In this paper, an iterative learning radial basis function neural-networks (RBF NN) control algorithm is developed for a class of unknown multi input multi output (MIMO) nonlinear systems with unknown control directions. The proposed control scheme is very simple in the sense that we use just a P-type iterative learning control (ILC) updating law in which an RBF neural network term is added to approximate the unknown nonlinear function, and an adaptive law for the weights of RBF neural network is proposed. We chose the RBF NN because it has universal approximation capabilities and can approximate any continuous function. In addition, among the advantages of our controller scheme is the fact that it is applicable to deal with a class of nonlinear systems without the need to satisfy the global Lipschitz continuity condition and we assume, only, that the unstructured uncertainty is norm-bounded by an unknown function. Another advantage of the proposed controller and unlike other works on ILC, we do not need any prior knowledge of the control directions for MIMO nonlinear system. Thus, the Nussbaum-type function is used to solve the problem of unknown control directions. In order to prove the asymptotic stability of the closed-loop system, a Lyapunov-like positive definite sequence is used, which is shown to be monotonically decreasing under the control design scheme. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

This article proposes an adaptive iterative learning radial basis function (RBF) scheme to solve the trajectory-tracking problem for perturbed robot manipulators with unknown iteration varying disturbances and unknown dead-zone input. It is well known that the presence of the dead zone in actuators and mechatronics devices gives rise to extra difficulty due to the presence of singularity in the input channels. Hence, it is interesting to take this problem into account when synthesizing a controller. This synthesis is made here. In addition, the control design is very simple in the sense that we use, only, the proportional gain. Therefore, the considerable amount noise caused by the sensors for velocity measurements of robot manipulators is avoided. Another advantage of this work is that the unknown disturbances are assumed to be time varying and also varying from iteration to iteration. Thus, the RBF neural network is used to approximate these unknown nonlinear functions. Using the Lyapunov theory, the analysis of the stability of the closed-loop system is guaranteed when the iteration number tends to infinity. Finally, simulation results on the PUMA 560 arm are provided to illustrate the effectiveness of the proposed method. In order to evaluate the performance of our controller, a comparison of our results with other method is also given. K E Y W O R D SIterative learning control, Radial basis function, Dead-zone, Adaptive, Robot manipulators, Lyapunov theory 1 Indeed, input uncertainties such as dead-zone, saturation, backlash, and hysteresis are kind of nonsmooth and nonaffine in input factor widely existing in actuators and sensors. In fact, in many practical applications, the presence of Int J Robust Nonlinear Control. 2020;30:4075-4094.wileyonlinelibrary.com/journal/rnc

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