Supervisory control synthesis for multilevel DES with local buses

Jacobus E. Rooda; Joanna M. v.d. Mortel-Fronczak; Martijn A. Goorden; Marzhan M. Baubekova; Michel A. Reniers; Wan J. Fokkink

arxiv: 2512.01101 · v2 · pith:EWM54TMLnew · submitted 2025-11-30 · 📡 eess.SY · cs.SY

Supervisory control synthesis for multilevel DES with local buses

Marzhan M. Baubekova , Martijn A. Goorden , Michel A. Reniers , Joanna M. v.d. Mortel-Fronczak , Jacobus E. Rooda , Wan J. Fokkink This is my paper

Pith reviewed 2026-05-25 07:18 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords multilevel discrete-event systemssupervisory control synthesislocal bus structuresdependency structure matrixhierarchical decompositionproduction linestate-space sizelocal supervisors

0 comments

The pith

Extending bus detection to every hierarchy level yields a tree-structured multilevel system for efficient supervisor synthesis.

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

The paper establishes that detecting and treating bus components at each level of a multilevel discrete-event system hierarchy, rather than only globally at the top, permits a dependency structure matrix decomposition into a tree. This avoids forcing many components into one large synthesis subproblem when a bus has cross dependencies. An algorithm constructs the resulting tree-structured MLDES, and a production line case study reports substantially smaller sums of controlled state-space sizes for the local supervisors. A sympathetic reader would care because state-space size directly limits whether supervisor synthesis remains computationally feasible for realistic plants.

Core claim

By allowing bus detection not only on the top level but at each level of the system hierarchy, the authors define a novel MLDES architecture. Given this architecture, they introduce an algorithm that constructs a tree-structured MLDES. A case study on a production line shows the effectiveness of the proposed method through significantly improved synthesis performance, measured by the sum of the controlled state-space sizes of the local supervisors.

What carries the argument

The multilevel discrete-event system (MLDES) architecture with per-level bus detection, which uses dependency structure matrices to produce a tree-structured hierarchical decomposition of plants and requirements.

If this is right

Local supervisors are synthesized over smaller state spaces because local buses no longer force oversized clusters at higher levels.
The overall synthesis procedure scales to systems containing multiple bus-like components without exponential growth in any single subproblem.
The tree structure produced by the algorithm respects both global and local dependencies, allowing independent computation of each local supervisor.
Performance gains appear directly as reductions in the summed sizes of the controlled state spaces across all local supervisors.

Where Pith is reading between the lines

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

The same per-level bus detection could be applied to other manufacturing or logistics plants to test whether state-space reductions remain consistent across domains.
If the tree can be recomputed incrementally when requirements change, the method might support online supervisor updates without full re-synthesis.
Combining the architecture with existing modular or decentralized synthesis techniques could compound the state-space savings.

Load-bearing premise

The system admits a hierarchical decomposition in which detecting buses at every level still preserves the clustering benefits of the dependency structure matrix technique.

What would settle it

Apply the synthesis algorithm to the production line example once with only top-level bus detection and once with the new per-level detection; if the sum of controlled state-space sizes is not markedly smaller in the per-level version, the performance claim is false.

Figures

Figures reproduced from arXiv: 2512.01101 by Jacobus E. Rooda, Joanna M. v.d. Mortel-Fronczak, Martijn A. Goorden, Marzhan M. Baubekova, Michel A. Reniers, Wan J. Fokkink.

**Figure 2.** Figure 2: The MLDES without bus. subsystems are clustered together, and the multilevel synthesis subproblems arising from these clustered subsystems contribute the most to the overall computational effort. Thus, we consider them in isolation to clarify the distinction between multilevel clusterings and their effect on the multilevel synthesis performance. The simplified model consists of six components and 12 cont… view at source ↗

**Figure 3.** Figure 3: The MLDES with global bus (highlighted in blue). [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: The MLDES with local buses (highlighted in blue). [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Festo station. of six stations (ordered from left to right): (1) Distributing Station – Products are initially placed in three tubes and released via pushers. (2) Handling Station – A pneumatic gripper transports products to an intermediate buffer. (3) Testing Station – Product height is measured; correct products move on, rejects go to a local buffer. (4) Buffering Station – Conveyor belt and separator ma… view at source ↗

**Figure 8.** Figure 8: Controlled state-space size of the multilevel super [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 6.** Figure 6: The result of DSM-based clustering of the Festo [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: The result of DSM-based clustering of the Festo [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

read the original abstract

In multilevel supervisor synthesis, dependency structure matrix techniques can be used to transform the models of plants and requirements into a tree-structured hierarchical decomposition of the synthesis problem and thus efficiently synthesize local supervisors. A bus component, which has many dependencies across a system, tends to lead to an undesirable clustering of many components in one synthesis subproblem. Prior work showed how to recognize and properly treat a global bus structure. In this paper we leverage this work from global to local bus structures through a novel multilevel discrete-event system (MLDES) architecture. Specifically, the hierarchical system decomposition is revisited by allowing bus detection not only on the top level but at each level of the system hierarchy. Given this architecture, an algorithm is introduced that constructs a tree-structured MLDES. A case study on a production line shows the effectiveness of the proposed method through significantly improved synthesis performance, measured by the sum of the controlled state-space sizes of the local supervisors.

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.

Desk Editor's Note private letter to a colleague

Extends their global-bus method to local buses detected at every hierarchy level, with an explicit construction algorithm and a production-line case study that reports smaller aggregate state spaces.

read the letter

The main point is that the authors push bus detection down from a single top-level step to every level in the hierarchy. This produces a tree-structured MLDES even when local buses cross components at lower levels, and they supply an algorithm that builds the decomposition from the revised dependency structure matrix approach. The production-line case study then measures the outcome by the sum of controlled state-space sizes of the local supervisors and reports a clear reduction compared with the prior global-only treatment. That is the concrete advance. The work stays grounded in the cited DSM techniques and does not introduce new free parameters or circular claims; the performance claim rests on the external case study rather than internal fitting. The central assumption that per-level detection preserves the clustering benefits appears to hold in their example without contradiction. The soft spots are modest. The abstract states the improvement but does not list the actual numbers, so the size of the gain depends on the full tables and any implementation details. If the paper supplies those numbers and shows the algorithm runs without post-hoc fixes, the claim is fine. No load-bearing gaps show up in the architecture description. This paper is for people already working on supervisory control of discrete-event systems who use hierarchical decompositions for manufacturing or similar plants. A reader who knows the authors' global-bus paper will see the extension immediately. It shows clear, incremental thinking that engages the existing literature directly. I would bring it to a reading group only if the group focuses on control applications. I would not cite it in my own work in the next year unless my projects overlap this niche. It deserves peer review because the extension is algorithmic, the metric is reproducible in principle, and the evidence from the case study is presented without obvious internal problems.

Referee Report

1 major / 0 minor

Summary. The paper extends dependency structure matrix (DSM) techniques for multilevel discrete-event systems (MLDES) by detecting and handling bus structures at every level of the hierarchy (not only the top level). It introduces an explicit algorithm to construct a tree-structured MLDES and reports a production-line case study in which the sum of the controlled state-space sizes of the resulting local supervisors is significantly smaller than with prior global-bus-only methods.

Significance. If the case-study improvement is reproducible, the work supplies a practical, algorithmic way to obtain finer-grained hierarchical decompositions for supervisory control synthesis when local buses are present. The explicit construction algorithm and the concrete performance metric (sum of controlled state-space sizes) are strengths that make the contribution falsifiable and directly usable by practitioners.

major comments (1)

[Case study] Case study: the manuscript asserts 'significantly improved synthesis performance' measured by the sum of controlled state-space sizes, yet the provided text supplies no numerical values, baseline comparison, or description of how the local-bus detection was applied at each level. Without these data the central empirical claim cannot be verified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive feedback. We address the single major comment below and will revise the manuscript to strengthen the empirical presentation.

read point-by-point responses

Referee: [Case study] Case study: the manuscript asserts 'significantly improved synthesis performance' measured by the sum of controlled state-space sizes, yet the provided text supplies no numerical values, baseline comparison, or description of how the local-bus detection was applied at each level. Without these data the central empirical claim cannot be verified.

Authors: We agree that the case-study section must supply explicit numerical values, a direct baseline comparison, and a transparent description of the per-level bus detection. The abstract and high-level description in the manuscript state the performance metric but do not tabulate the concrete state-space sizes or walk through the detection steps at each hierarchy level. We will add a table comparing the sum of controlled state-space sizes obtained with the proposed local-bus method against the prior global-bus-only approach, together with a step-by-step account of how local buses were identified and handled at every level of the production-line example. This revision will make the central empirical claim directly verifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces a novel MLDES architecture and construction algorithm that extends prior DSM-based global bus handling to local buses at every hierarchy level. The central result is an explicit algorithmic procedure whose output (tree-structured decomposition) is not defined in terms of its own performance metric; effectiveness is instead shown by an external case-study measurement (sum of controlled state-space sizes of local supervisors). The reference to prior global-bus work is a standard citation of an independent technique and does not serve as a load-bearing uniqueness theorem or self-definitional step inside the present derivation. No fitted parameters, ansatz smuggling, or renaming of known results occur.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that dependency structure matrix techniques produce valid tree decompositions and that the modeled systems contain detectable local bus structures at multiple levels; no free parameters or new invented entities are introduced.

axioms (1)

domain assumption Dependency structure matrix techniques can transform the models of plants and requirements into a tree-structured hierarchical decomposition
Stated as the foundation leveraged from prior work and extended in the abstract.

pith-pipeline@v0.9.0 · 5724 in / 1264 out tokens · 61535 ms · 2026-05-25T07:18:40.748064+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the sum of the controlled state-space sizes of the local supervisors

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

[1]

and Lafortune, S

Cassandras, C.G. and Lafortune, S. (2021). Introduction to discrete event systems . Springer, New York, 3rd edition. de Queiroz, M. and Cury, J. (2000). Modular control of composed systems. In Proceedings of the ACC, volume 6, 4051–4055. doi:10.1109/ACC.2000.876983

work page doi:10.1109/acc.2000.876983 2021
[2]

Feng, L., Cai, K., and Wonham, W. (2009). A structural approach to the non-blocking supervisory control of discrete-event systems. The IJAMT, 41(11), 1152–1168

work page 2009
[3]

Fronczak, J., Fokkink, W., and Rooda, J. (2019). Su- pervisory control of multilevel discrete-event systems with a bus structure. In 18th ECC , 3204–3211. doi: 10.23919/ECC.2019.8795835

work page doi:10.23919/ecc.2019.8795835 2019
[4]

Fokkink, W., and Rooda, J. (2020). Structuring multi- level discrete-event systems with dependence structure matrices. IEEE TACON, 65(4), 1625–1639. doi:10.1109/ TAC.2019.2928119

work page arXiv 2020
[5]

Komenda, J., Masopust, T., and van Schuppen, J.H. (2013). Multilevel coordination control of modular DES. In 52nd IEEE CDC , 6323–6328. doi:10.1109/CDC.2013. 6760889

work page doi:10.1109/cdc.2013 2013
[6]

Komenda, J., Masopust, T., and van Schuppen, J.H. (2016). Control of an engineering-structured multilevel discrete-event system. In 13th IF AC WODES, 103–108. doi:10.1109/WODES.2016.7497833

work page doi:10.1109/wodes.2016.7497833 2016
[7]

Leduc, R.J., Dai, P., and Song, R. (2009). Synthesis method for hierarchical interface-based supervisory con- trol. IEEE TACON , 54(7), 1548–1560. doi:10.1109/ TAC.2009.2022101

work page arXiv 2009
[8]

and Wonham, W

Ma, C. and Wonham, W. (2005). Nonblocking supervi- sory control of state tree structures. Springer, Berlin, Heidelberg. doi:10.1007/b105592

work page doi:10.1007/b105592 2005
[9]

Markovski, J., Jacobs, K., van Beek, D., Somers, L., and Rooda, J. (2010). Coordination of resources using generalized state-based requirements. IF AC Proceedings Volumes , 43(12), 287–292. doi:10.3182/ 20100830-3-DE-4013.00048. M.M. Baubekova, M.A.G., Reniers, M.A., van de Mortel-

work page arXiv 2010
[10]

Fronczak, J.M., Rooda, J.E., and Fokkink, W.J. (2025). Cif benchmark models used in the ifac 2026 paper. [Online]. https://github.com/mbaubek/IFAC2026

work page 2025
[11]

Mohajerani, S., Malik, R., and Fabian, M. (2016). A framework for compositional nonblocking verification of extended finite-state machines. DEDS, 26(1), 33–84

work page 2016
[12]

Ouedraogo, L., Kumar, R., Malik, R., and Akesson, K. (2011). Nonblocking and safe control of discrete-event systems modeled as extended finite automata. IEEE T- ASE, 8(3), 560–569. doi:10.1109/TASE.2011.2124457

work page doi:10.1109/tase.2011.2124457 2011
[13]

and Wonham, W.M

Ramadge, P.J. and Wonham, W.M. (1987). Supervisory control of a class of discrete event processes. SIAM journal on control and optimization , 25(1), 206–230

work page 1987
[14]

and Wonham, W

Ramadge, P.J. and Wonham, W. (1982). Supervisory control of discrete event processes. In Feedback Control of Linear and Nonlinear Systems. , 202–214. Springer

work page 1982
[15]

and Wonham, W

Ramadge, P. and Wonham, W. (1989). The control of discrete event systems. Proceedings of the IEEE , 77(1), 81–98. doi:10.1109/5.21072

work page doi:10.1109/5.21072 1989
[16]

Reniers, M., and Rooda, J. (2018). Application of dependency structure matrices and multilevel synthesis to a production line. In IEEE CCTA , 458–464. doi: 10.1109/CCTA.2018.8511449

work page doi:10.1109/ccta.2018.8511449 2018
[17]

Wilschut, T., Etman, L.F.P., Rooda, J.E., and Adan, I.J.B.F. (2017). Multilevel flow-based markov clustering for design structure matrices. JMD, 139(12), 121402. doi:10.1115/1.4037626

work page doi:10.1115/1.4037626 2017
[18]

and Cai, K

Wonham, M.W. and Cai, K. (2019). Supervisory control of discrete-event systems . Springer, Cham, 1st edition

work page 2019
[19]

Wonham, W., Cai, K., and Rudie, K. (2018). Supervi- sory control of discrete-event systems: A brief history. Annual Reviews in Control , 45, 250–256. doi:10.1016/j. arcontrol.2018.03.002

work page doi:10.1016/j 2018
[20]

and Lafortune, S

Yoo, T.S. and Lafortune, S. (2002). A general architec- ture for decentralized supervisory control of discrete- event systems. DEDS, 12(3), 335–377. doi:10.1023/ a:1015625600613

work page 2002
[21]

and Wonham, W

Zhong, H. and Wonham, W. (1990). On the consistency of hierarchical supervision in discrete-event systems. IEEE TACON, 35(10), 1125–1134. doi:10.1109/9.58555

work page doi:10.1109/9.58555 1990

[1] [1]

and Lafortune, S

Cassandras, C.G. and Lafortune, S. (2021). Introduction to discrete event systems . Springer, New York, 3rd edition. de Queiroz, M. and Cury, J. (2000). Modular control of composed systems. In Proceedings of the ACC, volume 6, 4051–4055. doi:10.1109/ACC.2000.876983

work page doi:10.1109/acc.2000.876983 2021

[2] [2]

Feng, L., Cai, K., and Wonham, W. (2009). A structural approach to the non-blocking supervisory control of discrete-event systems. The IJAMT, 41(11), 1152–1168

work page 2009

[3] [3]

Fronczak, J., Fokkink, W., and Rooda, J. (2019). Su- pervisory control of multilevel discrete-event systems with a bus structure. In 18th ECC , 3204–3211. doi: 10.23919/ECC.2019.8795835

work page doi:10.23919/ecc.2019.8795835 2019

[4] [4]

Fokkink, W., and Rooda, J. (2020). Structuring multi- level discrete-event systems with dependence structure matrices. IEEE TACON, 65(4), 1625–1639. doi:10.1109/ TAC.2019.2928119

work page arXiv 2020

[5] [5]

Komenda, J., Masopust, T., and van Schuppen, J.H. (2013). Multilevel coordination control of modular DES. In 52nd IEEE CDC , 6323–6328. doi:10.1109/CDC.2013. 6760889

work page doi:10.1109/cdc.2013 2013

[6] [6]

Komenda, J., Masopust, T., and van Schuppen, J.H. (2016). Control of an engineering-structured multilevel discrete-event system. In 13th IF AC WODES, 103–108. doi:10.1109/WODES.2016.7497833

work page doi:10.1109/wodes.2016.7497833 2016

[7] [7]

Leduc, R.J., Dai, P., and Song, R. (2009). Synthesis method for hierarchical interface-based supervisory con- trol. IEEE TACON , 54(7), 1548–1560. doi:10.1109/ TAC.2009.2022101

work page arXiv 2009

[8] [8]

and Wonham, W

Ma, C. and Wonham, W. (2005). Nonblocking supervi- sory control of state tree structures. Springer, Berlin, Heidelberg. doi:10.1007/b105592

work page doi:10.1007/b105592 2005

[9] [9]

Markovski, J., Jacobs, K., van Beek, D., Somers, L., and Rooda, J. (2010). Coordination of resources using generalized state-based requirements. IF AC Proceedings Volumes , 43(12), 287–292. doi:10.3182/ 20100830-3-DE-4013.00048. M.M. Baubekova, M.A.G., Reniers, M.A., van de Mortel-

work page arXiv 2010

[10] [10]

Fronczak, J.M., Rooda, J.E., and Fokkink, W.J. (2025). Cif benchmark models used in the ifac 2026 paper. [Online]. https://github.com/mbaubek/IFAC2026

work page 2025

[11] [11]

Mohajerani, S., Malik, R., and Fabian, M. (2016). A framework for compositional nonblocking verification of extended finite-state machines. DEDS, 26(1), 33–84

work page 2016

[12] [12]

Ouedraogo, L., Kumar, R., Malik, R., and Akesson, K. (2011). Nonblocking and safe control of discrete-event systems modeled as extended finite automata. IEEE T- ASE, 8(3), 560–569. doi:10.1109/TASE.2011.2124457

work page doi:10.1109/tase.2011.2124457 2011

[13] [13]

and Wonham, W.M

Ramadge, P.J. and Wonham, W.M. (1987). Supervisory control of a class of discrete event processes. SIAM journal on control and optimization , 25(1), 206–230

work page 1987

[14] [14]

and Wonham, W

Ramadge, P.J. and Wonham, W. (1982). Supervisory control of discrete event processes. In Feedback Control of Linear and Nonlinear Systems. , 202–214. Springer

work page 1982

[15] [15]

and Wonham, W

Ramadge, P. and Wonham, W. (1989). The control of discrete event systems. Proceedings of the IEEE , 77(1), 81–98. doi:10.1109/5.21072

work page doi:10.1109/5.21072 1989

[16] [16]

Reniers, M., and Rooda, J. (2018). Application of dependency structure matrices and multilevel synthesis to a production line. In IEEE CCTA , 458–464. doi: 10.1109/CCTA.2018.8511449

work page doi:10.1109/ccta.2018.8511449 2018

[17] [17]

Wilschut, T., Etman, L.F.P., Rooda, J.E., and Adan, I.J.B.F. (2017). Multilevel flow-based markov clustering for design structure matrices. JMD, 139(12), 121402. doi:10.1115/1.4037626

work page doi:10.1115/1.4037626 2017

[18] [18]

and Cai, K

Wonham, M.W. and Cai, K. (2019). Supervisory control of discrete-event systems . Springer, Cham, 1st edition

work page 2019

[19] [19]

Wonham, W., Cai, K., and Rudie, K. (2018). Supervi- sory control of discrete-event systems: A brief history. Annual Reviews in Control , 45, 250–256. doi:10.1016/j. arcontrol.2018.03.002

work page doi:10.1016/j 2018

[20] [20]

and Lafortune, S

Yoo, T.S. and Lafortune, S. (2002). A general architec- ture for decentralized supervisory control of discrete- event systems. DEDS, 12(3), 335–377. doi:10.1023/ a:1015625600613

work page 2002

[21] [21]

and Wonham, W

Zhong, H. and Wonham, W. (1990). On the consistency of hierarchical supervision in discrete-event systems. IEEE TACON, 35(10), 1125–1134. doi:10.1109/9.58555

work page doi:10.1109/9.58555 1990