Adaptive Iterative Learning Control For Nonlinear Systems With Time-varying Parametric Uncertainties

Abstract:In the actual project,because of the uncertainties brought by the modeling error and the external interference,in addition the complexity of the nonlinear characteristics,classical control theory often can not be applied directly.At this point, nonlinear systems with uncertainties show their superiorities.Because it can take full advantage of the nonlinear structural characteristics of the system, not only can improve the control performance, and it helps to simplify the controller design.Therefore, more and more people started to pay attention to the control problem for uncertain nonlinear systems.The uncertainties of systems are divided into two categories, one is the structural uncertainties expressed by unknown function, the other one is parametric uncertainties expressed by unknown parameters.In this paper,we use adaptive iterative learning control method to solve the problem for nonlinear systems with parametric uncertainties. We have got some meaningful results:Firstly,for high-order nonlinear systems with parametric uncertainties,an adaptive iterative learning control algorithm based on Lyapunov method is proposed.The parameters reconstructed technique is used to handle with unknown time-invariant and time-varying parameters.The tracking error converges to zero pointwisely on a finite interval by constructing a Lyapunov-like functional when the iteration number approachs to infinity. The approach presented here can deal with variable target trajectory tracking problem and has no special restrictions to the target changes.It is useful to the case of larger changes in the target and overcome the traditional iterative learning control restrictions on the target trajectory.Secondly,for high-order time delay nonlinear systems with nonlinear parametric uncertainties,which contain unknown time-invariant and time-varying parameters,an adaptive iterative learning control algorithm based on Backstepping and Lyapunov method is proposed.The signal replacement mechanism and the parameter separation technique is used to handle with time delay term and parametric uncertainties terms.The tracking error converges to zero pointwisely on a finite interval by constructing a Lyapunov-like functional when the iteration number approachs to infinity.Thirdly, based on the algorithm of the second chapter,we consider uncertain robot system with time-varying unknown interference.A sufficient condition for the convergence of tracking error is given. An example of two degrees rigid manipulator system illustrates the feasibility and effectiveness of the proposed method.