Optimal control of a class of linear nonautonomous parabolic PDE via two-parameter semigroup representation

2011 ◽  
Author(s):  
James Ng ◽  
Stevan Dubljevic ◽  
Ilyasse Aksikas
Keyword(s):  
Optimal Control ◽  
Parabolic Pde ◽  
Two Parameter

The optimal control of a two-parameter jump process

1986 ◽  
Vol 26 (1) ◽  
pp. 77-87
Author(s):  
Ata Al-Hussaini ◽  
R. J. Elliott
Keyword(s):  
Optimal Control ◽  
Jump Process ◽  
Two Parameter

scholarly journals Viscosity solutions of fully nonlinear functional parabolic PDE

2005 ◽  
Vol 2005 (22) ◽  
pp. 3539-3550
Author(s):  
Liu Wei-an ◽  
Lu Gang
Keyword(s):  
Optimal Control ◽  
Viscosity Solutions ◽  
Parabolic Equations ◽  
Optimal Control Theory ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fully Nonlinear ◽  
Nonlinear Functional ◽  
Parabolic Pde

By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

scholarly journals A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control

2016 ◽  
Vol 13 (05) ◽  
pp. 1650028 ◽  
Author(s):  
Benxue Gong ◽  
Tongjun Sun ◽  
Wanfang Shen ◽  
Wenbin Liu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Galerkin Method ◽  
A Priori ◽  
Galerkin Approximation ◽  
Sufficient Optimality Conditions ◽  
Backward Euler ◽  
Parabolic Pde ◽  
Stochastic Galerkin

A stochastic Galerkin approximation scheme is proposed for an optimal control problem governed by a parabolic PDE with random perturbation in its coefficients. The objective functional is to minimize the expectation of a cost functional, and the deterministic control is of the obstacle constrained type. We obtain the necessary and sufficient optimality conditions and establish a scheme to approximate the optimality system through the discretization with respect to both the spatial space and the probability space by Galerkin method and with respect to time by the backward Euler scheme. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results.

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