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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. 

This paper presents an integrated structure of arti cial neural networks, named state integrated matrix estimation (SIME), for linear parameter-varying (LPV) model identi cation. 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. 

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. 

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. 

Reactivity controlled compression ignition (RCCI) is a promising low temperature combustion (LTC) regime that offers lower nitrogen oxides (NOx), soot and particulate matter (PM) emissions along with higher combustion efficiency compared to conventional diesel engines. It is critical to control maximum pressure rise rate (MPRR) in RCCI engines in order to safely and efficiently operate at varying engine loads. In this paper, a data-driven modeling (DDM) approach using support vector machines (SVM) is adapted to develop a linear parameter-varying (LPV) representation of MPRR for RCCI combustion. This LPV representation is then used in the design of a model predictive controller (MPC) to control crank angle of 50% of fuel mass fraction burn (CA50) and indicated mean effective pressure (IMEP) while limiting the MPRR. The results show that the LPV-MPC control strategy can track CA50 and IMEP with mean tracking errors of 0.9 CAD and 4.7 kPa, respectively, while limiting the MPRR to the maximum allowable value of 5.8 bar/CAD. 

Reactivity controlled compression ignition (RCCI) engines center on a combustion strategy with higher thermal efficiency, lower particulate matter (PM), and lower oxides of nitrogen (NOx) emissions compared to conventional diesel combustion (CDC) engines. However, real time optimal control of RCCI engines is challenging during transient operation due to the need for high fidelity combustion models. Development of a simple, yet accurate control-oriented RCCI model from physical laws is time consuming and often requires substantial calibrations. To overcome these challenges, data-driven models can be developed. In this paper, a data-driven linear parametervarying (LPV) model for an RCCI engine is developed. An LPV state space model is identified to predict RCCI combustion phasing as a function of multiple RCCI control variables. The results show that the proposed method provides a fast and reliable route to identify an RCCI engine model. The developed model is then used for the design of a model predictive controller (MPC) to control crank angle for 50% fuel burnt (CA50) for varying engine conditions. The experimental results show that the designed MPC with the data-driven LPV model can track desired CA50 with less than 1 crank angle degree (CAD) error against changes in engine load.