Exact Controllability for Mean-Field Type Linear Game-Based Control Systems
Optimization and Control
2023-03-01 v2
Abstract
Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system (MF-GBCS, for short) generated by a linear-quadratic (LQ, for short) Nash game. A Gram-type criterion for the general timevarying coefficients case and a Kalman-type criterion for the special time-invariant coefficients case are obtained. At the same time, the equivalence between the exact controllability of this MF-GBCS and the exact observability of a dual system is established. Moreover, an admissible control that can steer the state from any initial vector to any terminal random variable is constructed in closed form.
Keywords
Cite
@article{arxiv.2302.03404,
title = {Exact Controllability for Mean-Field Type Linear Game-Based Control Systems},
author = {Cui Chen and Zhiyong Yu},
journal= {arXiv preprint arXiv:2302.03404},
year = {2023}
}