Infinite time regular synthesis
B. Piccoli (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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B. Piccoli (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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Alain Rapaport, Pierre Cartigny (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness...
Fabio Bagagiolo (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
Di Marco, Silvia C., González, Roberto L.V. (2003)
International Journal of Mathematics and Mathematical Sciences
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Baten, Md.Azizul (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Janković, Vladimir (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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Joël Blot, Naïla Hayek (2000)
ESAIM: Control, Optimisation and Calculus of Variations
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Fabio Bagagiolo (2004)
ESAIM: Control, Optimisation and Calculus of Variations
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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
Piermarco Cannarsa, Giuseppe Da Prato (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
Cyril Imbert, Régis Monneau, Hasnaa Zidani (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to...