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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Tadumadze, T., Gelashvili, K. (2000)
Memoirs on Differential Equations and Mathematical Physics
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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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Dean A. Carlson (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Alessia Marigo, Benedetto Piccoli (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
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.
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.
Kumar, Ramesh C., Naqib, Fadle M. (1995)
International Journal of Mathematics and Mathematical Sciences
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A. Adamski, A. Korytowski, W. Mitkowski (1977)
Applicationes Mathematicae
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Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence...
Edward W. Packel (1988)
Banach Center Publications
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Frisch, Uriel, Sobolevskii, A. (2004)
Journal of Mathematical Sciences (New York)
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Lee, W.R., Wang, S., Teo, K.L. (1999)
Mathematical Problems in Engineering
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