To　address　the　low　accuracy　and　stability　when　applying　classical　control　theory　in　distribution　networks　with　distributed　generation,　a　control　method　involving　flexible　multistate　switches　(FMSs)　is　proposed　in　this　study.　This　approach　is　based　on　an　improved　double-loop　recursive　fuzzy　neural　network　(DRFNN)　sliding　mode,　which　is　intended　to　stably　achieve　multiterminal　power　interaction　and　adaptive　arc　suppression　for　single-phase　ground　faults.　First,　an　improved　DRFNN　sliding　mode　control　(SMC)　method　is　proposed　to　overcome　the　chattering　and　transient　overshoot　inherent　in　the　classical　SMC　and　reduce　the　reliance　on　a　precise　mathematical　model　of　the　control　system.　To　improve　the　robustness　of　the　system,　an　adaptive　parameter-adjustment　strategy　for　the　DRFNN　is　designed,　where　its　dynamic　mapping　capabilities　are　leveraged　to　improve　the　transient　compensation　control.　Additionally,　a　quasi-continuous　secondorder　sliding　mode　controller　with　a　calculus-driven　sliding　mode　surface　is　developed　to　improve　the　current　monitoring　accuracy　and　enhance　the　system　stability.　The　stability　of　the　proposed　method　and　the　convergence　of　the　network　parameters　are　verified　using　the　Lyapunov　theorem.　A　simulation　model　of　the　three-port　FMS　with　its　control　system　is　constructed　in　MATLAB/Simulink.　The　simulation　result　confirms　the　feasibility　and　effectiveness　of　the　proposed　control　strategy　based　on　a　comparative　analysis.