A maximum principle for an optimal control problem with integral constraints

DOI10.1007/BF00935608zbMath0255.49016MaRDI QIDQ2558668

V. L. Bakke

Publication date: 1974

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

maximum principlemultiplier ruletransversality conditionsVolterra equationsFredholm equations

Mathematics Subject Classification ID

Fredholm integral equations (45B05) Volterra integral equations (45D05) Optimality conditions for problems involving relations other than differential equations (49K21)

Related Items (22)

Necessary conditions for optimal terminal time control problems governed by a Volterra integral equation ⋮ Maximum principle for Volterra integral equations with controlled delay time ⋮ Derived sets for weak multiobjective optimization problems with state and control variables ⋮ Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach ⋮ First- and second-order optimality conditions for optimal control problems of state constrained integral equations ⋮ Necessary conditions for a weak minimum in a general optimal control problem with integral equations on a variable time interval ⋮ A new direct method for solving optimal control problem of nonlinear Volterra-Fredholm integral equation via the Müntz-Legendre polynomials ⋮ Optimal control of state constrained integral equations ⋮ Optimal control problem governed by a highly nonlinear singular Volterra equation: Existence of solutions and maximum principle ⋮ Anwendungen des Maximumprinzips im Operations Research. I ⋮ Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations ⋮ Optimal control of Volterra equations with impulses ⋮ Boundary arcs for integral equations ⋮ Optimal fields for integral equations ⋮ Optimal control of nonlinear Fredholm integral equations ⋮ An embedding theorem for integral equations ⋮ Optimal control of a class of systems with continuous lags: Dynamic programming approach and economic interpretations ⋮ Optimal dynamic advertising policies for hereditary processes ⋮ APPROXIMATION OF THE SECTIONS OF THE SET OF TRAJECTORIES OF THE CONTROL SYSTEM DESCRIBED BY A NONLINEAR VOLTERRA INTEGRAL EQUATION ⋮ On the \(p\)-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation ⋮ Necessary conditions for a weak minimum in optimal control problems with integral equations on a variable time interval ⋮ A consequence of necessary conditions for optimal control problems involving differential equations with delays

Cites Work

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• A Lagrange multiplier rule in Hilbert space
• Relaxed controls for functional equations
• Optimal Controls for Systems with Time Lag
• Optimal Control of Processes Described by Integral Equations. I
• Unilateral and Minimax Control Problems Defined by Integral Equations
• Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov

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