Identification and control for singularly perturbed systems using multi-time-scale neural networks

Many well established singular perturbation theories for singularly perturbed systems require the full knowledge of system model parameters. In this paper, a new adaptive identification method for singularly perturbed nonlinear system using multi-time-scale recurrent high-order neural networks is proposed to obtain an accurate and faithful model. By extending the usage of the optimal bounded ellipsoid concept, which is originally designed for discrete time systems, a novel weight updating law is developed for tuning the weights of the continuous time neural networks during the identification process. Based on the identification results, an indirect adaptive control scheme using singular perturbation theory is developed. By using singular perturbation theory, the system order is reduced, and the controller structure is simplified. The upper bound ε∗ for the small parameter ε is also obtained, such that for all 0 < ε < ε∗, the estimated tracking errors will converge to 0 exponentially, and the tracking error will be bounded. The closed-loop stability is analyzed and the effectiveness of the identification and control scheme is demonstrated by simulation results.