An ADRC Approach for a Class of Nonlinear Hybrid Stochastic Systems with Fractional Noise

This paper extends the active disturbance rejection control (ADRC) approach to a class of nonlinear hybrid systems with uncertain fractional disturbances and unknown parameters, aiming to investigate the applicability of the ADRC approach in the presence of abrupt state changes and complex noise structures. By employing the fractional Wick–Itô–Skorohod (fWIS) integral, an extended state observer (ESO) together with an ESO-based control strategy is developed. It is shown that the resulting closed-loop hybrid stochastic system achieves mean-square stability under fractional noise. Furthermore, the proposed approach is generalized to enable the observation, tracking, and compensation of white noise disturbances with abrupt changes. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.