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Low-Rank Approximations for Estimation of Multivariable Dynamics with Application to Energy Systems


System identification is a powerful tool for estimation of the systematic and causal dynamic relations by learning from measurements of input/output data. It provides an effective alternative when first-principles modeling is intractable. It plays an important role in model-based controller design especially during the stage of software-in-the-loop (SIL) and has been widely exploited in a wide range of real-world applications. This dissertation presents a study of theories and applications on multi-input multi-output (MIMO) system identification for estimation of multivariable dynamics between input/output data. The objective is to finally obtain a simplified dynamic model by emphasizing low-rank information during estimation with the aid of singular value decomposition (SVD).

In this dissertation, we study the Covariance Based Realization Algorithm (CoBRA) for estimation of linear time-invariant and time-periodic dynamics and the tensor network (TN) based algorithm for estimation of nonlinear dynamics described by Volterra series. The CoBRA, one branch of subspace methods by using covariance data, is able to focus on the estimation of a low-order deterministic model from noisy data by exploiting the low-rank feature of the data matrix. We propose an optimal implementation of the CoBRA and investigate its efficacy in a closed-loop setting compared with other subspace methods. A MIMO Volterra model is powerful to approximate nonlinear dynamics on the basis of input/output observations. We cope with the curse of dimensionality during model formulation and present TN-based noniterative algorithms for MIMO Volterra system identification. The proposed algorithms show numerical advantages over iterative algorithms.

This dissertation also studies two real-world applications in energy systems which involve estimation of multivariable dynamics. First, we investigate the microgrid dynamic modeling with power flow covariance data. We propose a model structure which consists of a MIMO linear part concatenated by a static nonlinear part to account for the power loss in transmission lines. Second, we study the modeling for lithium-ion batteries to accurately predict the output terminal voltage. We develop a TN-based Volterra double-capacitor (VDC) model, which is capable of predicting both static and dynamic nonlinearities simultaneously in a more accurate way than other equivalent circuit models (ECMs).

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