Time Delay Estimation For Dynamic Systems Based On Graph Laplacian

Time delay(referred to as time delay)is common in practical dynamic systems.The pollution of the measurable data caused by the time delay makes the measurable data of the system mismatch randomly on the timeline,which greatly increases the difficulty of data modeling.Therefore,the problem of time delay estimation(Time-delay estimation,TDE)has received more and more attention.The existing time delay estimation methods based on input and output data cannot effectively eliminate the adverse effects of time delay on the time delay system modeling of unknown structures,and cannot guarantee the accuracy of system modeling.In view of the shortcomings of existing methods in computation and robustness,a time delay estimation method based on graph Laplacian is proposed in this paper.The main contributions include:(1)The graph Laplacian theory is applied to TDE tasks for the first time,and a TDE method suitable for SISO(Single input single output)delay systems is proposed.The graph is constructed based on the input data,on this basis,the global smoothness metric of the graph is calculated as the time delay metric,and the system delay is estimated by minimizing the global smoothness metric.The time delay estimation method based on graph Laplacian is used to simulate the typical SISO time delay system,the experimental results verify the reliability of the TDE method,and the robustness of the method to noise is verified by noise experiments.(2)The time delay estimation method based on graph Laplacian is extended to MIMO(Multiple input multiple output)time delay system.In order to reduce the computational load in the TDE process,the N-linked graph is constructed,the sparse N-linked graph adjacency matrix is obtained,and the sparseness of the adjacency matrix is used to further reduce the computational complexity of hour delay estimation.Based on the theory of multivariate continuous function,the TDE task of MIMO system is simplified to multiple TDE tasks of SISO system,and the TDE process is simplified.Simulation experiments and wind speed prediction experiments based on real data show that this method can accurately estimate the time delay of MIMO system.