Considering　the　distributed　controllers,　this　paper　studies　the　optimal　control　law　for　the　wireless　sensor　and　actuator　network　(WSAN)　with　stochastic　network-induced　delays.　First,　the　structure　of　the　WSAN　including　multiple　controllers　is　presented,　and　the　network　stochastic　properties　such　as　the　network　delay　and　plant　noise　are　analyzed.　Then,　the　optimization　problem　to　minimize　the　total　cost　in　order　to　keep　the　system　stability　is　formulated,　and　the　optimal　state　estimation　control　strategy　is　derived　using　the　Kalman　filter　approach　and　the　non-cooperative　game.　Finally,　the　proposed　algorithm　is　validated　by　the　simulation　experiments　of　a　stable　control　system　and　the　load　frequency　control　system.　©　2018　IEEE.