【作者】 齐国元；

【导师】 陈增强； 袁著祉；

【作者基本信息】 南开大学 ， 控制理论与控制工程， 2004， 博士

【摘要】 本文重点研究了模型未知,参数时变的受扰非线性系统的状态估计问题与控制问题,提出了几种新型估计器和控制器,本文创新性工作为: 1.提出非线性离散随机系统比例微分滤波,该滤波方法联合考虑极小化状态估计误差方差和状态误差变化率的方差,较扩展Kalman滤波稳定性强,提高了估计的精度. 2.给出了非线性MIMO随机系统可观性定义和条件,在系统模型和噪声统计未知情况下,提出基于神经网络的非线性离散随机系统自适应滤波器的设计方法. 3.提出了一种较为简单的微分器,能在任意时刻跟踪连续的非线性信号,并提取其一阶微分,无颤振现象,给出了渐近稳定性和收敛性分析. 4.设计了较为简单的三阶微分器,能提取信号的二阶和三阶微分,给出了完整的渐近稳定性和收敛性证明. 5.设计了能提取信号的n阶微分高阶微分器(High order differentiator—HOD).所设计的HOD能对含有噪声信号进行滤波,高精度地逼近真实信号,并高品质地提取信号的微分和高阶微分; 所提出的HOD不依赖产生信号的系统模型,只依赖于系统产生的信号. 6.对非线性仿射系统,将状态估计问题转化为微分和高阶微分提取问题.利用设计的高阶微分器成果,提出一类新型估计器,该估计器参数少、精度高、不依赖非线性系统的模型. 7.利用设计的不依赖模型的估计器,基于Lyapunov稳定性理论设计了使非线性不确定系统渐近稳定的神经网络自适应鲁棒控制器. 8.对SISO系统和MIMO非线性受扰时变仿射系统,提出基于HOD的自适应高阶微分反馈控制器HODFC.该控制器不依赖于系统的模型; 给出了闭环系统渐近稳定性证明和鲁棒性证明; 控制器实现了多变量解耦控制. 9.利用自适应高阶微分反馈控制器实现倒立摆的鲁棒镇定与调节,实现了SISO和MIMO混沌系统控制与同步.控制器不依赖于倒立摆系统和混沌系统的模型函数. 10.构造了一个新的4维自治混沌系统,该系统中四个微分方程均包含有耦合交叉项,给出了混沌特性的理论分析和基于Lyapunove指数谱和分叉图等特征量的仿真分析.最后,用提出的多变量高阶微分反馈控制器实现了该混沌系统的控制与同步.更多还原

【Abstract】 This paper stresses on the problems of states estimation and control for disturbed time-varying nonlinear system with unknown model. The following innovations are achieved: 1. Proportion-Differential filtering(PDF)is presented for nonlinear discrete time-varying stochastic systems. PDF is derived not only from taking into account minimizing variance of state estimation error, but regarding its rate of change. Therefore, it has higher estimating precision and stability than the extended Kalman filtering. 2. Definition and condition of the locally observability are given for the nonlinear MIMO stochastic system. Neural networks-based adaptive filter is presented for the nonlinear discrete stochastic system with unknown model and stochastic characteristics. 3. A new simple differentiator is proposed, which can extract differential of any smooth nonlinear signals to reach higher accuracy. The stability and convergence of the differentiator are analyzed. 4. A class of asymptotically stable and convergent three orders differentiator is designed, which is able to extract the second order and third order differentials of signal. 5. High order differentiator (HOD) is proposed, which is able to approximate the real signal and extract differentials up to n th-order differentials with high precision and filtering quality. Stability and convergence of the HOD are proved. The HOD doer not rely on the model of the system produced, and only depend on the signal produced from the system. 6. The problem of states estimate is converted into the one of extracting the differential and high orders differentials for nonlinear affine system. Based on the HOD, a new estimator is brought forward, which does not rely on the model of the estimated system and has higher accuracy with a few parameters. 7. Using the estimator that does not rely on the model, an adaptive neural networks controller is designed, which makes the closed-loop nonlinear uncertain system asymptotically stable and robust. 8. Based on the HOD, adaptive high order differentials feedback controller (HODFC) is presented for time-varying nonlinear SISO and MIMO affine systems, which does not rely on the model of the controlled plant. Presents the analysis of stability and robustness of the closed-loop system. Linearized decoupling control is achieved for MIMO system. 9. We applied successfully the proposed adaptive HODFC to the inverted pendulum stabilization and regulation, and the SISO and MIMO chaotic system control synchronization. The controllers do not rely on the models of the inverted pendulum and chaotic systems. 10. A new 4-dimensional autonomous chaotic system is coined, in which each equation contains a coupled cross-product terms with three factors. Chaos properties are analyzed both theory and simulation via Lyapunov-exponents-spectrums and bifurcation graphs. At last, the control and synchronization are achieved for the chaotic system by using the proposed adaptive HODFC.更多还原