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In this paper, the problem of adaptive control with disturbance attenuation is investigated for stochastic discrete-time nonlinear systems with Markovian jumping parameters and unknown system parameters. Using the proposed control law and the sufficient conditions, the closed-loop system achieved H<sub>&#x221E;</sub> performance. As a practical example of the considered problem, an air-fuel ratio controller for a gas engine intended as an electric vehicle extender is designed based on the proposed adaptive disturbance attenuation control algorithm. The air-fuel ratio controller is validated via a numerical simulation under three working conditions. The results of the numerical simulation show that the air-fuel ratio can be regulated into a range around its desired value by the proposed adaptive disturbance attenuation controller and that the adaptive law can be tuned to a steady value. The control performance indices of the proposed adaptive disturbance attenuation controller are smaller than those of the open-loop controller, which means that the proposed adaptive disturbance attenuation controller achieves a greater control effect.

Robust Adaptive Control for Stochastic Discrete-Time Nonlinear Systems and Application to Gas Engine as an Electric Vehicle Extender