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arxiv: 2606.11596 · v1 · pith:JRHOFKOC · submitted 2026-06-10 · eess.SY · cs.AI· cs.SY

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

Shirantha Welikala , Zihao Song , Hai Lin , Panos J. Antsaklis This is my paper

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classification eess.SY cs.AIcs.SY
keywords networked systemsdissipativityhierarchical controltopology co-designdata-driven controllinear matrix inequalitiesDC microgridrobust regulation
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The pith

Local dissipativity guarantees in linear subsystems enable co-design of distributed global controllers and interconnection topology via LMI problems to achieve global dissipativity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to make an interconnected set of linear subsystems robust by first giving each subsystem its own local controller that enforces dissipativity on its own. These local properties are then fed into a sequence of convex optimization problems that jointly pick the distributed global controllers and the network connections to enforce overall dissipativity while reducing interconnection costs. The same hierarchy works when only measured input-state-output trajectories are available instead of exact models, provided disturbances satisfy a quadratic bound that is handled by the matrix S-lemma. The approach stays fully decentralized and avoids non-convex iteration.

Core claim

For a networked system of linear subsystems, local controllers are first designed to make each subsystem dissipative; the resulting local supply rates and storage functions are then used to formulate and solve a sequence of LMI problems that simultaneously synthesize distributed global controllers and an interconnection topology enforcing global dissipativity from disturbance inputs to performance outputs while minimizing topology cost; the same structure applies in the data-driven case where only trajectory data is given and unknown disturbances obey a quadratic matrix inequality.

What carries the argument

Dissipativity theory together with a hierarchical sequence of linear matrix inequality problems that co-designs local controllers, global controllers, and topology.

If this is right

  • The closed-loop networked system remains dissipative from its disturbance inputs to its performance outputs.
  • The design process consists only of convex LMI problems and therefore stays compositional and decentralized.
  • The same hierarchy works for both exact subsystem models and input-state-output trajectory data.
  • In the DC microgrid example the design enforces robust voltage regulation and current sharing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the quadratic disturbance bound holds, the data-driven version can certify dissipativity without ever recovering an explicit subsystem model.
  • The topology co-design step may produce sparser interconnections that reduce the number of communication links needed for the global controller.
  • The local-to-global supply-rate composition could be reused as a modular test when subsystems are added or removed after initial design.

Load-bearing premise

The subsystems are linear time-invariant and the disturbances satisfy a quadratic matrix inequality bound.

What would settle it

Apply the designed local and global controllers plus the optimized topology to the networked system and supply a disturbance trajectory; if the integral of the global supply rate becomes negative for some finite-energy disturbance, global dissipativity fails.

Figures

Figures reproduced from arXiv: 2606.11596 by Hai Lin, Panos J. Antsaklis, Shirantha Welikala, Zihao Song.

Figure 1
Figure 1. Figure 1: A generic networked system Σ : w → z. Σi , i ∈ NN and a static interconnection matrix M that defines how the subsystem inputs and outputs, and the networked system’s exogenous inputs w ∈ R nw and per￾formance outputs z(t) ∈ R nz are interconnected. Each subsystem Σi , i ∈ NN follows the dynamics xi(t + 1) = fi(xi(t), ui(t)), yi(t) = hi(xi(t), ui(t)), (4) where the state xi(t) ∈ R nxi , input ui(t) ∈ R nui … view at source ↗
Figure 2
Figure 2. Figure 2: A linear networked system Σ : w → z. M is partially known. A specialized result for such a scenario is given in the following corollary. Corollary 3: Under Assumptions 1 and 2, the networked system Σ with Muw ≜ I, Mzy ≜ I and Mzw ≜ 0, is Y￾dissipative (from w to z) if the remaining interconnection matrix block Muy (5) is designed via the LMI problem: Find: Luy, {pi ∈ R : i ∈ NN } Sub. to: pi > 0, ∀i ∈ NN ,… view at source ↗
Figure 3
Figure 3. Figure 3: An example DCMG with 6 DGs and 7 lines (initial [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Electrical schematic diagram of a DG Σ DG i and a connected line Σ Line l in a DCMG. KDG i , [KDG ij ]j∈NN will be designed in the sequel. Now, combining (41) and (42), we can express the input ui(t) of Σ DG i as ui(t) = D¯ iVSti +  0 KDG i (xi(t) − xEi)  + X j∈NN  R¯ ijD⊤ j xj (t) KDG ij (xj (t) − xEj )  , (43) where D¯ i ≜ [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Numerical results comparison between stabilizing global control vs. dissipativating hierarchical distributed control [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proposes model-based and data-driven hierarchical strategies for co-designing local controllers, distributed global controllers, and interconnection topology in networks of LTI subsystems. Using dissipativity theory, local dissipativity is enforced first, then global dissipativity (with topology cost optimization) is achieved by reducing the problem to a sequence of LMIs; the data-driven variant employs the matrix S-lemma to convert a quadratic matrix inequality bound on disturbances into an LMI using input-state-output trajectories. The approach is illustrated on a DC microgrid example for robust voltage regulation and current sharing.

Significance. If the claimed LMI reductions hold without hidden iteration or conservatism, the work offers a compositional, decentralized alternative to centralized non-convex co-design methods for robust networked systems. The explicit use of dissipativity composition for topology optimization and the data-driven extension via the S-lemma are practical strengths that preserve decentralizability while handling model uncertainty.

minor comments (3)
  1. [§3] §3 (model-based design): the statement that the global dissipativity LMI is obtained 'directly' from local supply rates would benefit from an explicit reference to the interconnection matrix and the precise composition theorem used.
  2. [§4] §4 (data-driven): the quadratic matrix inequality bound on disturbances is introduced without a concrete example of how the data matrices are assembled into the QMI; adding this would clarify the S-lemma application.
  3. [Numerical example] Numerical example: the DC microgrid results report closed-loop performance but omit the dimensions of the solved LMIs or solver times, which would help assess scalability claims.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the constructive and positive assessment of our manuscript, including the recognition of the compositional and decentralized aspects of the proposed LMI-based co-design approach. The recommendation for minor revision is noted. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation relies on standard dissipativity theory for LTI systems (local supply rates implying global dissipativity via interconnection) and the matrix S-lemma to convert QMI disturbance bounds into LMIs. These are external, established results in control theory, not self-derived or fitted within the paper. The co-design reduces to a sequence of LMIs without any self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations. The abstract and approach are self-contained against external benchmarks with no reduction of claims to their own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on dissipativity theory for linear systems and the matrix S-lemma for handling bounded disturbances; no free parameters, ad-hoc axioms, or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Subsystems are linear time-invariant.
    Stated in the abstract as the class of networked systems considered.
  • domain assumption Disturbances in data-driven case are bounded by a quadratic matrix inequality.
    Explicitly invoked to relax conventional bounds and enable the matrix S-lemma.

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discussion (0)

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