Robust PCL Discovery of Data-Driven Mean-Field Game Systems and Control Problems

2021 ◽  
pp. 1-14
Author(s):  
Chun Li ◽  
Yunyun Yang ◽  
Hui Liang ◽  
Boying Wu
Keyword(s):  
Mean Field ◽  
Data Driven ◽  
Control Problems ◽  
Mean Field Game ◽  
Systems And Control ◽  
And Control

scholarly journals Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160214
Author(s):  
Navin Khaneja
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Spin Dynamics ◽  
Resonance Spectroscopy ◽  
Control Problems ◽  
State Variables ◽  
Systems And Control ◽  
Time Optimal ◽  
Optimal Efficiency ◽  
And Control

In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue ‘Horizons of cybernetical physics’.

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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