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Viscosity solutions of Bellman equations
2020The value function of a control problem does not satisfy, in general, the corresponding Bellman equation in the classical sense. In this chapter we show that under rather general conditions it is a unique viscosity solution of the equation, the concept introduced and developed by Crandall and Lions [21].
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Nonlinear potentials for Hamilton-Jacobi-Bellman equations
Acta Applicandae Mathematicae, 1993An approach is proposed, which makes it possible to construct viscosity solutions and to analyze their regularity properties for general Hamilton-Jacobi-Bellman type equations using only information on the corresponding linear equations and their solutions. This approach is a generalization of \textit{N. V.
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Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1993The value function of Mayer's problem arising in optimal control is investigated. Lower semicontinuous solutions of the associated Hamilton- Jacobi-Bellman equation (HJB) \[ -{\partial V \over \partial t} (t,x)+H \left( t,x,- {\partial V\over \partial t} (t,x) \right)=0, \quad V (T,\cdot) = g(\cdot) \text{ on Dom} (V).
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A feedback optimal control by Hamilton-Jacobi-Bellman equation
European Journal of Control, 2017Jinghao Zhu
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Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation
, 2018Seyed Ali Rakhshan +2 more
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IEEE/RJS International Conference on Intelligent RObots and Systems, 2016
Elis Stefansson, Yoke Peng Leong
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Elis Stefansson, Yoke Peng Leong
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Hamilton-Jacobi-Bellman Equations and Optimal Control
1998The aim of this paper is to offer a quick overview of some applications of the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations connected to nonlinear optimal control problems.
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A Risk-Averse Analog of the Hamilton-Jacobi-Bellman Equation
SIAM Conf. on Control and its Applications, 2015A. Ruszczynski, Jianing Yao
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