Aperiodically Intermittent Control for Stochastic McKean–Vlasov Equations with Markovian Switching

To address the challenge of effectively stabilizing inherently unstable hybrid stochastic McKean–Vlasov equations (HMVSDEs) while simultaneously minimizing control costs, this paper proposes a novel control strategy termed aperiodically intermittent control (AIC). Under the global Lipschitz condition, we first establish the existence and uniqueness theorem for the solutions to HMVSDEs. Subsequently, we derive a generalized Ito^ formula for HMVSDEs, based on which we construct a Lyapunov functional that explicitly incorporates both the law (distribution) of the solution and the underlying Markovian switching process. By employing the Lyapunov functional method, we rigorously construct AIC for the unstable HMVSDEs and analyze the mean-square exponential stability of the controlled system. Furthermore, we demonstrate the applicability of the proposed AIC strategy through a mean-field stochastic Cohen–Grossberg–Hopfield neural network model. Finally, a numerical example is provided to illustrate the effectiveness and practical feasibility of the developed control approach.