The Design of Full-order and Reduced-order Adaptive Observers for Nonlinear Systems

This paper deals with the existence and design method of adaptive observer for a kind of Lipschitz nonlinear system with unknown parameter. Under the assumption that a Riccati equation has a symmetric positive definite solution, a full-order adaptive observer which can estimate the states and the unknown parameters simultaneuouly is developed. Under the same assumptions, we also discusses a design method of reduced-order adaptive observer and the gain matrix of it is depended on the positive matrix solution of Riccati equation. The simulations to a real model show that the design methods have good performances.