Team Optimal Control of Coupled Subsystems with MeanField Sharing
Abstract
We investigate team optimal control of stochastic subsystems that are weakly coupled in dynamics (through the meanfield of the system) and are arbitrary coupled in the cost. The controller of each subsystem observes its local state and the meanfield of the state of all subsystems. The system has a nonclassical information structure. Exploiting the symmetry of the problem, we identify an information state and use that to obtain a dynamic programming decomposition. This dynamic program determines a globally optimal strategy for all controllers. Our solution approach works for arbitrary number of controllers and generalizes to the setup when the meanfield is observed with noise. The size of the information state is timeinvariant; thus, the results generalize to the infinitehorizon control setups as well. In addition, when the meanfield is observed without noise, the size of the corresponding information state increases polynomially (rather than exponentially) with the number of controllers which allows us to solve problems with moderate number of controllers. We illustrate our approach by an example motivated by smart grids that consists of $100$ coupled subsystems.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.01418
 arXiv:
 arXiv:2012.01418
 Bibcode:
 2020arXiv201201418A
 Keywords:

 Mathematics  Optimization and Control
 EPrint:
 Proceedings of IEEE Conference on Decision and Control, 2014