A primal-dual method for linear-quadratic gaussian control problems with quadratic constraints

1986 ◽  
Vol 7 (3) ◽  
pp. 305-314 ◽  
Author(s):  
H. T. Toivonen
Keyword(s):  
Dual Method ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Quadratic Constraints ◽  
Primal Dual

scholarly journals Route Planning: B

2021 ◽  
pp. 259-269
Author(s):  
Jean Walrand
Keyword(s):  
Route Planning ◽  
The State ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Certainty Equivalence ◽  
Markov Decision Problems ◽  
Markov Decision ◽  
The Cost ◽  
Elegant Solution

AbstractThere is a class of control problems that admit a particularly elegant solution: the linear quadratic Gaussian (LQG) problems. In these problems, the state dynamics and observations are linear, the cost is quadratic, and the noise is Gaussian. Section 14.1 explains the theory of LQG problems when one observes the state. Section 14.2 discusses the situation when the observations are noisy and shows the remarkable certainty equivalence property of the solution. Section 14.3 explains how noisy observations affect Markov decision problems.

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.

Sign in / Sign up

Export Citation Format

Share Document