Identification and trajectory tracking control of nonlinear singularly perturbed systems

In this paper, a new identification and control scheme using multitime scale recurrent high-order neural networks is proposed to control the singularly perturbed nonlinear systems with uncertainties. First, a novel identification scheme using modified optimal bounded ellipsoid based weight's updating laws is developed to identify the unknown nonlinear systems. By adding two additional terms to the original optimal bounded ellipsoid based weight's updating laws, the new modified identification scheme can achieve high convergence speed due to the adaptively adjusted learning gain at the beginning of the identification process and remain effective during the whole identification process. Based on the identified model, a new indirect adaptive control scheme for trajectory tracking problem using singular perturbation theory is developed, which is different from the control scheme proposed previously that can only be applied to a regulation problem. The closed-loop stability is analyzed and the convergence of system states is guaranteed. Experimental results are presented to demonstrate the effectiveness of the identification and control scheme.