Composite adaptive control with fast convergence for multilayer neural network

A composite adaptive control (CAC) that combines the benefits of direct and indirect adaptive controls has better parameter adaptation and control response. Multilayer neural networks (NNs) can be employed to enhance a model's representation capacity, but previous composite adaptive approaches cannot easily train the model due to its nonlinearities. A novel CAC is therefore developed in this study to tackle the above limitations. A modified robust version is adopted by focusing on the direct adaptive part to enhance robustness of adaption. Then, the indirect parameter adaptive law is improved by adopting a small learning rate in which a multistep adaption update is executed in one control interval. Moreover, multistep prediction errors are implemented to guarantee the consistency of the approximation errors, and an experience replay technique is adopted to attenuate the requirement of persistent excitation conditions. These improvements not only accelerate the convergence process but also smoothen the updating of NN parameters. Given that a nonlinear plant with MIMO strict-feedback structure is considered, the proposed CAC is integrated into the backstepping framework. The uniformly bounded property of the tracking errors and the approximation errors is proven by Lyapunov theory. The superiority of the proposed method and the roles of these improvements are demonstrated by comparative simulations.