Small-Gain Approach to Fuzzy Adaptive Control for Interconnected Systems With Unmodeled Dynamics
Bo Xu, Yuan‐Xin Li, Choon Ki Ahn
Abstract
This article presents a new stabilizing control scheme for a class of interconnected nonlinear systems subjected to unmodeled dynamics and immeasurable states. Fuzzy logic systems are applied to approximate the unknown functions, and a fuzzy-based state observer is constructed. The interconnection of the overall system is completely compensated via the cyclic-small-gain condition theorem, and the small-gain theorem is introduced to overcome the unmodeled dynamics in each subsystem. Furthermore, assumptions from prior literature are relaxed, and computing burden is reduced through the design of less adaptive laws. This article proves that under the designed control scheme, the closed-loop systems are controlled to be input-to-state practically stable and that all signals are guaranteed to be semiglobally uniformly ultimately bounded. Finally, this article’s simulation section illustrates the effectiveness of the proposed approach through an example derived from a practical system model.