Estimation of the dynamic spinal forces using a recurrent fuzzy neural network

Estimation of the dynamic spinal forces from kinematics data is very complicated because it involves the handling of the relationship between kinematic variables and electromyography (EMG) signals, as well as the relationship between EMG signals and the forces. A recurrent fuzzy neural network (RFNN) model is proposed to establish the kinematics-EMG-force relationship and model the dynamics of muscular activities. The EMG signals are used as an intermediate output and are fed back to the input layer. Since EMG is a direct reflection of muscular activities, the feedback of this model has a physical meaning. It expresses the dynamics of muscular activities in a straightforward way and takes advantage from the recurrent property. The trained model can then have the forces predicted directly from kinematic variables while bypassing the costly procedure of measuring EMG signals and avoiding the use of a biomechanics model. A learning algorithm is derived for the RFNN model.

Direct Adaptive Iterative Learning Control of Nonlinear Systems Using an Output-Recurrent Fuzzy Neural Network

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.