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 270
... control problem with state dynamics dx = u ( s ) ds + εdw ( s ) , control constraint | u ( s ) | ≤ R , and cost criterion IV ( 11.2 ) with L as in ( 6.14 ) . By ( 6.11c , d ) , L and satisfy I ( 9.2 ) . Theorem IV.11.1 and Remark IV ...
... control problem with state dynamics dx = u ( s ) ds + εdw ( s ) , control constraint | u ( s ) | ≤ R , and cost criterion IV ( 11.2 ) with L as in ( 6.14 ) . By ( 6.11c , d ) , L and satisfy I ( 9.2 ) . Theorem IV.11.1 and Remark IV ...
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 ...
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