Model reference adaptive iterative learning control for nonlinear systems using observer design

In this paper, we propose an observer based model reference adaptive iterative learning control (MRAILC) using model reference adaptive control strategy for more general class of uncertain nonlinear systems with non-canonical form and iteration-varying reference trajectories. Due to the system state vector is assumed to be unmeasurable, a state tracking error observer is applied for state tracking error estimation. Based on the state tracking error observer and a mixed time-domain and s-domain technique, a relative degree one output observation error model whose inputs are some uncertain nonlinearities and filtered signals which is derived to solve the relative degree problem caused by the system states are not measurable. Besides, we also apply some auxiliary signals and an averaging filter to transfer the original output observation error to a new formulation so that we can implement the AILC without using differentiators. The filtered fuzzy neural network (filtered-FNN) using the system state estimation vector as the input vector is applied for approximation of the unknown plant nonlinearities. In order to overcome the lumped uncertainties associated with function approximation error and state estimation error, a normalization signal is applied as a bounding function for designing a robust AILC. The stabilization learning component is used to guarantee the boundedness of internal signals. Based on a Lyapunov like analysis, we show that all the adjustable parameters as well as internal signals remain bounded for all iterations and the norm of output tracking error will asymptotically converge to a tunable residual set.