Data-driven Iterative Learning Control For Distributed Parameter Systems

Data-driven control is a new control method that does not rely on accurate mathematical models.It can effectively utilize the large amounts of data stored in production process to design the controller.Therefore,the calculation pressure is greatly reduced.At the same time,there is no need to change the structure of the controller when the external environment changes.Iterative learning control is known for its precise control,which can achieve complete tracking of the desired target after a limited number of iterations.Data-driven iterative learning control(DDILC)makes full use of the advantages of these two methods,which not only compensates for the deviation caused by the unknown model,but also achieves accurate control under certain conditions.However,most of the researches on data-driven iterative learning control methods in this area are centralized parameter systems.Therefore,this paper studies the distributed parameter system using data-driven iterative learning control methods,which has important practical significance and academic value.The main tasks are as follows:(1)The data-driven control models are established for parabolic distributed parameter systems and hyperbolic distributed parameter systems.The continuous parabolic system is described in Hilbert space to obtain the solution of the system and form a linear map of system from input to output.Considering the essence of data sampling and processing,two kinds of distributed parameter systems are discretized by forward difference scheme to obtain the general form of the system equation.Then,a data-driven control model with only input and output is derived for the system equation by solving and recursing respectively,which lays a foundation for future research.(2)The DDILC algorithm based on neural network is applied to the parabolic distributed parameter system to study the control situation of the system time terminal point.Based on the data-driven control model,the mapping from expected output to expected input is formed by neural network.In order to reduce the system bias caused by the estimation error,an auxiliary error function is defined,and an iterative learning update law with the weight of the auxiliary error function is designed to update the system input.Finally,Lyapunov performance index function and compression mapping principle are used to analyze the error convergence of the system.Numerical simulation of heat conduction system and traffic flow is given.(3)The point-to-point DDILC of the hyperbolic distributed parameter system is studied and extended to the case where the reference trajectory is fully tracked.The points to be tracked in the desired trajectory are determined,and a matrix of tracking information points is set.A radial basis neural network is introduced to form a mapping between the expected output and the expected input to train and learn the input of the system,and a similar iterative learning control law for unknown parameter estimation is designed.Meanwhile,the auxiliary error function is proposed to improve tracking accuracy.From the consideration of stability,the error equation is transformed into an inequality by means of the compression mapping principle to prove the rationality of the algorithm.Finally,the algorithm is extended to complete trajectory tracking and experimental simulation.