Adaptive Iterstive Learning Control For Uncertain Nonlinear Systems And Its Application

In practical engineering,because of the nonlinear characteristics of the physical system itself,the control system also inevitably shows some nonlinear behavior,so the control research for uncertain nonlinear system is particularly important.The primary focus of this paper is to provide a solution for the tracking control problem of three categories of uncertain nonlinear systems in a finite time,implemented through the exploration and formulation of relevant adaptive iterative learning control strategies.The main research contents of the paper are outlined as follows:(1)An adaptive Iterative learning control method is proposed for a class of nonlinear strict feedback systems with unknown time-varying parameters.The method uses Fourier series expansion to handle the unknown time-varying parameter terms in the system,introduces a first-order command filter and an error compensation mechanism for second-order and higherorder systems to prevent the computing inflation caused by virtual control laws and continuous differentiation of output variables,and uses a convergent series sequence to handle the truncation error produced by Fourier series expansion.With the use of the Lyapunov stability theorem,it has been proven that the suggested methodology can secure all signals within closed-loop systems of this type to remain finite over a specific time interval[0,T],while preserving accurate tracking of the system output along its desired trajectory.The practicality and efficacy of the approach are subsequently confirmed through its application in MATLAB simulation.In addition,a special case of unknown time-varying parameter nonlinear system,unknown constant parameter nonlinear system tracking control,is analyzed and designed by adaptive iterative learning control method.Aircraft track angle system tracking control is used as an example for the design analysis.Finally,the effectiveness of the designed adaptive iterative learning control method applied to the aircraft track angle system is verified through simulation,successfully achieving the goal of high-precision tracking of the ideal trajectory within a finite time[0,T]through controlling the flight path angle with the deflection angle of the control surface.(2)An adaptive iterative learning control method has been proposed,which is suitable for a particular class of nonlinear strict feedback systems featuring structural uncertainties.The approach employs RBF neural network functions or fuzzy logic systems to provide an approximation of the unknown structural functions within the system.Instruction filter processing is also introduced into the control law design for higher-order systems.Through the utilization of the Lyapunov theorem,it is determined that the proposed approach can ensure all signals within closed-loop systems of this nature to be bounded within a finite time[0,T].Additionally,the system output can effectively track the desired output with high precision.And the method was applied to the aircraft trajectory angle tracking system.At the same time,a comparative analysis was conducted on the simulation results with and without adding filters in the design of the method.It was found that the addition of instruction filters would be a powerful auxiliary tool in designing controllers for higher order systems.Overall,the simulation example serves as validation of the aircraft trajectory angle system’s tracking control method effectiveness.(3)A specific method has been suggested for adaptive iterative learning control,designed specifically to address a category of nonlinear strict feedback systems.These systems possess both time-varying parameters and structural uncertainties.The method can simultaneously handle these two types of uncertain control problems,using Fourier series expansion to handle the unknown time-varying parameter terms in the system and approximating the uncertain part of the system using an RBF neural network function.Whether it is Fourier series expansion or RBF neural network function approximation,corresponding error signals will be generated.These error signals are analyzed and processed using a convergent series sequence,and the stability of the proposed method is analyzed based on the Lyapunov stability theorem.The tracking control problem of this type of system is achieved within a finite time interval[0,T].Finally,the proposed method’s accuracy and efficiency are authenticated via numerical simulations’results.