Hierarchical Optimization Identification of LTI State-space Systems by Projected Gradient Search
基于正交梯度搜索的动态系统递阶优化辨识

A hierarchical optimization method for the identifi- cation of LTI state-space systems is proposed based on projected gradient search.The system parameters are determined by op- timizing an output-error cost function.To deal with the non- uniqueness of the fully parameterized state-space system,a pro- jected gradient search algorithm is presented by restricting the update of the parameters to the tangent space to the manifold of observationally equivalent state-space systems.The sufficient condition to employ L-M algorithm for optimizing parameters is also introduced.The proposed hierarchical optimization identi- fication method includes two steps:First,the parameter search direction is determined by the proposed adaptive L-M projected gradient approach;Second,the optimum step size is computed according to a line search method.Numerical simulation studies show that the proposed algorithm offers improved performance, such as faster convergence speed and better numerical stability, over existing EM and DDLC methods.