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
Wendell Helms Fleming, H. Mete Soner. I Deterministic Optimal Control I.1 Introduction The concept of control can be described as the process of influencing the behavior of a dynamical system to achieve a ... Optimal Control Introduction.
Wendell Helms Fleming, H. Mete Soner. I Deterministic Optimal Control I.1 Introduction The concept of control can be described as the process of influencing the behavior of a dynamical system to achieve a ... Optimal Control Introduction.
Page 11
... optimal control u * ( · ) € U ( t , x ) minimizes ( 4.3 ) at every r . Hence to determine the optimal control u * ( t ) , it suffices to analyze ( 4.3 ) with r arbitrarily close to t . Intuitively this yields a simple optimization ...
... optimal control u * ( · ) € U ( t , x ) minimizes ( 4.3 ) at every r . Hence to determine the optimal control u * ( t ) , it suffices to analyze ( 4.3 ) with r arbitrarily close to t . Intuitively this yields a simple optimization ...
Page 51
... optimal control problems considered in Sections 3-7 are of the type formulated during the 1950's by Pontryagin and ... control prob- lem , dynamic programming leads to the Hamilton - Jacobi - Bellman PDE derived in Section 5. In the ...
... optimal control problems considered in Sections 3-7 are of the type formulated during the 1950's by Pontryagin and ... control prob- lem , dynamic programming leads to the Hamilton - Jacobi - Bellman PDE derived in Section 5. In the ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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 C¹(Q calculus of variations Chapter classical solution consider constant convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields