# Hierarchical Coordinated Predictive Control of Multiagent Systems for Process Industries
## 6 Conclusions  
In this study, a novel hierarchical coordinated predictive control strategy of multiagent systems for process industries is proposed to perform efficient, accurate and energy-saving control for process industries with integrated \"distributed-decentralized\" characteristics based on the coordinated work of agents. To verify the effectiveness of the HCPC strategy in terms of control performance and energy-saving, several numerical calculations were performed in eight scenarios based on a heating device with 6 microwave sources. In all numerical calculations, the input electric power of each microwave source is the control variable or input and the temperature of each measurement point is the output of the system. First, each microwave source agent iteratively obtains consistent open-loop prediction with integrated \"distributed-decentralized\" characteristics. Then, each microwave source agent performs calculations to obtain an independent control scheme based on the consistent open-loop prediction and determines its priority by playing games with the economic performance of independent control schemes as the evaluation criterion. Finally, each microwave source agent solves an optimization problem and obtains control input increment that combines control performance and energy-saving based on its priority and consistent open-loop prediction. Numerical results of eight microwave heating control scenarios and corresponding qualitative and quantitative analyses demonstrate that the proposed HCPC strategy can provide satisfactory control performance while the power consumption is much lower than that of the widely used CMPC strategy. The superior control performance of the proposed HCPC strategy and its effectiveness in reducing energy consumption in engineering applications involving multiagent systems were verified, and this approach can assist in the development of new quality productive forces.  
To further improve the control performance, economic performance and generalizability of the proposed control strategy, we are currently working on (i) designing an evolutionary mechanism of communication topologies for multiagent systems, the mechanism is able to optimize the communication topology in real time by comprehensively considering the factors such as interactions between agents, communication constraints and system performance, resulting in a highly efficient, flexible and robust communication topology that is able to meet complex requirements from tasks and environments, (ii) developing a game-based meta-learning strategy of multiagent systems for complex industrial processes and (iii) investigating an overall scheme for intelligent modeling and control of heterogeneous nonlinear multiagent systems for large-scale complex industrial processes.  
Conceptualization, C.C., B.Y. and Q.X.; methodology, C.C. and B.Y.; software, C.C.; validation, C.C. and Q.X.; formal analysis, C.C. and Q.X.; investigation, C.C. and Q.X.; resources, B.Y.; data curation, C.C.; writing--original draft preparation, C.C. and Q.X.; writing--review and editing, B.Y.; visualization, C.C.; supervision, B.Y.; project administration, C.C. and B.Y.; funding acquisition, B.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 62363019.  
Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.