随机线性系统模型的集结简化

Approximate Aggregation of Linear Stochastic Systems

讨论集结法在简化随机线性系统模型中的应用,它可将n维状态空间模型的主要特征集结简化到r维(r<n)状态空间模型上,优化地再现原系统的基本性能和模型数据。在简化模型中,动态系统集结矩阵选定为原系统矩阵特征值的子集。这种方法既适用于离散系统,也适用于连续系统。高阶系统动态模型的这种简化处理方法,不仅克服与避免了对这类系统进行仿真分析时,占用较大内存空间与耗费大量机时的缺陷,而且提高了仿真与控制过程的稳定性和结果的准确性。

A method is proposed for aggregating the linear stochastic systems whereby the state of the original system is obtained in an optimal, way from the data on the state of its aggregated model. The aggregation matrix is chosen so that the eigen numbers in the dynamics matrix of the aggregated system are a specified subset of the eigen number dynamics matrix of the original system. The method is applicable to both the discontinuous and continuous systems.