TeamOptimal Solution of Finite Number of MeanField Coupled LQG Subsystems
Abstract
A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and perstep cost function are coupled through their meanfield (empirical average). The system has meanfield sharing information structure, i.e., each controller observes the state of its local subsystem (either perfectly or with noise) and the meanfield. It is shown that the optimal control law is unique, linear, and identical across all subsystems. Moreover, the optimal gains are computed by solving two decoupled Riccati equations in the full observation model and by solving an additional filter Riccati equation in the noisy observation model. These Riccati equations do not depend on the number of subsystems. It is also shown that the optimal decentralized performance is the same as the optimal centralized performance. An example, motivated by smart grids, is presented to illustrate the result.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.02052
 arXiv:
 arXiv:2012.02052
 Bibcode:
 2020arXiv201202052A
 Keywords:

 Mathematics  Optimization and Control
 EPrint:
 Proceedings of IEEE Conference on Decision and Control, 2015