMath1309.49021OpenAlexW1968813919MaRDI QIDQ742248

M. I. Zelikin, L. V. Lokutsievskiy, Roland Hildebrand

Publication date: 18 September 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543812040062

zbMATH Keywords

optimal control problemsmultidimensional controljunctions of optimal trajectoriessingular trajectories

Mathematics Subject Classification ID

Optimality conditions for problems involving ordinary differential equations (49K15) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (7)

Fractal theory of Saturn's ring ⋮ On an optimal flow in a class of nilpotent convex problems ⋮ Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems ⋮ Galois theory, the classification of finite simple groups and a dense winding of a torus ⋮ Fuller Singularities for Generic Control-Affine Systems with an Even Number of Controls ⋮ Typicality of chaotic fractal behavior of integral vortices in Hamiltonian systems with discontinuous right hand side ⋮ Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities

Cites Work

• Unnamed Item
• Theory of chattering control with applications to astronautics, robotics, economics, and engineering
• Optimal probabilistic search
• Definitions of Order and Junction Conditions in Singular Optimal Control Problems
• The High Order Maximal Principle and Its Application to Singular Extremals
• The Second Variation for the Singular Bolza Problem

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