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1. Identification of State-space Linear Parameter-varying Models Using Artificial Neural Networks

   Bao, Yajie; Mohammadpour Velni, Javad; Basina, Aditya; Shahbakhti, Mahdi (July 2020, IFAC World Congress)

   This paper presents an integrated structure of artificial neural networks, named state integrated matrix estimation (SIME), for linear parameter-varying (LPV) model identification. The proposed method simultaneously estimates states and explores structural dependency of matrix functions of a representative LPV model only using inputs/outputs data. The case with unknown (unmeasurable) states is circumvented by SIME using two estimators of the same state: one estimator represented by an ANN and the other obtained by LPV model equations. Minimizing the difference between these two estimators, as part of the cost function, is used to guarantee their consistency. The results from a complex nonlinear system, namely a reactivity controlled compression ignition (RCCI) engine, show high accuracy of the state-space LPV models obtained using the proposed SIME while requiring minimal hyperparameters tuning. 

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2. Epistemic Uncertainty Quantification in State-space LPV Model Identification Using Bayesian Neural Networks

   Bao, Yajie; Mohammadpour Velni, Javad; Shahbakhti, Mahdi (January 2020, IEEE control systems letters)

   This paper presents a variational Bayesian inference Neural Network (BNN) approach to quantify uncertainties in matrix function estimation for the state-space linear parameter-varying (LPV) model identification problem using only inputs/outputs data. The proposed method simultaneously estimates states and posteriors of matrix functions given data. In particular, states are estimated by reaching a consensus between an estimator based on past system trajectory and an estimator by recurrent equations of states; posteriors are approximated by minimizing the Kullback–Leibler (KL) divergence between the parameterized posterior distribution and the true posterior of the LPV model parameters. Furthermore, techniques such as transfer learning are explored in this work to reduce computational cost and prevent convergence failure of Bayesian inference. The proposed data-driven method is validated using experimental data for identification of a control-oriented reactivity controlled compression ignition (RCCI) engine model. 

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3. Input-output Data-driven Modeling and MIMO Predictive Control of an RCCI Engine Combustion

   Khoshbakht Irdmousa, Behrouz; Naber, Jeffrey Donald; Mohammadpour Velni, Javad; Borhan, Hoseinali; Shahbakhti, Mahdi (January 2021, IFAC Modeling, Estimation and Control Conference (MECC))

   null (Ed.)

   This study presents a data-driven identi cation method based on Kernelized Canonical Correlation Analysis (KCCA) approach to generate a state-space Linear Parameter-Varying (LPV) dynamic representation for the RCCI engine combustion. An LPV model is used to estimate RCCI combustion phasing (CA50) and indicated mean eective pressure (IMEP) based on fuel injection timing and quantity. The proposed data-driven method does not require prior knowledge of the plant model states and adjusts number of states to increase the accuracy of the identi ed state-space model. The results demonstrate that the proposed data-driven KCCA-LPV approach provides a dependable technique to establish a fast and reasonably accurate RCCI combustion model. The established model is then incorporated in a design of a constrained MIMO Model Predictive Controller (MPC) to track desired crank angle for 50% fuel burnt and IMEP at various engine conditions. The controller performance results demonstrate that the established data-driven constrained MPC combustion controller can follow desired CA50 and IMEP with less than 1.5 CAD and 37 kPa error, respectively. 

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4. Optimal sparse eigenspace and low-rank density matrix estimation for quantum systems

   https://doi.org/https://doi.org/10.1016/j.jspi.2020.11.002  

   Cai, Tony; Kim, Donggyu; Song, Xinyu; Wang, Yazhen (July 2021, Journal of statistical planning and inference)

   Dette, Holger; Lee, Stephen; Pensky, Marianna (Ed.)

   Quantum state tomography, which aims to estimate quantum states that are described by density matrices, plays an important role in quantum science and quantum technology. This paper examines the eigenspace estimation and the reconstruction of large low-rank density matrix based on Pauli measurements. Both ordinary principal component analysis (PCA) and iterative thresholding sparse PCA (ITSPCA) estimators of the eigenspace are studied, and their respective convergence rates are established. In particular, we show that the ITSPCA estimator is rate-optimal. We present the reconstruction of the large low-rank density matrix and obtain its optimal convergence rate by using the ITSPCA estimator. A numerical study is carried out to investigate the finite sample performance of the proposed estimators. 

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5. An Online Transfer Learning Approach for Identification and Predictive Control Design with Application to RCCI Engines

   Bao, Yajie; Mohammadpour Velni, Javad; Shahbakhti, Mahdi (January 2020, 2020 ASME Dynamic Systems Control Conference)

   null (Ed.)

   This paper presents a framework to refine identified artificial neural networks (ANN) based state-space linear parametervarying (LPV-SS) models with closed-loop data using online transfer learning. An LPV-SS model is assumed to be first identified offline using inputs/outputs data and a model predictive controller (MPC) designed based on this model. Using collected closed-loop batch data, the model is further refined using online transfer learning and thus the control performance is improved. Specifically, fine-tuning, a transfer learning technique, is employed to improve the model. Furthermore, the scenario where the offline identified model and the online controlled system are “similar but not identitical” is discussed. The proposed method is verified by testing on an experimentally validated high-fidelity reactivity controlled compression ignition (RCCI) engine model. The verification results show that the new online transfer learning technique combined with an adaptive MPC law improves the engine control performance to track requested engine loads and desired combustion phasing with minimum errors. 

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