Chapter 1
Introduction

1.1 Background and Motivation

Model predictive control (MPC), also known as receding horizon control, is an optimization-based control strategy. The fundamental concept of MPC dates back to the 1960s [1], and since the 1980s, it has been successfully applied to industrial systems to address constrained multivariable control problems. From that point onward, MPC emerged as an advanced control methodology and gathered increasing interest from both academia and industry. The term "model predictive control" comprises three elements-model, predictive, and control-each conveying essential aspects of the method's underlying principles.

Model: In practical control system design, engineers aim to gain deeper insights into the characteristics of physical systems and to construct accurate dynamic models. A well-defined model plays a critical role in controller synthesis. For systems lacking an explicit model, identification techniques can be employed to derive suitable representations. Despite potential mismatches and uncertainties in the identified models, they still serve as a solid foundation for controller design.

Predictive: The ability to make forward-looking predictions based on current conditions-coupled with strategic planning to achieve predefined objectives-is an innate biological capability. In the MPC framework, this predictive ability constitutes a core mechanism that enables the method to realize its superior performance characteristics.

Control: Control actions in MPC are determined by solving a mathematically tractable constrained optimization problem. This process entails necessary analysis of key properties of the resulting control system.

MPC offers the following features. It facilitates systematic and flexible handling of state and input constraints. It employs an optimization-centric strategy that can deliver near-optimal performance. The algorithm exhibits inherent robustness, which can be further enhanced through robust MPC formulations to mitigate external disturbances, parameter uncertainties, and noise. It harnesses predictive capabilities to proactively improve system performance. These attributes collectively establish MPC as a promising paradigm for future optimization-based control strategies.

Despite the promising prospects of MPC, the method relies on numerical optimization to compute control inputs, imposing stringent requirements on computational efficiency. Currently, most embedded system processors exhibit limited computational capabilities, thereby restricting the large-scale deployment of MPC. Furthermore, with the advancement of wireless communication technologies, the transmission of information between sensors and controllers is increasingly facilitated via wireless networks. Traditional communication protocols typically adopt time-triggered periodic transmission schemes, possibly resulting in communication and computation resource usage exceeding actual system needs, further constraining MPC applications.

Event-triggered control addresses these limitations by introducing an event mechanism and threshold condition such that updates occur only when specific criteria are met. The core concept behind the event-triggered control is to update the control only when the system violates predefined performance specifications. This enables a more favorable trade-off between control performance and overall communication load compared to conventional periodic schemes.

The integration of event-triggered control strategies with MPC can effectively harness this mechanism to reduce communication capacity and avoid unnecessary resource utilization. Moreover, it lowers the frequency of optimization problem-solving, thereby alleviating computational demands [2]. Event-triggered MPC continues to be a highly active research area, particularly in the context of systems subject to external disturbances, packet loss in communication, and multiagent cooperation-each scenario presenting compelling challenges and valuable research opportunities.

Control of multi-agent systems has become one of the prominent research topics in modern control theory. Within the framework of MPC, multi-agent coordination has achieved a number of representative advancements in recent years [3, 4]. However, the practical implementation of MPC in multi-agent systems remains limited due to the inherent complexity of inter-agent network communication and the computational demands of solving predictive control problems. Consequently, reducing the frequency of communication among agents as well as the individual computational burden associated with MPC updates presents a significant research challenge. Current investigations in this area are still in early stages. Event-triggered multi-agent MPC methods offer a compelling direction for further exploration. By selectively updating control actions only when specific triggering conditions are met, such approaches have the potential to improve scalability and efficiency while preserving desirable overall system performance.

This book is dedicated to exploring event-triggered MPC methodologies, with focused investigations into four main areas:

• Event-based two-phase MPC for nonlinear continuous-time systems.
• Event-based aperiodic sampling MPC for nonlinear discrete-time systems.
• Event-triggered MPC for disturbed systems.
• Periodic sampling-based event-triggered MPC for distributed systems.

Through a detailed examination of event-triggering mechanisms, robust handling of system uncertainties, and the study of inter-agent communication protocols, the objective is to reduce communication load and minimize the frequency of optimization computations. These efforts aim to enhance the practical value of event-triggered MPC and facilitate its wider application across engineering domains.

1.2 Model Predictive Control

Modern industrial control systems are influenced by a variety of factors. In addition to physical constraints such as actuator saturation, considerations of safety, process requirements, and economic performance must also be addressed. For instance, system parameters like pressure and temperature must be maintained within permissible limits. When dealing with constrained systems, the goal is not only to achieve stabilization but also to ensure enhanced performance. Moreover, industrial processes are often characterized by high-dimensional complexity, making the precise formulation of mathematical models exceedingly difficult. Due to external disturbances and parameter variations, uncertainties arise that render optimal control strategies-derived solely from idealized models-ineffective in practical applications. Such mismatches may even result in severe degradation of control performance. Consequently, the field of control engineering demands a new class of optimization-based methodologies that can simultaneously satisfy various system constraints, optimize performance indicators, and exhibit robustness against uncertainties and disturbances.

To address the aforementioned needs, MPC was proposed by researchers in the 1970s. Due to its capacity to handle complex multivariable control problems and its ability to enforce input, output, and state constraints in real time within an optimization framework, alongside its inherent disturbance-rejection capabilities, MPC has found extensive applications in practical industrial processes. Its application spans critical military and civilian sectors, including petroleum, chemical engineering, transportation, and aerospace [5-7]. In parallel, the theoretical development of MPC has attracted considerable attention from the research community [8, 9].

The underlying mechanism of MPC can be described as follows: At each sampling instant, the controller utilizes current state measurements to formulate and solve an optimization problem over a finite prediction horizon. The computed control sequence is then implemented by applying the first-or in some cases, a subset-of its elements to the plant. At the next sampling instant, the optimization problem is updated with new measurements and solved, and this process continues in a receding horizon fashion. MPC is particularly well-suited for addressing multivariable constrained optimization problems that Proportional-Integral-Derivative (PID) control struggles to manage. As a model-based control strategy, MPC is capable of handling nonlinear, time-varying, and time-delay systems subject to complex constraints. The MPC algorithm typically involves three main steps:

• Prediction: Estimating the future evolution of the system using a predictive model.
• Optimization: Solving a finite-horizon constrained optimization problem via numerical methods.
• Implementation: Implementing a portion of the optimal control sequence on the actual system.

Compared with other control methodologies, the primary characteristics of MPC include (but not limited to):

• Model-based Prediction: MPC relies on a model that describes the dynamic behavior of the controlled system. This model is used to forecast future system responses, hence the term "predictive model"-which is the reason MPC is considered a model-based control strategy. Within the MPC framework, the model serves as a tool to predict the system's future trajectory based on current states and anticipated future inputs. Notably, the formulation of the model itself is not restricted to any specific representation. To adjust future outputs toward desired reference trajectories, control...