Iterative learning of output feedback stabilising controller for a class of uncertain nonlinear systems with external disturbances

In this paper, an output feedback controller using iterative learning algorithm is proposed for stabilising a class of uncertain nonlinear single-input single-output (SISO) systems with unknown bounded disturbances. By dividing the time interval into equal iteration periods, iterative learning algorithm is integrated into output feedback control and is carried out under alignment condition. Using the output signal, control input and estimates of uncertain parameters, adaptive state observers are established to generate state estimates which will be employed to design the control law. Based on the backstepping technique, the output feedback controller is developed consisting of the ILC part and robust control part. Different from the traditional ILC update laws of uncertain parameters with constant gains, a novel type of parameter update law is developed where the ILC gain is variable and determined by the real-time state estimates such that system stability can be guaranteed. By virtue of the composite energy function, it is proved that all the signals of the closed-loop system are bounded and the output will uniformly converge to zero along the iteration axis, which indicates the stabilisation of the output signal over the time domain. Simulation verification is conducted to apply the proposed controller to a one-degree-of-freedom suspension system to validate the effectiveness of the control scheme.