Sampled-data Iterative Learning Control For Continuous-time Nonlinear Systems With Iteration Varying Lengths

Iterative Learning Control(ILC)can use the control and tracking information of previous iterations to generate the control signals for the current iteration.In this case,the tracking performance can be gradually improved as the number of iteration increases.Because the control method needs to use the learning experience of history to modify the control input signals,it is necessary to be able to run repeatedly for the controlled objects.However,in many practical applications,there is no guarantee of strict repeatability(such as initial state of each iteration may not be identical),thus the application of iterative learning control in practical systems is limited.In order to relax the constraint conditions of uniform iteration length in iterative learning control,this paper mainly does the following works:1.The first part addresses the problem of sampled-data iterative learning control for continuous-time nonlinear systems with iterative varying lengths and the relative degree of system is 1.To deal with the iteration varying lengths,a P-type sampled-data ILC method with a modified tracking error is proposed.Moreover,a sufficient condition is derived to guarantee the convergence of the nonlinear system at each sampling instant.Additionally,the convergence of the ILC algorithm is discussed in two cases:the identical initialization condition and the bounded initialization.Simulation results show that the proposed algorithm is effective.2.The second part addresses the problem of sampled-data iterative learning control for continuous-time nonlinear systems with iterative varying lengths and higher relative degree.To deal with the iteration varying lengths,2 PD-type sampled-data ILC methods with a modified tracking error are proposed.One is based on the traditional PD-type sampled-data ILC,the other is based on the iteratively moving average operator PD-type sampled-data ILC.Moreover,Sufficient conditions are derived guarantee the convergence of the nonlinear system at each sampling instant.Additionally,the convergence of the ILC algorithm is discussed in two cases:the identical initialization condition and the bounded initialization.Simulation results show that two proposed algorithms are effective.3.The third part is a simulation experiment of biped walking robot,and the simulation experiment carries out to verify the effectiveness of the P-type sampled-data ILC algorithm with a modified tracking error.