Adaptive neural control for a class of MIMO nonlinear systems with extreme learning machine

This paper presents two adaptive neural control schemes for a class of uncertain continuous-time multi-input multi-output (MIMO) nonlinear dynamic systems. Within these schemes, the single-hidden layer feedforward networks (SLFNs) are applied to approximate the unknown nonlinear functions of the systems and then the neural controller is built based on the approximated neural models. The parameters of the SLFNs are modified using the recently proposed neural algorithm named extreme learning machine (ELM), where the parameters of the hidden nodes are assigned randomly. Different from the original ELM algorithm, the output weights are updated using the adaptive laws derived based on the Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. The robustifying control term is also constructed to compensate for approximation errors of the SLFNs. In order to avoid the requirement of the approximation error bounds, the estimation laws derived based on the Lyapunov stability theorem and Barbalat's lemma are employed to estimate the error bounds in the second adaptive control scheme. Finally the proposed control schemes are applied to control a two-link robot manipulator. The simulation results demonstrate the effectiveness of the proposed control schemes for the MIMO nonlinear system.

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