On the application of a novel model order reduction algorithm for sequentially semi-separable matrices to the identification of one-dimensional distributed systems

The sequentially semiseparable (SSS) matrix approach provides an efficient framework for solving control and identification problems of one-dimensional (1-D) spatially interconnected systems. For this approach, model order reduction algorithm is essential for obtaining a low computational complexity. In this paper, we apply a novel model reduction algorithm to identify 1-D spatially interconnected system by the extended Kalman filter (EKF). The new algorithm is based on the model reduction of linear time-varying (LTV) systems by low-rank approximation of the controllability and observability gramians. To show the efficiency and advantage of the new algorithm, the conventional algorithm is also studied. Numerical experiments illustrate that, by exploiting the structure of the EKF, both model reduction algorithms lead to linear computational complexity for identification of 1-D spatially interconnected system, where standard EKF has cubic computational complexity. Compared with the conventional model order algorithm, the new one gives a significant reduction on computational time.