Stabilization of Stochastic McKean--Vlasov Equations with Feedback Control Based on Discrete-Time State Observation
Hao Wu, Junhao Hu, Shuaibin Gao, Chenggui Yuan
Abstract
In this paper, we study the stability of solutions of stochastic McKean--Vlasov equations via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of the solution is difficult to observe, 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.