Displaying similar documents to “Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities”

The vanishing viscosity method in infinite dimensions

Piermarco Cannarsa, Giuseppe Da Prato (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

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.

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

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.

Viscosity Solutions of the Bellman Equation for Exit Time Optimal Control Problems with Non-Lipschitz Dynamics

Michael Malisoff (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the Bellman equation for undiscounted exit time optimal control problems with fully nonlinear Lagrangians and fully nonlinear dynamics using the dynamic programming approach. We allow problems whose non-Lipschitz dynamics admit more than one solution trajectory for some choices of open loop controls and initial positions. We prove a uniqueness theorem which characterizes the value functions of these problems as the unique viscosity solutions of the corresponding Bellman equations...

A pension fund in the accumulation phase: a stochastic control approach

Salvatore Federico (2008)

Banach Center Publications

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In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund in the accumulation phase. The level of wealth is constrained to stay above a "solvency level". The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach....

A general Hamilton-Jacobi framework for non-linear state-constrained control problems

Albert Altarovici, Olivier Bokanowski, Hasnaa Zidani (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can...

The vanishing viscosity method in infinite dimensions

Piermarco Cannarsa, Giuseppe Da Prato (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

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.