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
... cost function ) which depends on the control inputs to the system , then the problem is one of optimal control . In ... cost functional to be optimized takes the form ( 3.4 ) . During the 1950's and 1960's aerospace engineering ...
... cost function ) which depends on the control inputs to the system , then the problem is one of optimal control . In ... cost functional to be optimized takes the form ( 3.4 ) . During the 1950's and 1960's aerospace engineering ...
Page 6
... cost function and the terminal cost function . B. Control until exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s E [ t , T ) , where 7 ...
... cost function and the terminal cost function . B. Control until exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s E [ t , T ) , where 7 ...
Page 55
... function of an opti- mal control problem with a state constraint . Since there is no need for the boundary cost function , the boundary value of the value function is not a priori known . Also at the boundary of the state space , the ...
... function of an opti- mal control problem with a state constraint . Since there is no need for the boundary cost function , the boundary value of the value function is not a priori known . Also at the boundary of the state space , the ...
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