Polynomial Solution of Predictive Optimal Control Problems For Systems in State-Equation Form

2003 ◽  
Vol 125 (3) ◽  
pp. 439-447 ◽  
Author(s):  
M. J. Grimble
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Systems Approach ◽  
Polynomial Solution ◽  
Polynomial Systems ◽  
State Equation ◽  
Current Control ◽  
Control Problems ◽  
Linear Quadratic ◽  
Novel Method

The solution of linear quadratic predictive optimal control problems for systems represented in state-equation form, but using a polynomial systems approach, is considered. A multistep cost-function is used that includes future set-point information. A novel method is introduced for computing the vector of future controls and for solving a simpler optimization problem for the current control.

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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