Stabilization Control for Stochastic High-order Fully-actuated Systems with Persistent Disturbances

Following the high-order fully actuated (HOFA) systems proposed by Prof. GR Duan, stochastic high-order fully actuated (SHOFA) systems were also developed to consider the stochastic disturbances. However, existing studies require that disturbances disappear at the equilibrium point, which limits the applicability of the method. This paper proposes a novel control scheme to stabilize the SHOFA systems with persistent disturbances. The characterization of SHOFA systems is analyzed utilizing the concepts of probabilistic ultimate bounds and probabilistic invariant sets. Therefore, the quantitative control indices in probability are available under general probability distributions. Finally, the effectiveness of the proposed control strategy is verified in the simulation.