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HamiltonJacobiBellman equations for Quantum Filtering and Control
, 2005
"... We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding HamiltonJacobiBellman equations using the elementary arguments of classical contr ..."
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Cited by 9 (3 self)
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We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding HamiltonJacobiBellman equations using the elementary arguments of classical
OPTIMAL SOARING WITH HAMILTONJACOBIBELLMAN EQUATIONS
"... Competition glider flying, like other outdoor sports, is a game of stochastic optimization, in which mathematics and quantitative strategies have historically played an important role. We address the problem of uncertain future atmospheric conditions by constructing a nonlinear HamiltonJacobiBellm ..."
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Cited by 2 (0 self)
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Competition glider flying, like other outdoor sports, is a game of stochastic optimization, in which mathematics and quantitative strategies have historically played an important role. We address the problem of uncertain future atmospheric conditions by constructing a nonlinear HamiltonJacobiBellman
Dynamic Programming and the HamiltonJacobiBellman Equation
"... In this chapter we turn our attention away from the derivation of necessary and sufficient conditions that can be used to find the optimal time paths of the state, costate, and control variables, and focus on the optimal value function more closely. In particular, we will derive the fundamental fi ..."
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mental firstorder partial differential equation obeyed by the optimal value function, known as the HamiltonJacobiBellman equation. This shift in our attention, moreover, will lead us to a different form for the optimal value of the control vector, namely the feedback or closedloop form of the control
Finite Element Methods with Artificial Diffusion for HamiltonJacobiBellman Equations
, 2013
"... In this short note we investigate the numerical performance of the method of artificial diffusion for secondorder fully nonlinear HamiltonJacobiBellman equations. The method was proposed in (M. Jensen and I. Smears, arXiv:1111.5423); where a framework of finite element methods for HamiltonJacobi ..."
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Cited by 1 (0 self)
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In this short note we investigate the numerical performance of the method of artificial diffusion for secondorder fully nonlinear HamiltonJacobiBellman equations. The method was proposed in (M. Jensen and I. Smears, arXiv:1111.5423); where a framework of finite element methods for HamiltonJacobiBellman
Numerically Efficient Approximations to the HamiltonJacobiBellman Equation
, 1998
"... In this paper we present an implementation of the Successive Galerkin Approximation (SGA) algorithm to the HamiltonJacobiBellman (HJB) equation which is less sensitive to Bellman's curse of dimensionality. The SGA algorithm takes an arbitrary stabilizing control law and improves the performan ..."
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Cited by 4 (3 self)
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In this paper we present an implementation of the Successive Galerkin Approximation (SGA) algorithm to the HamiltonJacobiBellman (HJB) equation which is less sensitive to Bellman's curse of dimensionality. The SGA algorithm takes an arbitrary stabilizing control law and improves
Verification Theorems for HamiltonJacobiBellman equations
, 2002
"... We study an optimal control problem in Bolza form and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a HamiltonJacobiBellman inequality outside a countably H n ..."
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Cited by 1 (1 self)
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We study an optimal control problem in Bolza form and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a HamiltonJacobiBellman inequality outside a countably H n
Homogenization of random Hamilton–Jacobi–Bellman Equations
"... ABSTRACT. We consider nonlinear parabolic equations of Hamilton–Jacobi– Bellman type. The Lagrangian is assumed to be convex, but with a spatial dependence which is stationary and random. Rescaling in space and time produces a similar equation with a rapidly varying spatial dependence and a small vi ..."
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ABSTRACT. We consider nonlinear parabolic equations of Hamilton–Jacobi– Bellman type. The Lagrangian is assumed to be convex, but with a spatial dependence which is stationary and random. Rescaling in space and time produces a similar equation with a rapidly varying spatial dependence and a small
HamiltonJacobiBellman equations in dimension 1
"... L 1error estimates for numerical approximations of ..."
HamiltonJacobiBellman Equation of an Optimal Consumption Problem
, 2009
"... Xc,pit is the wealth with the consumption policy (c, pi). pit is a trading strategy, ctX c,pi t is the rate of consumption. ..."
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Xc,pit is the wealth with the consumption policy (c, pi). pit is a trading strategy, ctX c,pi t is the rate of consumption.
Results 1  10
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1,662