scholarly journals Uncertainty Quantification in Control Problems for Flocking Models

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi ◽  
Mattia Zanella
Keyword(s):  
Optimal Control ◽  
Predictive Control ◽  
Polynomial Chaos ◽  
Point Of View ◽  
Type Model ◽  
Control Problems ◽  
Threshold Effects ◽  
Random Parameters ◽  
Random Inputs ◽  
Generalized Polynomial

The optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC) approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits steering of the system towards the desired state even in unstable regimes.

scholarly journals Optimal control of affine connection control systems from the point of view of Lie algebroids

2014 ◽  
Vol 11 (09) ◽  
pp. 1450038 ◽  
Author(s):  
Lígia Abrunheiro ◽  
Margarida Camarinha
Keyword(s):  
Optimal Control ◽  
Vector Field ◽  
Control Systems ◽  
Lie Groups ◽  
Optimal Control Problems ◽  
Affine Connection ◽  
Point Of View ◽  
Lie Algebroids ◽  
Control Problems ◽  
Hamiltonian Vector Field

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems (OCPs) for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

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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