Robust adaptive observer using fuzzy systems for uncertain nonlinear systems

This paper describes the design of a robust adaptive fuzzy observer for uncertain nonlinear dynamical system. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property of the state estimation error, as well as of all other signals in the closed-loop system. Especially, we have focused on the realization of minimal dynamic order of the observer. For the purpose, we propose a new method in which no strictly proper (SPR) condition is needed and combine dynamic rule insertion scheme with on-line estimation of fuzzy parameters. No a priori knowledge of upper bounds on the optimal parameters and modeling errors is required. The theoretical results are illustrated through a simulation example.