【作者】 衷路生；

【导师】 樊晓平；

【作者基本信息】 中南大学 ， 控制科学与工程， 2011， 博士

【摘要】 利用系统辨识方法建立对象数学模型是进行系统分析、设计和优化的前提,系统辨识在理论和工程方面都存在诸多有待解决的问题。本文开展了状态空间模型的辨识方法研究,论文的主要工作和创新点如下：(1)提出了线性状态空间系统的基于梯度优化的参数估计方法。首先,基于状态空间系统相似变换分析,给出了在观测等价类的相切平面正交子空间确定参数搜索方向的正交梯度方法,不仅能防止参数陷入局部极小值,还可以降低算法复杂度。然后,提出了能控能观的动态系统参数的递阶辨识方法。同时探讨了算法复杂度与系统的能控性、能观测性的内在联系。最后进行了状态空间系统的蒙特一卡罗数值仿真试验,结果表明提出的方法用于线性系统的参数估计是有效的。(2)提出了状态空间双线性系统基于投影梯度搜索的预报误差辨识方法。通过极小化输出预报误差而获得系统的参数估计。为解决全参数化引起的状态空间模型描述非唯一性问题,提出了在观测等价类相切面投影子空间更新系统参数的方法。给出了融合预报误差局部线性逼近性能的正则化因子自适应调整方法。探讨了算法复杂度与双线性模型子系统的能控性、能观测性的内在联系,给出了算法收敛速度的解析表达式。最后进行了稀土萃取过程的建模与输出预报试验,结果说明了所提出方法的有效性。(3)利用分段线性化的思想,提出了加权状态空间模型参数的正交梯度辨识方法,适用于非线性动态系统的建模。通过极小化系统输出预报误差而得到系统参数估计。采用径向基函数作为分状态的加权系数,给出了融合观测等价类信息的系统参数的正交梯度计算方法,同时获得了径向基函数参数梯度的递推计算方法,在此基础上,给出了系统参数的迭代辨识算法。揭示了加权状态空间模型各个子系统的能控性和能观测性对算法复杂度的影响机制。最后用提出的方法分别进行了非线性动态系统的建模以及预测的仿真试验,结果说明了提出的方法用于非线性动态系统的建模是有效的。(4)针对参考输入已知、控制器信息未知的闭环状态空间系统,提出了一种基于辅助变量的子空间辨识方法。针对辨识问题特点构造了辅助变量,通过将输入—输出数据块进行投影运算,而估计出系统扩展观测矩阵的正交补空间,结合SVD分解方法获得了系统扩展观测矩阵与下三角Toeplitz矩阵的估计。给出了系统参数的估计方法。闭环动态系统的仿真试验结果说明提出的子空间辨识方法是有效性。(5)基于期望极大原理提出了观测输出数据含有状态缺失的动态系统参数辨识方法。在期望极大算法框架下,给出了融合状态缺失信息的联合条件期望解析式,得到了极大化联合条件期望的系统参数计算方法,基于QR分解提高了算法的数值鲁棒性。数值仿真结果验证了所提辨识方法的性能。(6)基于自适应非参数核密度估计方法,提出了未知噪声分布的动态系统的极大似然辨识方法。设计了高斯型核密度估计器,进而给出了系统参数的极大似然估计算法,同时分析了算法的收敛性。仿真结果表明该算法的有效性。更多还原

【Abstract】 The aim of system identification is building dynamic models. It is an important step before system analysis, control and optimization. And there are many problems to be resolved in the field of system identification. The problems of parameter estimation of state-space models are considered in this thesis. The main work and the innovations of this thesis are as follows:(1) A parameter estimation method, based on gradient optimization search, is proposed for the linear time-invariant (LTI) state-space models. By the analysis of the similar transformation of LTI systems, the system parameters are updated to the orthogonal space to the manifold of observationally equivalent state-space systems, whose advantage is that local minimization can be advoided and the computational load can be decreased. Moreover, the relation between computational load and system properties such as the observability and controllability is also discussed in detail. Finally, simulation studies show the enhanced performance of the proposed method.(2) An output error identification method by projected gradient search is proposed for the parameter estimation of multivariable bilinear state-space systems. The system parameters are estimated by iteratively optimizing an output-error cost function. The nonuniqueness of the fully parameterized state-space model is taken into account by solving the optimization problem using a local gradient search that restricts the update of the parameters to directions that change the input-output behavior. In addition, the regulation parameter is adaptively determined by considering the local linear approximation of the output error. Moreover, the relation between the computational load and system properties such as the observability and controllability is discussed in detail. At the same time, the analytic expression of the convergence rate of the identification algorithm is also presented. Finally, the effectiveness of the proposed method is illustrated by practical study with data collected from a rare earth extraction process.(3) According to the local-linearization, a orthogonal gradient identification method is proposed for weighted state-space models, which is suited for nonlinear dynamical system modelling. The system parameters are determined by minimizing the output-error cost function. normalized radial basis functions are taken as weights of local state. And the orthogonal gradient computation method is given by considering the information of input-output equivalent class. At the same time, the iterative computation for parameters of system and radial basis function is given, and the iterative identification algorithm is also proposed. In addition, the influence of the subsystem’s controbility and observability to the computational load is discussed in detail. Finally, a numerical study is given to illustrate the performance of the proposede method for non-linear dynamic systems.(4) A subspace identification method based on instrumental variable is proposed for parameter estimation of closed-loop state-space systems with known setpoint input and unknown controller information. The instrumental variable is designed according to the characteristics of identification problem. In addition, the orthogonal complement to the extended observability matrix can be estimated. And the extended observability matrix and lower triangular block-Toeplitz matrix are computed by the SVD decomposition. Finally, a simulation study of closed-loop dynamic system is implemented and the result illustructed the performance of the proposed method.(5) An identification method, based on the expectation maximization (EM) algorithm, is proposed for dynamic systems with missing state information. In the framework of EM algorithm, the expression of joint conditional expectation is obtained and the parameter computation for the maximization of the joint conditional expectation is also derived. In addition, the algorithmic robustness can be enhanced by the QR decomposition. The result of the numerical simulation shows the performance of the proposed method.(6) Based on adaptive nonparametric density estimation method, a maximum likelihood (ML) identification method is proposed for dynamic systems with unknown noise density distribution. The Gaussian kernel density estimator is designed and the ML estimation algorithm is presented. At the same time, the algorithmic convergence is also analysized in detail. The performance of the proposed method is illustracted by the simulation result.更多还原