High-performance numerical algorithms and software for subspace-based linear multivariable system identification
Basic numerical algorithms and a newly developed software are described for subspace-based identification of linear discrete-time state space systems of the form \(x_{k+1}= Ax_k+ Bu_k+ w_k\), \(y_k = Cx_k+ Du_k+ v_k\), where \(x_k\in\mathbb{R}^n\) is the state vector at time \(k\), \(u_k\in\mathbb{R}^m\) is the input vector, \(y_k\in\mathbb{R}^l\) is the output vector, \(A\), \(B\), \(C\) and \(D\) are matrices of corresponding sizes and \(\{w_k\}\), \(\{v_k\}\) are zero-mean, stationary sequences, uncorrelated with \(\{u_k\}\). It is supposed that the system is controllable and observable. A particular model arises when \(w_k= Kv_k\) and \(\{v_k\}\) is a white noise sequence. The standard identification problem is to determine the system order \(n\) and the system matrices using the input and output data sequences. The implementation of two subspace-based algorithms, known as MOESP and N4SID, is considered and an identification toolbox, called SLIDENT, is described. The toolbox incorporates interfaces to the MATLAB and SCILAB environments and is included in the freely available library SLICOT. The main advantages of the SLICOT library include, among others, a greater efficiency and an improved numerical accuracy in comparison with other existing codes.
scientific article; zbMATH DE number 2085575
scientific article