# Hierarchical Coordinated Predictive Control of Multiagent Systems for Process Industries
## 1 Introduction  
As an advanced control method, model predictive control (MPC) has been widely used in the process industry, aerospace, water treatment, energy systems and many other fields [1, 2, 3, 4, 5]. The success of MPC is attributed to its ability to perform repeated real-time optimization over time based on the system model and to its excellent performance in handling the inputs, outputs, and process constraints of large multivariable systems, which enables MPC to perform well in most control scenarios [6]. However, with the continuous development of advanced communication and control technologies in recent decades, the automation, efficiency and networking of industrial processes have increased, and the scale of process industries such as the chemical, metallurgical, pharmaceutical and food industries has expanded. The effectiveness of MPC is continuously challenged by the increasing number of controllers, control objectives, decision variables and process constraints, as well as the vast spatial distribution of controllers. While conventional centralized MPC methods can achieve relatively good controlperformance with global information, architectures with coordinated control by multiple distributed or decentralized MPC systems are more suitable for large-scale processes in terms of engineering practice [7], and many studies have been conducted on such architectures [8; 9; 10]. In distributed or decentralized MPC architectures, a large-scale system is decomposed into multiple small-scale subsystems with a local controller, which retains the processing capability of the constraints of centralized MPC while enhancing the flexibility and the economy of computation [11]. The difference between distributed and decentralized architectures is whether or not the subsystems interact. However, both distributed and decentralized characteristics often arise in large-scale process industries, where distributed characteristics arise between subsystems with strong interactions and the opposite is true for decentralized characteristics. The integrated \"distributed-decentralized\" characteristics of process industries make it reasonable to utilize a multiagent system (MAS), which is highly modular, is highly scalable and features easily described interactions between subsystems, as the computational paradigm to provide analysis and solutions for process industries. Therefore, this study was carried out using an MAS as the computational paradigm. In MASs, different topologies of interactions (active communication or passive sensing) among agents can be represented by differently structured graphs [12; 13]. While complete graphs can be used to describe fully distributed systems, noncomplete graphs with integrated \"distributed-decentralized\" characteristics are more common. Existing studies have focused mainly on achieving consensus on states of interest through a series of effective interactions and control actions [14]. From a narrow perspective, many studies have focused on consensus and its derivatives, such as the formation, rendezvous and swarming of agents in different situations, and a series of consensus schemes have been proposed [15; 16; 17; 18; 19; 20; 21]. However, despite the differences in agent dynamics and consensus schemes, these studies involve the formation of a certain rigid pattern of the states or outputs of agents, which may lead to poor flexibility in decision-making. To extend the control of MASs from narrow consensus to coordination and cooperation, many researchers have investigated coordination and cooperation in scenarios such as clustering and task allocation [22; 23], intelligent transportation [24; 25], heat processing [26], electric power systems [27], demand response in society [28; 29] and resilience [30] using the MAS paradigm. In addition, game theory has been utilized in some studies to analyze the interrelationships between agents and their impact on information interactions. For example, cooperative decision-making for on-ramp merging was achieved by [PERSON] et al.