Decentralised stabilisation of a class of large-scale high-order stochastic non-linear systems

For a class of large-scale high-order stochastic non-linear systems which are neither necessarily feedback linearisable nor affine in the control input, this study investigates the decentralised stabilisation for the first time. Under some moderate assumptions, smooth decentralised state-feedback controllers are designed, which ensure that the closed-loop system has an almost surely unique solution on [0, infinity), the equilibrium at the origin of the closed-loop system is globally asymptotically stable (GAS) in probability, the states can be regulated to the origin almost surely, and the problem of inverse optimal stabilisation (IOS) in probability is solved. The efficiency of the control scheme is demonstrated by a simulation example.