一类不确定时滞系统的有限维状态观测器设计理论及方法研究

Observer design is a basic and central issue in control theory,and it is widely used in feedback control,status monitoring and fault diagnosis. Based on robust adaptive control (RAC), this project develops a finite-dimensional state observer (FDSO) design method for a class of uncertain time-delay systems satisfying finite growth condition. By decomposing the uncertain time-delay state term into an unknown bounded disturbance and a certain current state term, we firsly propose a FDSO for a class of uncertain linear time-delay systems based on RAC and boundary-layer control methods. Secondly, for a class of uncertain nonlinear time-delay systems that do not satsify Lipschitz condition, an adaptive neural network based FDSO is synthesized by utlizing Lyapunov-Krasovskii functional approach. In order to improve transient performance of the proposed observer, method of optimizing the observer parameters is presented. Finally, for uncertain time-delay systems with time-delay sampled outputs, an adaptive FDSO design method is presented by modeling the original systems as systems with continuous-time outputs with time-varying delays. Computer simulations and experimental verification will be performed to demonstrate the actual application of the proposed FDSO. The purpose of the this project is to develop a new effective and practical observer design method. The outcome of this project is of both theoretical and practical importance, and it will further promote the development in the field of observer design.

观测器设计是控制理论的基本和核心问题之一，在反馈控制、状态监测以及故障诊断中具有广泛应用。本项目针对一类满足有限增长条件的不确定时滞系统，基于鲁棒自适应控制（RAC），提出一种有限维状态观测器（FDSO）设计方法。首先，通过将不确定时滞状态分解为未知有界干扰和已知当前状态两部分之和，基于RAC和边界层控制提出不确定线性时滞系统的FDSO设计方法。其次，针对不满足李普希兹条件的不确定非线性时滞系统，基于李亚普罗夫-克拉索夫斯基泛函提出神经网络自适应FDSO设计方法并研究参数整定方法以优化观测器的暂态性能。最后，对于具有延时采样输出的不确定时滞系统，利用输出时滞方法将原系统建模成具有时变时滞的连续输出系统，进而提出其FDSO设计方法。通过仿真和实验验证，探讨所提FDSO设计方法的应用。本项目的研究将提供一种有效、实用的观测器设计新方法，促进观测器理论的发展，具有重要的理论意义和应用价值。

状态观测器在动态输出反馈控制，状态监测以及故障诊断中得到了广泛应用。确定性系统的观测器设计基于龙伯格状态观测器的设计思路，即复制原系统再加误差校正项以使得观测误差收敛。然而对于不确定系统，尤其是不确定时滞系统，复制加校正的思路不再有效，观测器结构的确定无现成规律可循。本项目首先针对不确定线性时滞系统，将时滞状态分解为无时滞状态和未知干扰两部分之和，在有限增长条件的基础上利用自适应控制方法构造出了有限维状态观测器，其有效性通过了数字仿真实验验证。其次，对于一类不满足Lipschitz条件的不确定非线性时滞系统，通过选择合适的Lyapunov-Krasovskii泛函对不确定非线性时滞项对消并利用神经网络对不确定非线性项进行逼近，设计出了有限维神经网络自适应状态观测器并提出优化观测器参数的方法，其有效性通过了混沌同步数字仿真以及一级直线倒立摆状态监测实验的验证。最后，针对具有延时采样输出的不确定非线性时滞系统，通过输出时滞方法将原系统建模成具有时变时滞输出的连续时间系统，进而基于有限增长条件和自适应控制，提出了其有限维状态观测器设计方法并通过数字仿真和实验验证了有效性。本项目的研究成果为时滞系统的状态观测器设计提供了新的思路和理论指导，发展和完善了观测器设计理论。