Stabilization of stochastic McKean-Vlasov equations with feedback control based on discrete-time state observation
Probability
2021-10-25 v1 Optimization and Control
Abstract
In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of solution is difficult to be observed, we study the corresponding particle system which can be observed for the feedback control. We prove that the exponential stability of control system is equivalent to the the exponential stability of the corresponding particle system. Finally, an example is provided to show the effectiveness of the theory.
Keywords
Cite
@article{arxiv.2110.11544,
title = {Stabilization of stochastic McKean-Vlasov equations with feedback control based on discrete-time state observation},
author = {Hao Wu and Junhao Hu and Shuaibin Gao and Chenggui Yuan},
journal= {arXiv preprint arXiv:2110.11544},
year = {2021}
}