1
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Abdullah F, Christofides PD. Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results. Comput Chem Eng 2023. [DOI: 10.1016/j.compchemeng.2023.108247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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2
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Abdullah F, Alhajeri MS, Christofides PD. Modeling and Control of Nonlinear Processes Using Sparse Identification: Using Dropout to Handle Noisy Data. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c02639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Affiliation(s)
- Fahim Abdullah
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, California90095, United States
| | - Mohammed S. Alhajeri
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, California90095, United States
- Department of Chemical Engineering, Kuwait University, P.O.Box 5969, Safat13060, Kuwait
| | - Panagiotis D. Christofides
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, California90095, United States
- Department of Electrical and Computer Engineering, University of California, Los Angeles, California90095, United States
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3
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Abdullah F, Wu Z, Christofides PD. Handling noisy data in sparse model identification using subsampling and co-teaching. Comput Chem Eng 2022. [DOI: 10.1016/j.compchemeng.2021.107628] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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4
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Computationally Efficient Nonlinear Model Predictive Control Using the L 1 Cost-Function. SENSORS 2021; 21:s21175835. [PMID: 34502727 PMCID: PMC8434402 DOI: 10.3390/s21175835] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Revised: 08/25/2021] [Accepted: 08/25/2021] [Indexed: 11/30/2022]
Abstract
Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.
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5
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Qing X, Song J, Jin J, Zhao S. Nonlinear model predictive control for distributed parameter systems by time–space‐coupled model reduction. AIChE J 2021. [DOI: 10.1002/aic.17246] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Xiangyun Qing
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education East China University of Science and Technology Shanghai China
| | - Jun Song
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education East China University of Science and Technology Shanghai China
| | - Jing Jin
- Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education East China University of Science and Technology Shanghai China
| | - Shuangliang Zhao
- State Key Laboratory of Chemical Engineering and School of Chemical Engineering East China University of Science and Technology Shanghai China
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6
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Least Squares Support Vector Machine-Based Multivariate Generalized Predictive Control for Parabolic Distributed Parameter Systems with Control Constraints. Symmetry (Basel) 2021. [DOI: 10.3390/sym13030453] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis functions constructed from a carefully selected set of data is used in a Galerkin projection for the building of an approximate low-dimensional lumped parameter systems. Then, the temporal autoregressive exogenous model obtained by the least squares support vector machine is applied in the design of a multivariate generalized predictive control strategy. Finally, the effectiveness of the proposed multivariate generalized predictive control strategy is verified through a numerical simulation study on a typical diffusion-reaction process in radical symmetry.
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7
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Wu Z, Rincon D, Luo J, Christofides PD. Machine learning modeling and predictive control of nonlinear processes using noisy data. AIChE J 2021. [DOI: 10.1002/aic.17164] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Zhe Wu
- Department of Chemical and Biomolecular Engineering University of California Los Angeles California USA
| | - David Rincon
- Department of Chemical and Biomolecular Engineering University of California Los Angeles California USA
| | - Junwei Luo
- Department of Chemical and Biomolecular Engineering University of California Los Angeles California USA
| | - Panagiotis D. Christofides
- Department of Chemical and Biomolecular Engineering University of California Los Angeles California USA
- Department of Electrical and Computer Engineering University of California Los Angeles California USA
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8
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Xu W, Peng H, Tian X, Peng X. DBN based SD-ARX model for nonlinear time series prediction and analysis. APPL INTELL 2020. [DOI: 10.1007/s10489-020-01804-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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9
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Tang W, Daoutidis P. Dissipativity learning control (DLC): A framework of input–output data-driven control. Comput Chem Eng 2019. [DOI: 10.1016/j.compchemeng.2019.106576] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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10
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Tsay C, Baldea M. 110th Anniversary: Using Data to Bridge the Time and Length Scales of Process Systems. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b02282] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Calvin Tsay
- McKetta Department of Chemical Engineering The University of Texas at Austin, Austin, Texas 78712, United States
| | - Michael Baldea
- McKetta Department of Chemical Engineering The University of Texas at Austin, Austin, Texas 78712, United States
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11
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Kaiser E, Kutz JN, Brunton SL. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proc Math Phys Eng Sci 2018; 474:20180335. [PMID: 30839858 PMCID: PMC6283900 DOI: 10.1098/rspa.2018.0335] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Accepted: 10/11/2018] [Indexed: 02/07/2023] Open
Abstract
Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.
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Affiliation(s)
- E. Kaiser
- Department of Mechanical Engineering, University of Washington, Seattle, WA, 98195
| | - J. N. Kutz
- Department of Applied Mathematics, University of Washington, Seattle, WA, 98195
| | - S. L. Brunton
- Department of Mechanical Engineering, University of Washington, Seattle, WA, 98195
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12
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Zhang R, Tao J, Lu R, Jin Q. Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:457-469. [PMID: 27959823 DOI: 10.1109/tnnls.2016.2631481] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.
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13
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Stogiannos M, Alexandridis A, Sarimveis H. Model predictive control for systems with fast dynamics using inverse neural models. ISA TRANSACTIONS 2018; 72:161-177. [PMID: 29054316 DOI: 10.1016/j.isatra.2017.09.016] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Revised: 09/19/2017] [Accepted: 09/22/2017] [Indexed: 06/07/2023]
Abstract
In this work, a novel model predictive control (MPC) scheme is introduced, by integrating direct and indirect neural control methodologies. The proposed approach makes use of a robust inverse radial basis function (RBF) model taking into account the applicability domain criterion, in order to provide a suitable initial starting point for the optimizer, thus helping to solve the optimization problem faster. The performance of the proposed controller is evaluated on the control of a highly nonlinear system with fast dynamics and compared with different control schemes. Results show that the proposed approach outperforms the rivaling schemes in terms of response; moreover, it solves the optimization problem in less than one sampling period, thus effectively rendering MPC-based controllers capable of handling systems with fast dynamics.
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Affiliation(s)
- Marios Stogiannos
- Department of Electronic Engineering, Technological Educational Institute of Athens, Agiou Spiridonos, Aigaleo 12243, Greece; School of Chemical Engineering, National Technical University of Athens, Iroon Polytechneiou 9, Zografos 15780, Greece
| | - Alex Alexandridis
- Department of Electronic Engineering, Technological Educational Institute of Athens, Agiou Spiridonos, Aigaleo 12243, Greece.
| | - Haralambos Sarimveis
- School of Chemical Engineering, National Technical University of Athens, Iroon Polytechneiou 9, Zografos 15780, Greece
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14
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Aguilar-Leal O, Fuentes-Aguilar R, Chairez I, García-González A, Huegel J. Distributed parameter system identification using finite element differential neural networks. Appl Soft Comput 2016. [DOI: 10.1016/j.asoc.2016.01.004] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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15
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Wang M, Qi C, Yan H, Shi H. Hybrid neural network predictor for distributed parameter system based on nonlinear dimension reduction. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.08.005] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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16
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Chen C, Yan X. Burning Side Reaction Model of the INVISTA Oxidation Process Using a Radial Basis Function Neural Network Integrated with Partial Mutual Information-Least Square Regression. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 2015. [DOI: 10.1252/jcej.14we212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Chao Chen
- Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology
| | - Xuefeng Yan
- Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology
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17
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Qi C, Li HX, Li S, Zhao X, Gao F. A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes. Appl Soft Comput 2014. [DOI: 10.1016/j.asoc.2014.09.003] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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18
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Wang M, Shi H. An adaptive neural network prediction for nonlinear parabolic distributed parameter system based on block-wise moving window technique. Neurocomputing 2014. [DOI: 10.1016/j.neucom.2013.11.030] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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19
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Wang M, Yan X, Shi H. Spatiotemporal prediction for nonlinear parabolic distributed parameter system using an artificial neural network trained by group search optimization. Neurocomputing 2013. [DOI: 10.1016/j.neucom.2013.01.037] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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20
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Qi C, Li HX, Li S, Zhao X, Gao F. Kernel-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Industrial Processes. Ind Eng Chem Res 2012. [DOI: 10.1021/ie301593u] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Chenkun Qi
- School of Mechanical Engineering, Shanghai Jiao Tong University, State Key Laboratory
of Mechanical System and Vibration, Shanghai 200240, China
| | - Han-Xiong Li
- Department of Systems Engineering & Engineering Management, City University of Hong Kong, Hong Kong, China and School of Mechanical & Electrical Engineering, Central South University, China
| | - Shaoyuan Li
- Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xianchao Zhao
- School of Mechanical Engineering, Shanghai Jiao Tong University, State Key Laboratory
of Mechanical System and Vibration, Shanghai 200240, China
| | - Feng Gao
- School of Mechanical Engineering, Shanghai Jiao Tong University, State Key Laboratory
of Mechanical System and Vibration, Shanghai 200240, China
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21
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Wang M, Zhang Y, Shi H. Local Model-Based Predictive Control for Spatially-Distributed Systems Based on Linear Programming. Ind Eng Chem Res 2012. [DOI: 10.1021/ie2027519] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Mengling Wang
- Key Laboratory of Advanced Control
and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, 130,
Meilong Road, Shanghai 200237, China
| | - Yang Zhang
- Shanghai Municipal Transportation
Information Center, Shanghai Urban and Rural Construction and Transportation Committee, Shanghai 200032, China
| | - Hongbo Shi
- Key Laboratory of Advanced Control
and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, 130,
Meilong Road, Shanghai 200237, China
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22
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Qi C, Li HX, Li S, Zhao X, Gao F. Probabilistic PCA-Based Spatiotemporal Multimodeling for Nonlinear Distributed Parameter Processes. Ind Eng Chem Res 2012. [DOI: 10.1021/ie202613t] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Han-Xiong Li
- Department of Systems Engineering & Engineering Management, City University of Hong Kong, Hong Kong, China
- State Key Laboratory of High Performance Complex Manufacturing, Central South University, China
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23
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Wang M, Li N, Li S, Shi H. Embedded Interval Type-2 T-S Fuzzy Time/Space Separation Modeling Approach for Nonlinear Distributed Parameter System. Ind Eng Chem Res 2011. [DOI: 10.1021/ie201556u] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mengling Wang
- Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, 130, Meilong Road, Shanghai 200237, China
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China
| | - Ning Li
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China
| | - Shaoyuan Li
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China
| | - Hongbo Shi
- Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, 130, Meilong Road, Shanghai 200237, China
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24
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Li N, Hua C, Wang H, Li S, Ge SS. Time–Space Decomposition-Based Generalized Predictive Control of a Transport-Reaction Process. Ind Eng Chem Res 2011. [DOI: 10.1021/ie101862c] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ning Li
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China
- Department of Electrical and Computer Engineering and Centre for Offshore Research and Engineering, National University of Singapore, 117576 Singapore
| | - Chen Hua
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China
| | - Haifeng Wang
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China
| | - Shaoyuan Li
- Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China
| | - Shuzhi Sam Ge
- Department of Electrical and Computer Engineering and Centre for Offshore Research and Engineering, National University of Singapore, 117576 Singapore
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25
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Bonis I, Xie W, Theodoropoulos C. A linear model predictive control algorithm for nonlinear large-scale distributed parameter systems. AIChE J 2011. [DOI: 10.1002/aic.12626] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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26
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Wang M, Li N, Li S. Local Modeling Approach for Spatially Distributed System Based on Interval Type-2 T-S Fuzzy Sets. Ind Eng Chem Res 2010. [DOI: 10.1021/ie901278r] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Mengling Wang
- Institute of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ning Li
- Institute of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Shaoyuan Li
- Institute of Automation, Shanghai Jiao Tong University, Shanghai 200240, China
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27
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Bombard I, Da Silva B, Dufour P, Laurent P. Experimental predictive control of the infrared cure of a powder coating: A non-linear distributed parameter model based approach. Chem Eng Sci 2010. [DOI: 10.1016/j.ces.2009.09.050] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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28
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Qi C, Li HX. Nonlinear dimension reduction based neural modeling for distributed parameter processes. Chem Eng Sci 2009. [DOI: 10.1016/j.ces.2009.06.053] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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29
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Ławryńczuk M. Explicit Nonlinear Predictive Control of a Distillation Column Based on Neural Models. Chem Eng Technol 2009. [DOI: 10.1002/ceat.200900074] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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30
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Wu W, Ding SY. Model Predictive Control of Nonlinear Distributed Parameter Systems Using Spatial Neural-Network Architectures. Ind Eng Chem Res 2008. [DOI: 10.1021/ie800474m] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wei Wu
- Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan, ROC
| | - San-Yin Ding
- Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan, ROC
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