Global Performance Guarantees for Localized Model Predictive Control

Jing Shuang Li;Carmen Amo Alonso
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Abstract

Recent advances in model predictive control (MPC) leverage local communication constraints to produce localized MPC algorithms whose complexities scale independently of total network size. However, no characterization is available regarding global performance, i.e. whether localized MPC (with communication constraints) performs just as well as global MPC (no communication constraints). In this paper, we provide analysis and guarantees on global performance of localized MPC — in particular, we derive sufficient conditions for optimal global performance in the presence of local communication constraints. We also present an algorithm to determine the communication structure for a given system that will preserve performance while minimizing computational complexity. The effectiveness of the algorithm is verified in simulations, and additional relationships between network properties and performance-preserving communication constraints are characterized. A striking finding is that in a network of 121 coupled pendula, each node only needs to communicate with its immediate neighbors to preserve optimal global performance. Overall, this work offers theoretical understanding on the effect of local communication on global performance, and provides practitioners with the tools necessary to deploy localized model predictive control by establishing a rigorous method of selecting local communication constraints. This work also demonstrates — surprisingly — that the inclusion of severe communication constraints need not compromise global performance.
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局部模型预测控制的全局性能保证
模型预测控制(MPC)的最新进展利用局部通信约束来产生局部MPC算法,其复杂性与总网络大小无关。然而,没有关于全局性能的特征,即局部MPC(具有通信约束)是否与全局MPC(没有通信约束)一样好。在本文中,我们对局部MPC的全局性能进行了分析和保证——特别是,我们推导了在存在局部通信约束的情况下最优全局性能的充分条件。我们还提出了一种算法来确定给定系统的通信结构,该算法将在最小化计算复杂性的同时保持性能。仿真验证了该算法的有效性,并描述了网络特性和性能保持通信约束之间的额外关系。一个惊人的发现是,在一个由121个耦合钟摆组成的网络中,每个节点只需要与其近邻通信,就可以保持最佳的全局性能。总的来说,这项工作为局部通信对全局性能的影响提供了理论理解,并通过建立严格的局部通信约束选择方法,为从业者提供了部署局部模型预测控制所需的工具。令人惊讶的是,这项工作还表明,包含严格的通信约束不需要损害全局性能。
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Erratum to “Learning to Boost the Performance of Stable Nonlinear Systems” Generalizing Robust Control Barrier Functions From a Controller Design Perspective 2024 Index IEEE Open Journal of Control Systems Vol. 3 Front Cover Table of Contents
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