Multi-task sparse identification for closed-loop systems with general observation sequences

Abstract

To achieve the simultaneous and accurate identification of sparse parameters for multiple systems, a multi-task sparse identification algorithm is proposed for systems with general sequences, including stationary time series and feedback control. By minimizing the sum of L2-norm and weighted multi-task L2,1 regularization terms, the sparse pattern of parameters are shared between different tasks, which leads to a reduction in workload while improving the sparsity and accuracy of the estimates. To cope with online identification, an online multi-task sparse identification algorithm is presented, together with proof of convergence of the estimates. Finally, two closed-loop identification are given to support the theoretical analysis and to demonstrate the advantages of the proposed algorithm.