一类非线性系统的自适应观测器设计

Adaptive observer design for a class of nonlinear systems

在故障诊断应用中,状态方程中的未知参数和输出方程中的未知参数分别表征执行机构故障和传感器故障,所以研究状态方程和输出方程同时含有未知参数的自适应观测器有着实际的应用意义.本文基于高增益观测器和自适应估计理论,针对状态方程和输出方程同时含有未知参数的一类一致可观的非线性系统,用构造性方法设计了一种联合估计状态和未知参数的自适应观测器.该自适应观测器的参数估计采用时变增益矩阵,结构形式及参数设置简单.给出了使该自适应观测器满足全局指数收敛性的持续激励条件,并在理论上简洁地证明了该自适应观测器的全局指数收敛性.数值仿真结果表明该自适应观测器具有良好的快速收敛性、跟踪性等期望性能.

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 highgain 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.