Necessary conditions, controllability and the value function for differential-difference inclusions

DOI10.1016/0362-546X(86)90057-XzbMath0609.49013MaRDI QIDQ3749658

G. G. Watkins, Frank H. Clarke

Publication date: 1986

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

maximum principlevalue functiondifferential-difference inclusionlocal null-controllability

Mathematics Subject Classification ID

Controllability (93B05) Nonsmooth analysis (49J52) Methods involving semicontinuity and convergence; relaxation (49J45) Ordinary differential inclusions (34A60) Control problems for functional-differential equations (34K35) Attainable sets, reachability (93B03) Optimality conditions for problems involving ordinary differential equations (49K15) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

Related Items (14)

Necessary optimality conditions for differential-difference inclusions with state constraints ⋮ On the controllability of convex processes with delay ⋮ Sufficient conditions for optimal control problems with time delay ⋮ Necessary conditions for functional differential inclusions ⋮ Necessary conditions, controllability and the value function for differential-difference inclusions ⋮ State constrained optimal control problems with time delays ⋮ The Maximum Principle for Optimal Control Problems with Time Delays ⋮ Optimality Conditions (in Pontryagin Form) ⋮ New results in the theory of multivalued mappings. II: Analysis and applications ⋮ Second-order necessary conditions for differential-difference inclusion problems ⋮ Optimal Control Problems with Time Delays: Constancy of the Hamiltonian ⋮ Optimal control of difference, differential, and differential-difference inclusions ⋮ Necessary optimality conditions for differential–difference inclusions ⋮ Value function and necessary conditions in optimal control problems for differential-difference inclusions

Cites Work

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• Perturbation theory for abstract optimization problems
• Optimal solutions to differential inclusions
• The Euler-Lagrange differential inclusion
• Admissible relaxation in variational and control problems
• Variational and optimal control problems with delayed argument
• The Maximum Principle for Relaxed Hereditary Differential Systems with Function Space end Condition
• The Value Function in Optimal Control: Sensitivity, Controllability, and Time-Optimality
• Necessary conditions, controllability and the value function for differential-difference inclusions
• The Generalized Gradient of a Marginal Function in Mathematical Programming
• The Erdmann Condition and Hamiltonian Inclusions in Optimal Control and the Calculus of Variations
• Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming
• On Some Extremal Problems in the Theory of Differential Equations with Applications to the Theory of Optimal Control
• Optimal Control and the True Hamiltonian
• Application of abstract variational theory to hereditary systems--A survey
• Variational Problems Involving Functional Differential Equations
• On the Controllability of Delay-Differential Systems
• Controllability, Observability and Optimal Feedback Control of Affine Hereditary Differential Systems
• Control of Functional Differential Equations of Retarded and Neutral Type to Target Sets in Function Space

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