Second order optimality conditions for optimal control problems on Riemannian manifolds

DOI10.1051/cocv/2018028zbMath1444.49012arXiv1508.06175OpenAlexW2802652258WikidataQ115334431 ScholiaQ115334431MaRDI QIDQ5107939

Zhang, X., Qing Cui, Li Deng

Publication date: 29 April 2020

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06175

zbMATH Keywords

optimal controlcurvature tensorRiemannian manifoldsecond order necessary and sufficient conditions

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Control/observation systems governed by ordinary differential equations (93C15) Optimality conditions for problems in abstract spaces (49K27) Applications of variational problems to control theory (58E25) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30) Manifolds and measure-geometric topics (49Q99)

Related Items (2)

Second order necessary conditions for endpoints-constrained optimal control problems on Riemannian manifolds ⋮ Second-Order Necessary Conditions for Optimal Control Problems with Endpoints-Constraints and Convex Control-Constraints

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric optimal control. Theory, methods and examples
• Pointwise second-order necessary conditions for optimal control problems evolved on Riemannian manifolds
• Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure
• Dynamic programming principle of control systems on manifolds and its relations to maximum principle
• Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
• Higher order necessary conditions in optimal control theory
• Singular optimal control problems
• A second-order condition that strengthens Pontryagin's maximum principle
• Singular optimal control: The linearquadratic problem
• Optimal syntheses for control systems on 2-D manifolds
• Second-order sufficient conditions for state-constrained optimal control problems
• Singular trajectories and their role in control theory
• Control theory from the geometric viewpoint.
• Feedback-invariant optimal control theory and differential geometry. I: Regular extremals
• Pointwise Second-Order Necessary Optimality Conditions for the Mayer Problem with Control Constraints
• Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints
• Sufficient Optimality Conditions for Optimal Control Subject to State Constraints
• Second order optimality conditions in the smooth case and applications in optimal control
• The High Order Maximal Principle and Its Application to Singular Extremals
• Optimal Control Problems with Set-Valued Control and State Constraints
• Riemannian Geometry
• Variational Approach to Second-Order Sufficient Optimality Conditions in Optimal Control
• The Second Variation for the Singular Bolza Problem
• Necessary Conditions for Singular Extremals Involving Multiple Control Variables
• High Order Necessary Conditions for Optimality
• No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

This page was built for publication: Second order optimality conditions for optimal control problems on Riemannian manifolds