Abstract
This article presents a method based on linear matrix inequalities (LMIs) for designing a modular feedback control law, whose synthesis guarantees the system stability, while switching to different network topologies. Such stability is achieved by means of a common Lyapunov function to all network admissible configurations. Several mechanisms to relieve the computational burden of this methodology in large-scale systems are also presented. To assess its applicability, the modular controller is tested on a real case study, namely the Barcelona drinking water network (DWN), and its performance is compared with that of other control strategies, showing the effectiveness of the proposed approach.
Highlights
A modular feedback design method has been presented to generate a family of feedback controllers suitable for different topologies in a networked control system
The proposed method leverages linear matrix inequalities (LMIs) to attain the modular structure adding a certain upper-level of robustness against fault events, while guaranteeing stability despite topology switchings
The method starts from a linear model of the system and requires to solve an optimization problem subject to as many LMI constraints as possible cooperation scenarios can be defined using the available communication resources
Summary
In recent years, distributed control architectures have gained relevance due to the multiple advances in information and communication technologies [1]. This approach is useful in many practical problems that cannot be addressed from a centralized perspective, e.g., due to the sheer size of the system and/or limits in the information exchange between controllers [2] In this context, we are interested in the design of feedback controllers that respect the constraints imposed by the communication topology. A design method based on LMIs for distributed linear systems is proposed in the context of coalitional control first in [7] and later in [8]. Under this framework, communication links remain enabled as long as they provide a significant performance increase, and otherwise they are disconnected.
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