In this paper, a direct adaptive iterative learning control (DAILC) based on a new output-recurrent fuzzy neural network (ORFNN) is presented for a class of repeatable nonlinear systems with unknown nonlinearities and variable initial resetting errors. In order to overcome the design difficulty due to initial state errors at the beginning of each iteration, a concept of time-varying boundary layer is employed to construct an error equation. The learning controller is then designed by using the given ORFNN to approximate an optimal equivalent controller. Some auxiliary control components are applied to eliminate approximation error and ensure learning convergence. Since the optimal ORFNN parameters for a best approximation are generally unavailable, an adaptive algorithm with projection mechanism is derived to update all the consequent, premise, and recurrent parameters during iteration processes. Only one network is required to design the ORFNN-based DAILC and the plant nonlinearities, especially the nonlinear input gain, are allowed to be totally unknown. Based on a Lyapunov-like analysis, we show that all adjustable parameters and internal signals remain bounded for all iterations. Furthermore, the norm of state tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity. Finally, iterative learning control of two nonlinear systems, inverted pendulum system and Chua's chaotic circuit, are performed to verify the tracking performance of the proposed learning scheme.

Because of its nonlinear discharge characteristics, the residual electric energy of a battery remains to be an open problem. As a result, the reliability of electric scooters or electric vehicles is lacking. To alleviate this problem and enhance the capabilities of present electric scooters or vehicles, we propose a state-of-charge learning system that can provide more accurate information about the state-of-charge or residual capacity when a battery discharges under dynamic conditions. The proposed system is implemented by learning controllers, fuzzy neural networks and cerebellar model articulation controller networks, which can estimate and predict nonlinear characteristics of the energy consumption of a battery. With this learning system, not only could it give an estimate of how much residual battery power is available, but it also could provide users with more useful information such as an estimated traveling distance at a given speed, and the maximum allowable speed to guarantee safety arrival at the destination.

In this paper, we study the design of iterative learning controllers for nonaffine nonlinear interconnected systems with repeatable control tasks. The interaction between each subsystem can be a general type of unknown nonlinear function if a bounding condition is satisfied. An error model is derived such that only local subsystem information is required for the controller design. An adaptive iterative learning controller for each subsystem is constructed based on a fuzzy neural learning component and a robust learning component. The fuzzy neural learning component designed by an output recurrent fuzzy neural network is utilized as an approximator to approximate the system nonaffine nonlinearities and interconnections. The approximation error due to the fuzzy neural learning component will be then compensated by a robust learning component. Stable adaptive laws are derived to update the control parameters in order to guarantee the stability and convergence. We show that the internal signals are bounded during the learning process and the state tracking errors of each subsystem converge asymptotically along the iteration axis to a tunable residual set.

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We present a design method for iterative learning control system by using an output recurrent neural network (ORNN). Two ORNNs are employed to design the learning control structure. The first ORNN, which is called the output recurrent neural controller (ORNC), is used as an iterative learning controller to achieve the learning control objective. To guarantee the convergence of learning error, some information of plant sensitivity is required to design a suitable adaptive law for the ORNC. Hence, a second ORNN, which is called the output recurrent neural identifier (ORNI), is used as an identifier to provide the required information. All the weights of ORNC and ORNI will be tuned during the control iteration and identification process, respectively, in order to achieve a desired learning performance. The adaptive laws for the weights of ORNC and ORNI and the analysis of learning performances are determined via a Lyapunov like analysis. It is shown that the identification error will asymptotically converge to zero and repetitive output tracking error will asymptotically converge to zero except the initial resetting error.