First and Second Order Necessary Optimality Conditions for Discrete Optimal Control Problems
Boban Marinković (2006)
The Yugoslav Journal of Operations Research
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Displaying similar documents to “Regularity along optimal trajectories of the value function of a Mayer problem”
First and Second Order Necessary Optimality Conditions for Discrete Optimal Control Problems
Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control
Mustapha Serhani, Nadia Raïssi (2009)
RAIRO - Operations Research
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In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential,...
Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
Dariusz Idczak, Marek Majewski, Stanisław Walczak (2003)
International Journal of Applied Mathematics and Computer Science
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In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
Monotonicity and differential properties of the value functions in optimal control.
Mirică, Ştefan (2004)
International Journal of Mathematics and Mathematical Sciences
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Regularity along optimal trajectories of the value function of a Mayer problem
Carlo Sinestrari (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.
Nonsmooth optimal regulation and discontinuous stabilization.
Bacciotti, A., Ceragioli, F. (2003)
Abstract and Applied Analysis
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Switchings of optimal controls and the equation ,
Pavol Brunovský, John J. Mallet-Paret (1985)
Časopis pro pěstování matematiky
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On the determination of optimal time horizon in a control problem in natural resource economics.
Kumar, Ramesh C., Naqib, Fadle M. (1995)
International Journal of Mathematics and Mathematical Sciences
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The existence of optimal solutions for infinite horizon optimal control problems
Dean A. Carlson (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The existence of optimal solutions for infinite horizon optimal control problems
Dean A. Carlson (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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An existence theorem for a class of optimal problems with delayed argument.
Tadumadze, T., Gelashvili, K. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Existence of optimal nonanticipating controls in piecewise deterministic control problems
Atle Seierstad (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.