Reset MPC-Based Control for Consensus of Multiagent Systems

In multiagent systems, conventional methods for addressing consensus problems typically rely on utilizing local and smooth control inputs; however, the focus of these methods is often on achieving asymptotic behavior, rather than transient response. In the existing literature, it has been shown that resetting some controller states can improve the transient response of linear systems. In this article, by utilizing a model predictive control (MPC)-based reset strategy, a new design framework is proposed that ensures not only the asymptotic stability but also the achievement of a desired transient performance. The proposed approach entails minimizing a quadratic cost function to determine the optimal after-reset values for controller states. The problem is then reformulated as a linear matrix inequality (LMI) optimization problem, which is solved to determine the reset law at specific reset instants, enabling the controller to achieve optimal performance and stability in a given multiagent system. The proposed method can be implemented in two distinct modalities. In the first one, characterized as distributed, when the reset conditions are satisfied in a particular agent at any given moment, only the controller state of that specific agent undergoes a reset in that moment, consequently, the transient performance improvement is exclusively limited to that particular agent. On the other hand, in the second modality, known as centralized, when the reset conditions hold in one agent, the controller states of all agents are reset simultaneously, thereby the transient performances of all agents concurrently experience improvement. Finally, numerical simulations are provided to demonstrate the superior performance of both suggested approaches in comparison with conventional reset methods. Furthermore, a comparison between the two suggested strategies is conducted.