# Hierarchical Coordinated Predictive Control of Multiagent Systems for Process Industries
## 1 Introduction
[31] through coalitional game theory, which coordinates the communication and decision-making of autonomous vehicles. [PERSON] [32] considered ship-collision avoidance based on differential game implementation for nautical safety control. The architectural diversity and high decision-making flexibility of these generalized MASs for coordinated cooperation suggest that the utilization of the MAS paradigm for solving distributed-decentralized control problems in complex process industries or other complex systems has a promising future. Our study develops a novel hierarchical coordinated control strategy for process industries based on the MAS paradigm from a generalized perspective. Furthermore, economic performance needs to be considered along with control performance to address the challenges of energy consumption and economic efficiency due to environmentally friendly policies and increasing global competition. In summary, a novel hierarchical coordinated predictive control (HCPC) strategy of MASs for process industries is proposed. The proposed strategy aims to achieve efficient and accurate control of process industries with integrated \"distributed-decentralized\" characteristics by coordinating among agents while improving economic performance by reducing energy consumption. First, each agent iteratively collects open-loop predictions of other agents from its neighbors in a distributed way utilizing a \"leader-follower\"-like protocol and achieves consistent open-loop prediction. Then, each agent provides its control scheme independently, with the consistent open-loop prediction as the basis for the closed-loop prediction, and plays a game with each of its adjacency agents to determine its priority,using the economic performance of the control scheme as the criterion. Subsequently, each agent solves and obtains its optimal control input increments that balance control performance and energy-saving on the basis of the priority. Finally, the proposed HCPC strategy is utilized to control the temperature of a ceramic block in multisource high-power microwave heating processes under seven different communication topologies of agents, and numerical results are compared with the centralized model predictive control (CMPC), which verify that the proposed HCPC strategy can provide satisfactory control performance and reduce the energy consumption. The main contributions of our study are as follows:  
1. A novel hierarchical coordinated predictive control strategy is proposed utilizing MAS as the computational paradigm for accurate energy-saving control for large-scale process industries with integrated \"distributed-decentralized\" characteristics;
2. An implementation of consistent open-loop prediction is designed that utilizes a \"leader-follower\"-like protocol to enable agents to collect decentralized information from their neighbors in a distributed way at each time step, thereby providing a consistent prediction basis for closed-loop control;
3. A game-based prioritization method is designed to determine the priority of each agent at each time step through an autonomous game with the economic performance of the independent control scheme as the criterion;
4. A sequential game-based model predictive control method is designed for dynamic predictive control according to real-time changing priorities, which can effectively reduce energy consumption.