Adaptive Observer Design for a Class of Nonlinear Interconnected Systems with Uncertain Time Varying Parameters

Abstract

In this paper, a class of nonlinear interconnected systems with uncertain time varying parameters is considered, in which both the interconnections and the isolated subsystems are nonlinear. The difference between the unknown time varying parameter and its corresponding nominal value is assumed to be bounded where the nominal value is not required to be known. A dynamical system is proposed and then, the error systems between the original interconnected system and the designed dynamical systems are analysed based on the Lyapunov direct method. A set of conditions is developed such that the augmented systems formed by the error dynamical systems and the designed adaptive laws, are globally uniformly bounded. Specifically, the estimation errors are asymptotically convergent to zero using LaSalle-Yoshizawa Theorem. Case study on a coupled inverted pendulum system is presented to demonstrate the developed methodology, and simulation shows that the proposed approach is effective and practicable.