An observer-based model reference adaptive iterative learning controller for MIMO nonlinear systems

TIn this paper, an observer based model reference adaptive iterative learning control (MRAILC) is proposed for a general class of uncertain MIMO nonlinear systems. Since the system state vector is assumed to be not measurable, a state tracking error observer is introduced for state estimation. Based on the proposed observer, we apply a model reference adaptive control technique to derive an output observation error model. In order to implement the MRAILC without using differentiators, the output observation error model will be further transformed into a new formulation by an averaging filter matrix and some auxiliary signals vector. There are three components in this MRAILC. The main learning component which performs as a nonlinear function approximator is constructed by an MIMO filtered fuzzy neural network using the system state estimation vector as the input vector. To overcome the lumped uncertainties vector from function approximation error vector and state estimation error vector, a normalization signal is applied as a bounding function to design a robust learning component. Finally, a stabilization learning component is used to guarantee the boundedness of internal signals. By using Lyapunov-like analysis, we show that all the adjustable parameters as well as internal signals remain bounded for all iterations. The norm of output tracking error vector will asymptotically converge to a tunable residual set.