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Linearization of the Hamilton–Jacobi equation
Journal of Mathematical Physics, 1986Through a canonoid transformation the integration for the Hamilton–Jacobi equations is transformed into a two step procedure: the first being a linear problem and the second a quasilinear one. Examples are given.
Espindola, Maria L. +2 more
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2001
We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0.
Walter Dittrich, Martin Reuter
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We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0.
Walter Dittrich, Martin Reuter
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Hamilton–Jacobi–Bellman Equations
2017In 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 +6 more
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2020
Abstract This chapter discusses the motion of particles which are scattered by and fall towards the center of the dipol, the motion of a particle in the Coulomb and the constant electric fields, and a particle inside a smooth elastic ellipsoid.
Gleb L. Kotkin, Valeriy G. Serbo
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Abstract This chapter discusses the motion of particles which are scattered by and fall towards the center of the dipol, the motion of a particle in the Coulomb and the constant electric fields, and a particle inside a smooth elastic ellipsoid.
Gleb L. Kotkin, Valeriy G. Serbo
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Solution of Hamilton Jacobi Bellman equations
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002We 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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Homogenization of Metric Hamilton–Jacobi Equations
Multiscale Modeling & Simulation, 2009In this work we provide a novel approach to homogenization for a class of static Hamilton–Jacobi (HJ) equations, which we call metric HJ equations. We relate the solutions of the HJ equations to the distance function in a corresponding Riemannian or Finslerian metric.
Adam M. Oberman +2 more
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R-separation for the Hamilton?Jacobi equation
Letters in Mathematical Physics, 1982We present a non-trivial example of the occurrence of R-separation for the Hamilton—Jacobi equation on a complex Riemannian manifold. In our example the R-separation functions depends on a free parameter, this gives rise to a one-parameter family of R-separable solutions of the corresponding Helmholtz equation.
Kalnins, E. G., Reid, G. J.
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The Fractional Hamilton-Jacobi-Bellman Equation
Journal of Applied Nonlinear Dynamics, 2017Summary: 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 extension of the solutions of Hamilton–Jacobi equations
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stochastic Hamilton–Jacobi–Bellman Equations
SIAM Journal on Control and Optimization, 1992Summary: 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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