Uncertain Nonlinear Systems, Adaptive Iterative Learning Control

Uncertain nonlinear systems are widely existed in practice engineering. Controllerdesign can be simplified and control performance can be improved by using the nonlinearcharacteristics fully. Two classes of typical nonlinear systems with uncertain parametersare discussed and adaptive iterative learning control (AILC) approaches are designedaccordingly. Moreover, theoretical analysis, numerical simulations and applicationresearches are given.For a class of nonlinear systems with unknown disturbance or time-varyingparameters, a robust adaptive iterative learning control (RAILC) algorithm is proposed.The unknown parameters are estimated in time-domain and the disturbance is inhibited byrobust control. Feedback control is also introduced to improve the control performance; fora class of nonlinear systems with unknown time-invariant or time-varying parameters, acomposite adaptive iterative learning control (CAILC) algorithm is proposed. Through theanalysis of the structure properties, time-invariant and time-varying parameters areestimated in time-domain and iteration-domain respectively in the algorithm, which makesfull use of the time-domain and the iteration-domain information. Both of the algorithmsare promoted to the second order uncertain nonlinear systems by means of backsteppingtechnology. The convergence analysis of the two approaches under identical initialcondition and alignment condition are carried out based on Lyapunov stability theory. Theeffectiveness of these algorithms is demonstrated by simulations.The applications of the above algorithms in parametric uncertain robot manipulatorswith unknown nonrepeatbal disturbance and in those with unknown repeatbal time-varyingdisturbance are discussed. The dynamic modal of the robot manipulator system is given,and the algorithms are adjusted according to the system properties. The boundedness of allinternal siginals and the convergence along the iteration horizon of output tracking errorare proved. Compared with a traditional AILC, the simulation results show that betterperformance can be obtained with the proposed methods, and the accurate tracking ofdesired trajectory on specified time interval can be achieved.