Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |
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Page 1
... problem is one of optimal control . In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ordinary differential equations ...
... problem is one of optimal control . In this introductory chapter we are concerned with deterministic optimal control models in which the dynamics of the system being controlled are governed by a set of ordinary differential equations ...
Page 315
... control problems , in which the displacement of the state due to control effort is differentiable in time , the ... problem in their study of a sim- plified model of spacecraft control . Since then singular control has found many other ...
... control problems , in which the displacement of the state due to control effort is differentiable in time , the ... problem in their study of a sim- plified model of spacecraft control . Since then singular control has found many other ...
Page 362
... control problems were formulated by Bather and Chernoff ( BC1-2 ] . In 1980 Benes , Shepp and Witsenhaussen explicitly solved a one dimensional example by observing that the value function in their example is twice continuously ...
... control problems were formulated by Bather and Chernoff ( BC1-2 ] . In 1980 Benes , Shepp and Witsenhaussen explicitly solved a one dimensional example by observing that the value function in their example is twice continuously ...
Other editions - View all
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |
Common terms and phrases
admissible control assume assumptions boundary condition boundary data bounded c₁ Cą(Q calculus of variations Chapter classical solution consider constant continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields