Adaptive observer design for a class of nonlinear systems
一类非线性系统的自适应观测器设计

In analyzing faulty systems, actuator faults and sensor faults can be modeled respectively by unknown parameters in the state equation and the output equation. Thus, it is of practical significance to develop an adaptive observer for the state equation and the output equation containing unknown parameters simultaneously. Based on the techniques of high-gain observer and adaptive estimation, we constructively design an adaptive observer for jointly estimating the states and the unknown parameters of a class of uniformly observable nonlinear systems. This adaptive observer employs a timevarying gain matrix for estimating unknown parameters, which is simple in construction and requires simple parameter tuning. We have also derived the required persistent excitation condition for the adaptive observer to be global exponential convergence, and give the corresponding proof succinctly. A numerical example is presented to illustrate the performance of this adaptive observer.