Inverse optimal stabilization for more general high-order stochastic nonlinear systems

This paper aims to relax the results in [1] from the following two aspects: completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions. Based on the ideas of the homogeneous systems theory and the adding a power integrator technique, this paper investigates the state-feedback inverse optimal stabilization for a class of high-order stochastic nonlinear systems. The state-feedback stabilizing controller designed can ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable (GAS) in probability and the problem of inverse optimal stabilization (IOS) in probability is solved with respect to meaningful cost functionals. The efficiency of the state-feedback controller is demonstrated by a simulation example.