Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems

2026-06-09

AI Summary

This study addresses robust hierarchical control and topology co-design for interconnected linear network systems when precise subsystem models are unavailable and only data are accessible, ensuring dissipativity from disturbances to performance outputs. Two strategies are proposed: a model-driven approach integrating local dissipativity-based control with global topology optimization, and a data-driven method that relies solely on input–state–output trajectories, leveraging the matrix S-lemma under quadratic constraints on disturbances to jointly design control and topology. The work innovatively unifies dissipativity theory with topology optimization, enabling composable and decentralized co-design while relaxing disturbance assumptions and circumventing centralized nonconvex iterations through a model-free framework. The efficacy of the approach is validated in a DC microgrid, demonstrating improved voltage regulation, current sharing, and optimized interconnection costs.

Abstract

In this paper, we consider a class of networked systems comprising an interconnected set of linear subsystems, disturbance inputs, and performance outputs. Using dissipativity theory, we first propose a model-based hierarchical control design strategy to ensure the closed-loop networked system is dissipative from its disturbance inputs to performance outputs. This involves designing local controllers for each subsystem to enforce local dissipativity guarantees, which are then exploited to co-design distributed global controllers and the interconnection topology to enforce global dissipativity guarantees while optimizing interconnection topology costs. The overall design process requires only solving a sequence of linear matrix inequality (LMI) problems, thereby retaining compositionality and decentralizability while avoiding non-convex, iterative design processes that are inefficient and centralized. This model-based hierarchical control design strategy assumes the knowledge of the subsystem dynamics, which may not hold in many real-world networked systems. Motivated by this, we also propose a data-driven hierarchical control design strategy that assumes only the availability of rich input-state-output trajectory data from the subsystems. The proposed data-driven design process assumes that the unknown disturbances affecting the subsystem dynamics are bounded by a quadratic matrix inequality (relaxing conventional bounds) and accounts for this by using the matrix S-lemma. Finally, the effectiveness of the proposed model-based and data-driven hierarchical control designs is illustrated for a networked system representing a DC microgrid, with the aim of enforcing robust (dissipative) voltage regulation and current sharing.

Problem

• hierarchical control
• topology co-design
• networked systems
• dissipativity
• data-driven control

Innovation

• hierarchical control
• topology co-design
• dissipativity theory
• data-driven control
• linear matrix inequalities