Conjugate points and shocks in nonlinear optimal control

DOI10.1090/S0002-9947-96-01577-2zbMath0924.49016MaRDI QIDQ4896194

Hélène Frankowska, Nathalie Caroff

Publication date: 10 November 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hamilton-Jacobi-Bellman equationnecessary and sufficient conditionsshocksmatrix Riccati differential equationBolza control problemJacobi conjugate points

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (14)

Neighboring extremal optimal control for mechanical systems on Riemannian manifolds ⋮ Semiconcavity of the value function for the Bolza control problem ⋮ Combined homotopy and neighboring extremal optimal control ⋮ Local regularity of the value function in optimal control ⋮ Second-Order Sensitivity Relations and Regularity of the Value Function for Mayer's Problem in Optimal Control ⋮ Conjugate Times and Regularity of the Minimum Time Function with Differential Inclusions ⋮ Pointwise second-order necessary optimality conditions and second-order sensitivity relations in optimal control ⋮ Optimality Conditions (in Pontryagin Form) ⋮ From pointwise to local regularity for solutions of Hamilton-Jacobi equations ⋮ Sufficient conditions for strong local optimality in optimal control problems with \(L_{2}\)-type objectives and control constraints ⋮ Generalizing mutational equations for uniqueness of some nonlocal first-order geometric evolutions ⋮ On singularities of value function for Bolza optimal control problem ⋮ Local regularity of the minimum time function ⋮ JACOBI VECTOR FIELDS FOR LAGRANGIAN SYSTEMS ON ALGEBROIDS

Cites Work

• A modified Hamilton-Jacobi approach in the generalized problem of Bolza
• First and second order sufficient conditions for optimal control and the calculus of variations
• Another Jacobi sufficiency criterion for optimal control with smooth constraints
• The conjugate point condition for smooth control sets
• Hamilton-Jacobi equations and synthesis of nonlinear control processes in Hilbert spaces
• Sufficient conditions for a control to be a strong minimum
• Sufficiency conditions with minimal regularity assumptions
• Riccati differential equations
• Extended Jacobi Sufficiency Criterion for Optimal Control
• Semicontinuous Viscosity Solutions For Hamilton–Jacobi Equations With Convex Hamiltonians
• Sufficient Conditions for the Generalized Problem of Bolza
• Viscosity Solutions of Hamilton-Jacobi Equations
• Necessary Conditions for Optimal Control Problems: Conjugate Points
• Contingent Cones to Reachable Sets of Control Systems
• Coupled Points in the Calculus of Variations and Applications to Periodic Problems
• Some Characterizations of Optimal Trajectories in Control Theory
• Lower Semicontinuous Solutions of Hamilton–Jacobi–Bellman Equations
• Set-valued analysis
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