scholarly journals Infinite Horizon Linear Quadratic Overtaking Optimal Control Problems

2021 ◽  
Vol 59 (2) ◽  
pp. 1312-1340
Author(s):  
Jianping Huang ◽  
Jiongmin Yong ◽  
Hua-Cheng Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Infinite Horizon ◽  
Control Problems ◽  
Linear Quadratic

scholarly journals A pseudospectral method for budget-constrained infinite horizon optimal control problems

2021 ◽  
Vol 71 ◽  
pp. 145-154
Author(s):  
Angie Burtchen ◽  
Valeriya Lykina ◽  
Sabine Pickenhain
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Infinite Horizon ◽  
Pseudospectral Method ◽  
Linear Quadratic Regulator ◽  
Approximate Solutions ◽  
Control Problems ◽  
Linear Quadratic ◽  
Weighted Functional Spaces

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example.

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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