Displaying similar documents to “A general Hamilton-Jacobi framework for non-linear state-constrained control problems”

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position...

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

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.

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position ....

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

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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.

Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods

Mohsen Mehrali-Varjani, Mostafa Shamsi, Alaeddin Malek (2018)

Kybernetika

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This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for...