Abstract
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 $H_{\infty }$ 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.
Highlights
Research on robust and/or adaptive control algorithms for stochastic systems has become an interesting area in the theory of control
The above factors have a large influence on the air-fuel ratio control performance of gas engines, and the proposed robust adaptive control design technology of stochastic discrete-time nonlinear systems with Markovian jumping parameters and unknown system parameters is a suitable approach to solving the problem
Remark 1: The computation process of the adaptive disturbance attenuation air-fuel ratio controller (37) is the same as the one of the robust adaptive control algorithm (13), i.e., (37) can be calculated by replacing the multi-dimensional variables in system (13) by the corresponding one-dimension variables of the gas engine intended as an electric vehicle extender because system (27) is the typical form of system (1)
Summary
Research on robust and/or adaptive control algorithms for stochastic systems has become an interesting area in the theory of control. The robust adaptive air-fuel ratio control problem of a gas engine intended as an electric vehicle extender is a practical application of the proposed robust adaptive control problem of stochastic discrete-time nonlinear systems with Markovian jumping parameters and unknown system parameters. The above factors have a large influence on the air-fuel ratio control performance of gas engines, and the proposed robust adaptive control design technology of stochastic discrete-time nonlinear systems with Markovian jumping parameters and unknown system parameters is a suitable approach to solving the problem. Based on the results of [13] and [33], the robust adaptive controller, the adaptive law and the sufficient conditions of the stochastic nonlinear discrete-time systems with Markovian jumping parameters and unknown system parameters are given in this paper by solving a discrete-time Lyapunov function.
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