非线性不确定系统的自适应观测器设计

Design of Adaptive Observer for Nonlinear Systems under Uncertainty

非线性状态观测器可改善过程控制性能和故障诊断,针对一类参数不确定非线性系统提出了自适应观测器设计方法。通过微分同胚变换,将非线性系统转换为仅依赖原系统输入、输出的自适应观测器规范形式。利用自适应调节器估计未知参数,用构造的观测器实现状态的重构。Lyapunov稳定性理论分析了状态观测误差动态方程的稳定性,用来证明所设计的自适应观测器为全局渐近收敛的,既实现了系统状态的渐近重构又确保了在持续激励条件下未知参数估计以指数快速收敛到真值,并通过仿真试验。仿真结果表明提出方法的有效性。

An adaptive observer is designed for a class of nonlinear systems with unknown parameters.The nonlinear system is diffeomorphically transformed into a canonical system by using an adaptive regulator to estimate the unknown parameters and building the observer to reconstruct the systems states.Based on Lyapunov stability theory,the stability of dynamical error equation is proved and a conclusion is given that the observer designed guarantees fast exponential convergence both of parameter and state estimates to actual parameters and states when persistency of excitation conditions are satisfied.A simulation example is provided to verify the effectiveness of the method.