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Journal articles on the topic 'Explicit Approximated Model Predictive Control'

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Author: Grafiati

Published: 11 March 2023

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1

Pregelj, Boštjan, and Samo Gerkšič. "Hybrid explicit model predictive control of a nonlinear process approximated with a piecewise affine model." Journal of Process Control 20, no. 7 (August 2010): 832–39. http://dx.doi.org/10.1016/j.jprocont.2010.05.002.

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2

Grancharova, Alexandra, and Tor A. Johansen. "Reduced Dimension Approach to Approximate Explicit Model Predictive Control." IFAC Proceedings Volumes 36, no. 18 (September 2003): 531–36. http://dx.doi.org/10.1016/s1474-6670(17)34723-7.

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3

Bussell, E. H., and N. J. Cunniffe. "Applying optimal control theory to a spatial simulation model of sudden oak death: ongoing surveillance protects tanoak while conserving biodiversity." Journal of The Royal Society Interface 17, no. 165 (April 2020): 20190671. http://dx.doi.org/10.1098/rsif.2019.0671.

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Sudden oak death has devastated tree populations across California. However, management might still slow disease spread at local scales. We demonstrate how to unambiguously characterize effective, local management strategies using a detailed, spatially explicit simulation model of spread in a single forest stand. This pre-existing, parameterized simulation is approximated here by a carefully calibrated, non-spatial model, explicitly constructed to be sufficiently simple to allow optimal control theory (OCT) to be applied. By lifting management strategies from the approximate model to the detailed simulation, effective time-dependent controls can be identified. These protect tanoak—a culturally and ecologically important species—while conserving forest biodiversity within a limited budget. We also consider model predictive control, in which both the approximating model and optimal control are repeatedly updated as the epidemic progresses. This allows management which is robust to both parameter uncertainty and systematic differences between simulation and approximate models. Including the costs of disease surveillance then introduces an optimal intensity of surveillance. Our study demonstrates that successful control of sudden oak death is likely to rely on adaptive strategies updated via ongoing surveillance. More broadly, it illustrates how OCT can inform effective real-world management, even when underpinning disease spread models are highly complex.

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4

Johansen, T. A., and A. Grancharova. "Approximate explicit constrained linear model predictive control via orthogonal search tree." IEEE Transactions on Automatic Control 48, no. 5 (May 2003): 810–15. http://dx.doi.org/10.1109/tac.2003.811259.

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5

Johansen, Tor A., and Alexandra Grancharova. "APPROXIMATE EXPLICIT MODEL PREDICTIVE CONTROL IMPLEMENTED VIA ORTHOGONAL SEARCH TREE PARTITIONING." IFAC Proceedings Volumes 35, no. 1 (2002): 195–200. http://dx.doi.org/10.3182/20020721-6-es-1901.00601.

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6

Sun, Weiquan, Min Li, and Kexin Wang. "Approximate explicit model predictive control using high-level canonical piecewise-affine functions." International Journal of Automation and Control 6, no. 1 (2012): 66. http://dx.doi.org/10.1504/ijaac.2012.045441.

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7

Bakaráč, Peter, and Michal Kvasnica. "Approximate explicit robust model predictive control of a CSTR with fast reactions." Chemical Papers 73, no. 3 (November 9, 2018): 611–18. http://dx.doi.org/10.1007/s11696-018-0630-4.

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8

Charitopoulos, Vassilis M., Lazaros G. Papageorgiou, and Vivek Dua. "Multi Set-Point Explicit Model Predictive Control for Nonlinear Process Systems." Processes 9, no. 7 (July 2, 2021): 1156. http://dx.doi.org/10.3390/pr9071156.

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In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

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9

Kiš, Karol, and Martin Klaučo. "Neural network based explicit MPC for chemical reactor control." Acta Chimica Slovaca 12, no. 2 (October 1, 2019): 218–23. http://dx.doi.org/10.2478/acs-2019-0030.

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Abstract In this paper, implementation of deep neural networks applied in process control is presented. In our approach, training of the neural network is based on model predictive control, which is popular for its ability to be tuned by the weighting matrices and for it respecting the system constraints. A neural network that can approximate the MPC behavior by mimicking the control input trajectory while the constraints on states and control input remain unimpaired by the weighting matrices is introduced. This approach is demonstrated in a simulation case study involving a continuous stirred tank reactor where a multi-component chemical reaction takes place.

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10

Ławryńczuk, Maciej, Piotr M. Marusak, Patryk Chaber, and Dawid Seredyński. "Initialisation of Optimisation Solvers for Nonlinear Model Predictive Control: Classical vs. Hybrid Methods." Energies 15, no. 7 (March 28, 2022): 2483. http://dx.doi.org/10.3390/en15072483.

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In nonlinear Model Predictive Control (MPC) algorithms, the number of cost-function evaluations and the resulting calculation time depend on the initial solution to the nonlinear optimisation task. Since calculations must be performed fast on-line, the objective is to minimise these indicators. This work discusses twelve initialisation strategies for nonlinear MPC. In general, three categories of strategies are discussed: (a) five simple strategies, including constant and random guesses as well as the one based on the previous optimal solution, (b) three strategies that utilise a neural approximator and an inverse nonlinear static model of the process and (c) four hybrid original methods developed by the authors in which an auxiliary quadratic optimisation task is solved or an explicit MPC controller is used; in both approaches, linear or successively linearised on-line models can be used. Efficiency of all methods is thoroughly discussed for a neutralisation reactor benchmark process and some of them are evaluated for a robot manipulator, which is a multivariable process. Two strategies are found to be the fastest and most robust to model imperfections and disturbances acting on the process: the hybrid strategy with an auxiliary explicit MPC controller based on a successively linearised model and the method which uses the optimal solution obtained at the previous sampling instant. Concerning the hybrid strategies, since a simplified model is used in the auxiliary controller, they perform much better than the approximation-based ones with complex neural networks. It is because the auxiliary controller has a negative feedback mechanism that allows it to compensate model errors and disturbances efficiently. Thus, when the auxiliary MPC controller based on a successively linearised model is available, it may be successfully and efficiently used for the initialisation of nonlinear MPC, whereas quite sophisticated methods based on a neural approximator are very disappointing.

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11

Du, Yanli, and Quanmin Zhu. "Decentralized adaptive force/position control of reconfigurable manipulator based on soft sensors." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 232, no. 9 (June 18, 2018): 1260–71. http://dx.doi.org/10.1177/0959651818779848.

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Two soft sensor control methods are proposed to deal with force/position control of reconfigurable manipulator without using wrist force sensors. First, modeling uncertainties and coupled interconnection terms between the subsystems are approximated by using adaptive radial basis function neural network, and the soft sensor model of the contact force is established by means of adaptive radial basis function neural network to design hybrid force/position controller. Then, a decentralized explicit force controller based on impedance inner control is designed. The reference trajectory of impedance inner controller is provided by explicit force controller based on the fuzzy prediction, and the soft sensor model of the contact force is established by the fuzzy system. The proposed soft sensor models do not request the exact mathematical relationship between the contact force and auxiliary variables and provide a feasible method to replace the wrist force sensors which are expensive and easily influenced by the external factors. Compared with the observer method, the proposed soft sensor methods do not depend on the knowledge about the model of reconfigurable manipulator, so provide better position and force tracking precision.

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12

Sasaki, Yasuo, and Daisuke Tsubakino. "Designs of Feedback Controllers for Fluid Flows Based On Model Predictive Control and Regression Analysis." Energies 13, no. 6 (March 12, 2020): 1325. http://dx.doi.org/10.3390/en13061325.

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Complexity of online computation is a drawback of model predictive control (MPC) when applied to the Navier–Stokes equations. To reduce the computational complexity, we propose a method to approximate the MPC with an explicit control law by using regression analysis. In this paper, we extracted two state-feedback control laws and two output-feedback control laws for flow around a cylinder as a benchmark. The state-feedback control laws that feed back different quantities to each other were extracted by ridge regression, and the two output-feedback control laws, whose measurement output is the surface pressure, were extracted by ridge regression and Gaussian process regression. In numerical simulations, the state-feedback control laws were able to suppress vortex shedding almost completely. While the output-feedback control laws could not suppress vortex shedding completely, they moderately improved the drag of the cylinder. Moreover, we confirmed that these control laws have some degree of robustness to the change in the Reynolds number. The computation times of the control input in all the extracted control laws were considerably shorter than that of the MPC.

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13

Zhao, Hong Shan, Xiao Ming Lan, Yu Si Zhao, and Yang Xia. "Nonlinear Prediction Control of Synchronous Generator Excitation Based on Subsection Approximation." Advanced Materials Research 590 (November 2012): 155–60. http://dx.doi.org/10.4028/www.scientific.net/amr.590.155.

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This paper presents a subsection approximate nonlinear model predictive control (SANMPC) method for synchronous generator excitation control in the regional power grid. The proposed SANMPC considers the voltage as the reference trajectories and the change range of active power, reactive power and voltage as unequal constraints. Segmenting for a sampling interval, it uses sampled values and the control input initial value at the current sampling moment to predict the state at each segment by the Explicit Euler method. The predictive equations of the next sampling moment can be obtained by the predictive state and the control input at the penultimate segment, and form the optimal control problem which may be solved by the interior-point method. We take advantage of a four-machine power system to verify the effectiveness of the proposed SANMPC method under MATLAB platform. The simulating results show that the SANMPC method is simple and efficient, and greatly improves the transient stability compared with the conventional controller both.

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14

Bussell, E. H., C. E. Dangerfield, C. A. Gilligan, and N. J. Cunniffe. "Applying optimal control theory to complex epidemiological models to inform real-world disease management." Philosophical Transactions of the Royal Society B: Biological Sciences 374, no. 1776 (May 20, 2019): 20180284. http://dx.doi.org/10.1098/rstb.2018.0284.

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Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach—optimal control theory—allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.

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15

Bartlett, Peter L., Andrea Montanari, and Alexander Rakhlin. "Deep learning: a statistical viewpoint." Acta Numerica 30 (May 2021): 87–201. http://dx.doi.org/10.1017/s0962492921000027.

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The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting, that is, accurate predictions despite overfitting training data. In this article, we survey recent progress in statistical learning theory that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behaviour of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favourable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

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16

Radac, Mircea-Bogdan, and Timotei Lala. "Hierarchical Cognitive Control for Unknown Dynamic Systems Tracking." Mathematics 9, no. 21 (October 29, 2021): 2752. http://dx.doi.org/10.3390/math9212752.

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A general control system tracking learning framework is proposed, by which an optimal learned tracking behavior called ‘primitive’ is extrapolated to new unseen trajectories without requiring relearning. This is considered intelligent behavior and strongly related to the neuro-motor cognitive control of biological (human-like) systems that deliver suboptimal executions for tasks outside of their current knowledge base, by using previously memorized experience. However, biological systems do not solve explicit mathematical equations for solving learning and prediction tasks. This stimulates the proposed hierarchical cognitive-like learning framework, based on state-of-the-art model-free control: (1) at the low-level L1, an approximated iterative Value Iteration for linearizing the closed-loop system (CLS) behavior by a linear reference model output tracking is first employed; (2) an experiment-driven Iterative Learning Control (EDILC) applied to the CLS from the reference input to the controlled output learns simple tracking tasks called ‘primitives’ in the secondary L2 level, and (3) the tertiary level L3 extrapolates the primitives’ optimal tracking behavior to new tracking tasks without trial-based relearning. The learning framework relies only on input-output system data to build a virtual state space representation of the underlying controlled system that is assumed to be observable. It has been shown to be effective by experimental validation on a representative, coupled, nonlinear, multivariable real-world system. Able to cope with new unseen scenarios in an optimal fashion, the hierarchical learning framework is an advance toward cognitive control systems.

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17

Danielson, Claus, and Francesco Borrelli. "Symmetric Explicit Model Predictive Control." IFAC Proceedings Volumes 45, no. 17 (2012): 132–37. http://dx.doi.org/10.3182/20120823-5-nl-3013.00083.

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18

Lamburn, Darren, Peter Gibbens, and Steven Dumble. "Explicit efficient constrained model predictive control." International Journal of Automation and Control 10, no. 4 (2016): 329. http://dx.doi.org/10.1504/ijaac.2016.079538.

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19

Takács, Gergely, Gabriel Batista, Martin Gulan, and Boris Rohaľ-Ilkiv. "Embedded explicit model predictive vibration control." Mechatronics 36 (June 2016): 54–62. http://dx.doi.org/10.1016/j.mechatronics.2016.04.008.

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20

Hegrenæs, Øyvind, Jan Tommy Gravdahl, and Petter Tøndel. "Spacecraft attitude control using explicit model predictive control." Automatica 41, no. 12 (December 2005): 2107–14. http://dx.doi.org/10.1016/j.automatica.2005.06.015.

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21

Scibilia, Francesco, Morten Hovd, and Sorin Olaru. "Explicit model predictive control via Delaunay tessellations." Journal Européen des Systèmes Automatisés 46, no. 2-3 (April 30, 2012): 267–90. http://dx.doi.org/10.3166/jesa.46.267-290.

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22

Sheikhbahaei, Reza, Aria Alasty, and Gholamreza Vossoughi. "Robust fault tolerant explicit model predictive control." Automatica 97 (November 2018): 248–53. http://dx.doi.org/10.1016/j.automatica.2018.08.013.

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23

Zhong, Guo Qi, and Zhi Yuan Liu. "Cooperation-Based Explicit Distributed Model Predictive Control." Applied Mechanics and Materials 380-384 (August 2013): 707–11. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.707.

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in this paper, an explicit distributed model predictive control method for a class of linear system with control information coupling by means of multi-parametric programming is established. In order to get close to the optimal performance of centralized MPC, the method is based on cooperation, which solving weighted global cost instead of local ones. The method is employed on distillation column control problem to verify the efficiency.

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24

Fonseca, Daniel Guerra Vale da, André Felipe O. de A. Dantas, Carlos Eduardo Trabuco Dórea, and André Laurindo Maitelli. "Explicit GPC Control Applied to an Approximated Linearized Crane System." Journal of Control Science and Engineering 2019 (February 3, 2019): 1–13. http://dx.doi.org/10.1155/2019/3612634.

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This paper proposes a MIMO Explicit Generalized Predictive Control (EGPC) for minimizing payload oscillation of a Gantry Crane System subject to input and output constraints. In order to control the crane system efficiently, the traditional GPC formulation, based on online Quadratic Programming (QP), is rewritten as a multiparametric quadratic programming problem (mp-QP). An explicit Piecewise Affine (PWA) control law is obtained and holds the same performance as online QP. To test effectiveness, the proposed method is compared with two GPC formulations: one that handle constraints (CGPC) and another that does not handle constraints (UGPC). Results show that both EGPC and CGPC have better performance, reducing the payload swing when compared to UGPC. Also both EGPC and CGPC are able to control the system without constraint violation. When comparing EGPC to CGPC, the first is able to calculate (during time step) the control action faster than the second. The simulations prove that the overall performance of EGPC is superior to the other used formulations.

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25

Holaza, Juraj, Juraj Oravec, Michal Kvasnica, Raphael Dyrska, Martin Mönnigmann, and Miroslav Fikar. "Accelerating Explicit Model Predictive Control by Constraint Sorting." IFAC-PapersOnLine 53, no. 2 (2020): 11356–61. http://dx.doi.org/10.1016/j.ifacol.2020.12.545.

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26

., Nitin Prajapati. "EXPLICIT MODEL PREDICTIVE CONTROL OF FAST DYNAMIC SYSTEM." International Journal of Research in Engineering and Technology 02, no. 04 (April 25, 2013): 692–95. http://dx.doi.org/10.15623/ijret.2013.0204051.

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27

Tøndel, Petter, and Tor A. Johansen. "COMPLEXITY REDUCTION IN EXPLICIT LINEAR MODEL PREDICTIVE CONTROL." IFAC Proceedings Volumes 35, no. 1 (2002): 189–94. http://dx.doi.org/10.3182/20020721-6-es-1901.00600.

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28

Oberdieck, Richard, and Efstratios N. Pistikopoulos. "Explicit hybrid model-predictive control: The exact solution." Automatica 58 (August 2015): 152–59. http://dx.doi.org/10.1016/j.automatica.2015.05.021.

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29

Oberdieck, Richard, Nikolaos A. Diangelakis, and Efstratios N. Pistikopoulos. "Explicit model predictive control: A connected-graph approach." Automatica 76 (February 2017): 103–12. http://dx.doi.org/10.1016/j.automatica.2016.10.005.

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30

Nguyen, Hoai-Nam, Sorin Olaru, and Morten Hovd. "A patchy approximation of explicit model predictive control." International Journal of Control 85, no. 12 (December 2012): 1929–41. http://dx.doi.org/10.1080/00207179.2012.713516.

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31

Yin, Fang Chen, Geng Sheng Ma, Ya Feng Ji, Zhong Ping Li, and Dian Hua Zhang. "Explicit Indirect Predictive Control Algorithm in the Application of AWC Control." Advanced Materials Research 926-930 (May 2014): 1344–47. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.1344.

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Using the characteristics of prediction model, rolling optimization and feedback correction, a AWC system based on explicit indirect predictive control was designed, and its control performance was simulated based on a hot strip continuous mill. The results show that explicit indirect predictive control achieves better control effects than the normal PID on response time and steady precision with matching model; when model mismatching is caused by inaccuracy of plastic coefficient and pure delay time, the normal PID is overshot or even oscillation, but the control performance of the explicit indirect predictive control is not influenced by model parameter variations [1].

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32

Tavernini, Davide, Mathias Metzler, Patrick Gruber, and Aldo Sorniotti. "Explicit Nonlinear Model Predictive Control for Electric Vehicle Traction Control." IEEE Transactions on Control Systems Technology 27, no. 4 (July 2019): 1438–51. http://dx.doi.org/10.1109/tcst.2018.2837097.

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33

Lee, Junho, and Hyuk-Jun Chang. "Analysis of explicit model predictive control for path-following control." PLOS ONE 13, no. 3 (March 13, 2018): e0194110. http://dx.doi.org/10.1371/journal.pone.0194110.

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34

Kallies, Christian, Mohamed Ibrahim, and Rolf Findeisen. "Continuous-Time Approximated Parametric Output-Feedback Nonlinear Model Predictive Control." IFAC-PapersOnLine 54, no. 6 (2021): 251–56. http://dx.doi.org/10.1016/j.ifacol.2021.08.553.

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35

Ganesh, Hari S., Styliani Avraamidou, Iosif Pappas, and Efstratios N. Pistikopoulos. "Explicit Model Predictive Control for a Highly Interacting System." IFAC-PapersOnLine 55, no. 1 (2022): 247–52. http://dx.doi.org/10.1016/j.ifacol.2022.04.041.

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36

Grancharova, Alexandra, and Tor A. Johansen. "Explicit Approaches to Constrained Model Predictive Control: A Survey." Modeling, Identification and Control: A Norwegian Research Bulletin 25, no. 3 (2004): 131–57. http://dx.doi.org/10.4173/mic.2004.3.1.

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37

Mariethoz, Sébastien, Alexander Domahidi, and Manfred Morari. "High-Bandwidth Explicit Model Predictive Control of Electrical Drives." IEEE Transactions on Industry Applications 48, no. 6 (November 2012): 1980–92. http://dx.doi.org/10.1109/tia.2012.2226198.

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38

Scaglioni, Bruno, Luca Previtera, James Martin, Joseph Norton, Keith L. Obstein, and Pietro Valdastri. "Explicit Model Predictive Control of a Magnetic Flexible Endoscope." IEEE Robotics and Automation Letters 4, no. 2 (April 2019): 716–23. http://dx.doi.org/10.1109/lra.2019.2893418.

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39

Domínguez, Luis F., and Efstratios N. Pistikopoulos. "Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control." Industrial & Engineering Chemistry Research 50, no. 2 (January 19, 2011): 609–19. http://dx.doi.org/10.1021/ie100245z.

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40

Wallace, Matt, Steven Spielberg Pon Kumar, and Prashant Mhaskar. "Offset-Free Model Predictive Control with Explicit Performance Specification." Industrial & Engineering Chemistry Research 55, no. 4 (January 20, 2016): 995–1003. http://dx.doi.org/10.1021/acs.iecr.5b03772.

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41

Kvasnica, Michal, Juraj Hledík, Ivana Rauová, and Miroslav Fikar. "Complexity reduction of explicit model predictive control via separation." Automatica 49, no. 6 (June 2013): 1776–81. http://dx.doi.org/10.1016/j.automatica.2013.02.018.

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42

Patne, Vaishali, Deepak Ingole, and Dayaram Sonawane. "FPGA Implementation Framework for Explicit Hybrid Model Predictive Control." IFAC-PapersOnLine 53, no. 1 (2020): 362–67. http://dx.doi.org/10.1016/j.ifacol.2020.06.061.

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43

Gupta, Arun, Sharad Bhartiya, and P. S. V. Nataraj. "Explicit-Model Predictive Control: A simulation based scalability study." IFAC Proceedings Volumes 45, no. 15 (2012): 204–9. http://dx.doi.org/10.3182/20120710-4-sg-2026.00072.

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44

Liu, C., W.-H. Chen, and J. Andrews. "Explicit non-linear model predictive control for autonomous helicopters." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 226, no. 9 (November 21, 2011): 1171–82. http://dx.doi.org/10.1177/0954410011418585.

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45

Nașcu, Ioana, Richard Oberdieck, and Efstratios N. Pistikopoulos. "Explicit hybrid model predictive control strategies for intravenous anaesthesia." Computers & Chemical Engineering 106 (November 2017): 814–25. http://dx.doi.org/10.1016/j.compchemeng.2017.01.033.

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46

Pistikopoulos, E. N. "Perspectives in multiparametric programming and explicit model predictive control." AIChE Journal 55, no. 8 (August 2009): 1918–25. http://dx.doi.org/10.1002/aic.11965.

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47

Hovland, Svein, Jan Tommy Gravdahl, and Karen E. Willcox. "Explicit Model Predictive Control for Large-Scale Systems via Model Reduction." Journal of Guidance, Control, and Dynamics 31, no. 4 (July 2008): 918–26. http://dx.doi.org/10.2514/1.33079.

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48

Bayat, Farhad, and Tor Arne Johansen. "Multi-Resolution Explicit Model Predictive Control: Delta-Model Formulation and Approximation." IEEE Transactions on Automatic Control 58, no. 11 (November 2013): 2979–84. http://dx.doi.org/10.1109/tac.2013.2259982.

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49

Johansen, Tor A., Warren Jackson, Robert Schreiber, and Petter Tondel. "Hardware Synthesis of Explicit Model Predictive Controllers." IEEE Transactions on Control Systems Technology 15, no. 1 (January 2007): 191–97. http://dx.doi.org/10.1109/tcst.2006.883206.

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Drgoňa, Ján, Karol Kiš, Aaron Tuor, Draguna Vrabie, and Martin Klaučo. "Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems." Journal of Process Control 116 (August 2022): 80–92. http://dx.doi.org/10.1016/j.jprocont.2022.06.001.

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