Sliding Mode Based Data-driven Adaptive Learning Control Method

This work proposes a sliding mode based model-free adaptive control for non-linear non-affine discrete-time systems,and explores significantly how to design a data-driven adaptive learning control method based on sliding mode for non-affine non-affine repetitive system.Rigorously mathematical analysis and simulation studies verify the effectiveness of the proposed method.The main innovations of this thesis are summarized as follows:First,a linear data model of a general nonlinear non-affine system is established using dynamic linearization techniques.On this basis,a quadratic performance index is designed by introducing the traditional time dynamic sliding mode surface in order to deal with the uncertainties of the system and other factors.Then,a slide-mode based model-free adaptive control(SM-MFAC)scheme is proposed by virtue of the optimal technology.The SM-MFAC includes a learning control law and a parameter adaptation law.The difference of the proposed SM-MFAC from the traditional model-free adaptive control is that the objective function uses sliding mode dynamic surface to replace the traditional single error signal,and thus the proposed control law contains more additional error information from previous time instants,therefore improving control performance.Rigorous analysis and simulation results have been provided to show the effectiveness of the proposed SM-MFAC.Second,a dynamic linear data model between two consecutive iterations is established for nonlinear non-affine discrete-time SISO and MIMO systems to re-express the linear input-output data relationship of the nonlinear system.And the dynamic linear data model is used for the subsequent controller design and analysis.Then,a new iterative sliding mode surface is proposed to replace the traditional time dynamic sliding mode surface,which makes it more suitable for the two-dimensional(time and iterative)dynamic characteristics of the controlled system.Consequently,a sliding-mode based data-driven adaptive ILC method I(SM-DDAILC-I)is proposed by design ane objective function using the iterative sliding-mode dynamic surface to replace the tracking errors.This method is a combined feedforward and feedback mechanism,which contains feedback information with parameter iterative updating law.As a result,SM-DDAILC-I can effectively deal with the problems of initial condition changes and random disturbances and making the control effect better.Strict convergence analysis and simulation studies have proved the effectiveness of the proposed method.Third,a new optimal index function is designed on the basis of the evolution along the iterative direction.Then,a different sliding-mode based data-driven adaptive ILC II(SM-DDAILC-II)is proposed using the iterative sliding mode surface to replace the tracking errors.The proposed SM-DDAILC-II contains a parameter estimation law of the linear data model to adapt to the system uncertainties.Further,the learning law of proposed SM-DDAILC-II is similar to that of the higher-order ILC and can use more error information from the previous iterations to improve the control performance.In addition,the proposed method is also data-driven and can effectively deal with problems such as initial condition changes and random disturbances.Strict theoretical analysis and simulation results verify the effectiveness of the algorithm.