Summary Antidisturbance control problem is discussed for stochastic systems with multiple heterogeneous disturbances, which include the white noise and the disturbance with unknown frequencies and amplitudes. An adaptive disturbance observer is designed to estimate the disturbance with unknown frequencies and amplitudes, based on which, an adaptive disturbance observer‐based control scheme is proposed by combining adaptive technique and linear matrix inequality method. It is proved that the closed‐loop system is asymptotically bounded in mean square when multiple heterogeneous disturbances exist simultaneously and that the equilibrium is globally asymptotically stable in probability as additive disturbance disappears. Finally, two simulation examples, including a wind turbine system, are given to show the effectiveness of the proposed scheme.

In engineering, there exist lots of nonlinear disturbance dynamics, which can be described by nonlinear exogenous systems. The current stochastic linear disturbance observer is conservative and is not applicable for nonlinear disturbance dynamics. This paper studies a class of stochastic systems with multiple disturbances, including white noise and disturbances modelled by a nonlinear exogenous system. To estimate the disturbance with nonlinear dynamics, a stochastic nonlinear disturbance observer is proposed. Based on the observer, a nonlinear disturbance observer-based disturbance attenuation control (NDOBDAC) scheme is constructed such that the composite closed-loop system is asymptotically mean-square bounded. According to the simulation example, the state responses of the system diverge in the absence of control, but it tends to be ± 0 . 01 under NDOBDAC, which demonstrates the effectiveness of the proposed scheme. In addition, the anti-disturbance control accuracy of NDOBDAC approximately improves 60 ~ 200 times compared with H ∞ control and active disturbance rejection control (ADRC). The simulation results demonstrate the feasibility and effectiveness of the proposed scheme.

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Summary In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.