带遗忘因子的线性系统自适应观测器设计

针对状态方程和输出方程同时含有未知参数的多输入-多输出连续线性时变系统,采用构造性方法设计一种带指数遗忘因子的自适应观测器.证明当系统无噪声时该自适应观测器的全局指数收敛性,在此基础上考虑有噪声系统,在若干假设成立的条件下证明了该自适应观测器的估计误差均值也是全局指数收敛于0的.该自适应观测器采用带指数遗忘因子的时变增益矩阵,以自适应的方式克服噪声的影响,改善了估计的一致性.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、跟踪性及抗干扰性等期望性能.

Design of adaptive observer with forgetting factor for linear system

An adaptive observer with exponential forgetting factor was designed constructively for continuous-time multiple-input multiple-output linear time-varying systems with unknown parameters in both state and output equations. The global exponential convergence of the adaptive observer was established for the noise-free case. For the noise-corrupted case, the estimation errors converged in the mean to zero exponentially fast under appropriate assumptions. The adaptive observer used a time-varying gain matrix with exponential forgetting factor in order to overcome noises and improve the consistency of estimation. A numerical example was presented to illustrate the performance of the adaptive observer.