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Article overview
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Multi-Task System Identification of Similar Linear Time-Invariant Dynamical Systems | | Yiting Chen
; Ana M. Ospina
; Fabio Pasqualetti
; Emiliano Dall'Anese
; | | Date: |
4 Jan 2023 | | Abstract: | Existing works on identification of the dynamics of linear time-invariant
(LTI) systems primarily focus on the least squares (LS) method when the
recorded trajectories are rich and satisfy conditions such as the persistency
of excitation. In this paper, we consider the case where the recorded states
and inputs are not sufficiently rich, and present a system identification
framework -- inspired by multi-task learning -- that estimates the matrices of
a given number of LTI systems jointly, by leveraging structural similarities
across the LTI systems. By regularizing the LS fit for each system with a
function that enforces common structural properties, the proposed method
alleviates the ill-conditioning of the LS when the recorded trajectories are
not sufficiently rich. We consider priors where, for example, the LTI systems
are similar in the sense that the system matrices share a common sparsity
pattern, some matrices are linear combinations of others, or their norm
difference is small. We outline a proximal-gradient method to solve the
multi-task identification problem, and we propose a decentralized algorithm in
the spirit of existing federated learning architectures. We provide empirical
evidence of the effectiveness of the proposed method by considering a synthetic
dataset, and by applying our method to the problem of estimating the dynamics
of brain networks. For the latter, the proposed method requires a significantly
smaller number of fMRI readings to achieve similar error levels of the LS when
estimating the brain dynamics across subjects. | | Source: | arXiv, 2301.01430 | | Services: | Forum | Review | PDF | Favorites | |
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