无未知参数先验信息的非线性自适应观测器设计

Nonlinear adaptive observer design without a priori knowledge on the unknown parameters

研究了一类具有未知参数的非线性系统自适应观测器设计问题.不同于现有结果,本文所研究的非线性系统更为一般,已知的系统信息更少:1)系统未知参数的范数的上界未知;2)具有关于可测输出非Lipschitz连续的非线性动态;3)系统输出显式地依赖于控制输入.通过设计自适应调节器来估计未知参数范数,从而给出了不基于未知参数先验信息的非线性自适应观测器设计的新方法.所设计的观测器为全局渐近收敛的,即实现了系统状态的渐近重构,确保了未知参数估计的一致有界性.此外,在系统输出不显式地依赖于控制输入的条件下,研究了降维观测器的设计问题.仿真例子验证了本文理论结果的正确性.

The adaptive observer design is investigated for a class of nonlinear systems with unknown parameters. Being different from the existing results, the nonlinear system studied here is more general and less dependent on a priori knowledge including 1） the upper bound of the （Euclidean） norm of the system unknown parameters; 2） the non-Lipschitz continuous nonlinear dynamics of the measurable output; 3） the explicitly dependence of the system output upon the control input. By adding an adaptive regulator to estimate the norm of the unknown parameters, a novel approach is developed under some conditions to design the nonlinear adaptive observer. The observer designed is globally asymptotically convergent, i.e., it not only gives the convergent reconstruction of the system states, but also guarantees the uniform boundedness of the estimations of the unknown parameters. In addition, the reduced-order observer design is considered when the system output is independent of the control input. A simulation example is given to illustrate the correctness of the theoretical results of this paper.