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However, with the growth of the scale of industrial processes leading to increasing computational complexity, the online optimization capability of the double-layer model predictive control algorithm is challenged, exacerbating the difficulty of the widespread implementation of this algorithm in the industry. This paper proposes a distributed double-layer model predictive control algorithm based on dual decomposition for multivariate constrained systems to reduce the computational complexity of process control. Firstly, to solve the problem that the original dual decomposition method does not apply to constrained systems, two improved dual decomposition model prediction control methods are proposed: the dual decomposition method based on the quadratic programming in the subsystem and the dual decomposition method based on constraint zones, respectively. It is proved that the latter will certainly converge to the constraint boundaries with appropriate convergence factors for the controlled variables. The online optimization ability of the proposed two methods is compared in discussion and simulation, concluding that the dual decomposition method based on the constraint zones exhibits superior online optimization ability. Further, a distributed double-layer model predictive control algorithm with dual decomposition based on constraint zones is proposed. Different from the objective function of the original dual decomposition model predictive control, the proposed algorithm\u2019s dynamic control-layer objective function simultaneously tracks the steady-state optimization values of the controlled and manipulated variables, giving the optimal solution formulation of the optimization problem consisting of this objective function and the constraints. The algorithm proposed in this paper achieves the control goals while significantly reducing the computational complexity and has research significance for promoting the industrial implementation of double-layer model predictive control.<\/jats:p>","DOI":"10.3390\/e25010017","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T02:09:03Z","timestamp":1671761343000},"page":"17","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Decomposition\u2013Coordination of Double-Layer MPC for Constrained Systems"],"prefix":"10.3390","volume":"25","author":[{"given":"Hongrui","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Key Laboratory of Networked Control Systems, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengbin","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Key Laboratory of Networked Control Systems, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijia","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Key Laboratory of Networked Control Systems, Chinese Academy of Sciences, Shenyang 110016, China"},{"name":"Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.arcontrol.2008.03.003","article-title":"Advanced control and on-line process optimization in multilayer structures","volume":"32","author":"Tatjewski","year":"2008","journal-title":"Annu. 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