摘要
基于H∞滤波系统的最优性能指标与相应的Hamilton微分方程特征值之间的对应关系,利用微分方程特征值的摄动法研究了参数摄动H∞滤波系统的性能指标计算问题。当原滤波系统的最优性能指标已知时,利用系统参数的变化量就可以确定摄动系统的最优性能指标。
An eigenvalue perturbation method for the computation of optimal performance index of H∞ filtering systems with perturbed parameters is presented. The method is based on the correspondence between the optimal performance index and the first order eigenvalue of a linear Hamiltonian two-point boundary value problem (TPBVP) associated with the H∞ filtering problem. Determination of the optimal performance is a key step in designing H∞ filters, and the performance index will be influenced by parameters difference between the real system and its nominal model. From the viewpoint of differential eigenvalue problems, optimal performance of the actual H∞ filter, i.e. the perturbed filtering system relative to the nominal H∞ filter, can be calculated by eigenvalue perturbation technique provided that the eigensolutions of the nominal system have been obtained. The orthogonality of eigenfunctions of the Hamiltonian TPBVP is shown first. Then, eigenvalues and eigenfunctions of the perturbed system are expanded in terms of the eigensolutions of the nominal system. With these expansions, the optimal performance index of the perturbed filtering system is calculated by using the changes of the system parameters and the eigensolution of the Hamiltonian TPBVP associated with the nominal filtering system.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2005年第2期165-169,共5页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(10202004)资助项目.
