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Solving the Hamilton-Jacobi-Bellman equation for animation.

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Solution of Hamilton Jacobi Bellman equations

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
We present a method for the numerical solution of the Hamilton Jacobi Bellman PDE that arises in an infinite time optimal control problem. The method can be of higher order to reduce "the curse of dimensionality". It proceeds in two stages. First the HJB PDE is solved in a neighborhood of the origin using the power series method of Al'brecht (1961 ...
C. L. Navasca, Arthur J. Krener
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The Fractional Hamilton-Jacobi-Bellman Equation

Journal of Applied Nonlinear Dynamics, 2017
Summary: In this paper we initiate the rigorous analysis of controlled Continuous Time Random Walks (CTRWs) and their scaling limits, which paves the way to the real application of the research on CTRWs, anomalous diffusion and related processes. For the first time the convergence is proved for payoff functions of controlled scaled CTRWs and their ...
Veretennikova, M., Kolokoltsov, V.
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On the geometry of the Hamilton-Jacobi-Bellman equation

Journal of Geometric Mechanics, 2009
We show how a minimal deformation of the geometry of the classical Hamilton-Jacobi equation provides a probabilistic theory whose cornerstone is the Hamilton-Jacobi-Bellman equation. This is the basis for a novel dynamical system approach to Stochastic Analysis.
Jean-Claude Zambrini
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A relaxation scheme for Hamilton–Jacobi–Bellman equations

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuzi Zhou, Zhanyong Zou
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A feedback optimal control by Hamilton–Jacobi–Bellman equation

European Journal of Control, 2017
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Jinghao Zhu
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Hamilton–Jacobi–Bellman Equations

2017
In this chapter we present recent developments in the theory of Hamilton–Jacobi–Bellman (HJB) equations as well as applications. The intention of this chapter is to exhibit novel methods and techniques introduced few years ago in order to solve long-standing questions in nonlinear optimal control theory of Ordinary Differential Equations (ODEs).
Festa, Adriano, Guglielmi, Roberto, Hermosilla, Christopher, Picarelli, Athena, Sahu, Smita, Sassi, Achille, Silva, Francisco J.   +6 more
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Stochastic Hamilton–Jacobi–Bellman Equations

SIAM Journal on Control and Optimization, 1992
Summary: This paper studies the following form of nonlinear stochastic partial differential equation: \[ \begin{multlined} -d\Phi_ t=\inf_{v\in U}\left\{\frac12 \sum_{i,j}[\sigma\sigma^*]_{ij}(x,v,t)\partial_{x_ ix_ j}\Phi_ t(x)+\sum_ i b_ i(x,v,t)\partial_{x_ i}\Phi_ t(x)+L(x,v,t)+\right. \\ \left.+\sum_{i,j}\sigma_{ij}(x,v,t)\partial _{x_ i}\Psi_{j,t}
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A splitting algorithm for Hamilton-Jacobi-Bellman equations

Applied Numerical Mathematics, 1994
The dynamic programming approach to the solution of deterministic optimal control problems gives the characterization of the value function in terms of a partial differential equation of the first order, the Hamilton-Jacobi-Bellman equation. This approach permits to compute controls in feedback form and, as a consequence, approximate optimal ...
FALCONE, Maurizio, P. LANUCARA, SEGHINI, Alessandra   +2 more
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Multigrid Methods for Second Order Hamilton--Jacobi--Bellman and Hamilton--Jacobi--Bellman--Isaacs Equations

SIAM Journal on Scientific Computing, 2013
We propose multigrid methods for solving the discrete algebraic equations arising from the discretization of the second order Hamilton--Jacobi--Bellman (HJB) and Hamilton--Jacobi--Bellman--Isaacs (HJBI) equations. We propose a damped-relaxation method as a smoother for multigrid.
Dong Han, Justin W. L. Wan
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