Displaying similar documents to “Discrete dynamic programming and viscosity solutions of the Bellman equation”

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.

A method for constructing ε-value functions for the Bolza problem of optimal control

Jan Pustelnik (2005)

International Journal of Applied Mathematics and Computer Science

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The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function. ...

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...

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Fabio Bagagiolo (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

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...

An algorithm for construction of ε-value functions for the Bolza control problem

Edyta Jacewicz (2001)

International Journal of Applied Mathematics and Computer Science

Similarity:

The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm....