scholarly journals An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems

2015 ◽  
Vol 37 (2) ◽  
pp. A946-A969
Author(s):  
Jesper Karlsson ◽  
Stig Larsson ◽  
Mattias Sandberg ◽  
Anders Szepessy ◽  
Raúl Tempone
Keyword(s):  
Optimal Control ◽  
Error Estimate ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Euler Approximation

scholarly journals Constants within Error Estimates for Legendre-Galerkin Spectral Approximations of Control-Constrained Optimal Control Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jianwei Zhou
Keyword(s):  
Optimal Control ◽  
Error Estimate ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
One Dimensional ◽  
Error Indicator ◽  
Spectral Approximations ◽  
Explicit Formulae

Explicit formulae of constants within the aposteriorierror estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable. For simpleness, one-dimensional bounded domain is taken. Meanwhile, the corresponding aposteriorierror indicator is established with explicit constants.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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