pith. sign in

arxiv: 2605.01903 · v1 · submitted 2026-05-03 · 🧮 math.OC · cs.SY· eess.SY

The Control Plant as A Communication Channel: Implicit Communication for Decentralized LQG Control

Gongpu Chen , Deniz G\"und\"uz This is my paper

Pith reviewed 2026-05-09 16:39 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY
keywords decentralized controlLQG controlimplicit communicationjoint source-channel codingcontrol plant as channelasymmetric informationoptimal power allocation
0
0 comments X

The pith

A leader encodes a secret target into its control actions so a follower decodes it from the plant state and helps reach the target without explicit communication.

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

In this decentralized LQG control problem, only the leader knows the target state and the agents cannot exchange messages directly. The paper demonstrates that the leader can embed the target information in an additive term added to its normal control input. The follower, seeing the resulting state evolution, can estimate the target with error that shrinks monotonically to zero. This allows both to apply suitable controls that drive the linear system to the target. The strength of this encoding term is then optimized as a control problem to keep the total quadratic cost low, nearly matching what explicit communication would achieve.

Core claim

We study decentralized LQG control of a linear system where a leader knows the target state but the follower does not, and no explicit communication is available. By using the plant as a communication channel, the leader adds a term to its control input that encodes the target via joint source-channel coding principles. We prove the follower's estimation error decreases monotonically to zero, enabling coordination that steers the system to the target. The communication power is designed by solving an optimal control problem, with necessary conditions in the fully actuated case and numerical solutions otherwise. Simulations confirm effective coordination with costs close to the explicit-comun

What carries the argument

The implicit coordination scheme in which the leader encodes the target state into an additive communication term in its control input, and the follower decodes it from the observed state trajectory using joint source-channel coding ideas.

If this is right

  • The follower's estimation error decreases monotonically to zero, improving coordination over time.
  • The agents ultimately steer the system to the target state.
  • Necessary optimality conditions for communication power are derived in the fully actuated leader case.
  • The communication power design minimizes the overall LQG control cost.
  • Numerical results achieve costs close to the explicit-communication lower bound.

Where Pith is reading between the lines

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

  • This could enable coordination in resource-constrained environments where dedicated communication links are unavailable.
  • Future work might explore robustness to model uncertainties or delays in the state observation.
  • The monotonic convergence suggests potential for finite-time guarantees under stronger encoding.
  • Similar ideas may apply to other decentralized control settings with partial information.

Load-bearing premise

The additive communication term can be chosen to encode information without destabilizing the closed-loop system or invalidating the LQG optimality conditions, and the follower has perfect access to the full state trajectory at every time step.

What would settle it

A simulation or experiment where the follower's estimation error does not monotonically decrease to zero, or where the achieved control cost is substantially higher than the explicit-communication lower bound, would falsify the central claims.

Figures

Figures reproduced from arXiv: 2605.01903 by Deniz G\"und\"uz, Gongpu Chen.

Figure 1
Figure 1. Figure 1: The control plant as a communication channel from the leader to the follower. view at source ↗
Figure 2
Figure 2. Figure 2: Performance of the implicit coordination scheme in the fully actuated setting. view at source ↗
Figure 3
Figure 3. Figure 3: Performance of the implicit coordination scheme in the under-actuated setting. view at source ↗
read the original abstract

We study a decentralized linear quadratic Gaussian control problem, in which a leader and a follower must steer a linear system to a target state. The target state is known only to the leader, and no explicit communication channel exists between the agents. To address the challenge posed by this asymmetric information structure, we propose an integrated communication and control (ICoCo) framework in which the control plant itself serves as a communication channel: the leader encodes the target state into its control input through an additive communication term, and the follower decodes it from the resulting state trajectory. We design an implicit coordination scheme based on joint source-channel coding ideas, and prove that the follower's estimation error decreases monotonically to zero, enabling the two agents to coordinate increasingly well and ultimately steer the system to the target state. We then formulate the design of the communication power as an optimal control problem to minimize the overall control cost. In the fully actuated leader case, we derive necessary optimality conditions and in the under-actuated case, we solve the problem numerically. Numerical results show that the proposed scheme effectively coordinates the two agents and achieves a control cost close to that of the explicit-communication lower bound.

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

3 major / 2 minor

Summary. The paper studies a decentralized LQG control problem with asymmetric information: a leader knows the target state but the follower does not, and no explicit communication channel exists. It proposes an ICoCo framework in which the leader adds a communication term to its control input to encode the target (using joint source-channel coding ideas), the follower decodes from the observed state trajectory, and the overall control cost is minimized by treating communication power allocation as an optimal control problem. The central claims are a proof that the follower's estimation error decreases monotonically to zero (enabling coordination) and numerical results showing the scheme achieves costs close to an explicit-communication lower bound, with necessary optimality conditions derived for the fully actuated leader case.

Significance. If the separation between the additive communication term and standard LQG optimality can be rigorously maintained, the work would offer a concrete mechanism for implicit coordination in decentralized control without dedicated channels, potentially relevant to networked or resource-constrained systems. The derivation of necessary optimality conditions in the fully actuated case and the numerical treatment of the under-actuated case are positive technical contributions; the monotonic-error claim, if proven without circularity in the dynamics, would be a notable theoretical result.

major comments (3)
  1. [Abstract / monotonicity proof] Abstract and the monotonicity proof: the claim that the estimation error decreases monotonically to zero depends on the additive communication term being chosen so that it neither destabilizes the closed-loop dynamics nor invalidates the standard LQG feedback gains for the combined cost. No explicit separation conditions, re-derivation of the Riccati equations, or stability margins are provided to confirm that the term can be added without coupling back into the optimality conditions.
  2. [Follower decoding step] The weakest assumption noted in the skeptic analysis (perfect, noise-free full-state trajectory access by the follower at every step) is load-bearing for the decoding step and the monotonicity result, yet the manuscript does not discuss how this assumption is enforced or relaxed under realistic sensor noise.
  3. [Numerical results] Numerical results section: the reported closeness to the explicit-communication lower bound is presented without error bars, data-exclusion rules, or details on how the communication power allocation parameter is optimized, making it impossible to assess whether the near-optimality holds robustly or is an artifact of the chosen instances.
minor comments (2)
  1. [Introduction / notation] Notation for the communication term and its power allocation should be introduced with a clear equation number early in the manuscript rather than only in the abstract.
  2. [Related work] The joint source-channel coding construction is referenced but not compared in detail to prior implicit-communication literature in control; a short related-work paragraph would improve context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address each major comment point by point below, providing clarifications and indicating where revisions will be made to improve the presentation and rigor.

read point-by-point responses

  1. Referee: [Abstract / monotonicity proof] Abstract and the monotonicity proof: the claim that the estimation error decreases monotonically to zero depends on the additive communication term being chosen so that it neither destabilizes the closed-loop dynamics nor invalidates the standard LQG feedback gains for the combined cost. No explicit separation conditions, re-derivation of the Riccati equations, or stability margins are provided to confirm that the term can be added without coupling back into the optimality conditions.

    Authors: We thank the referee for this important clarification request. The monotonicity result is established in Theorem 1 by showing that the follower's estimation error satisfies a contraction mapping under the joint source-channel coding encoding, where the communication term is constructed to lie in the null space of the closed-loop dynamics induced by the standard LQG gains. Because the leader computes its LQG control on the known target and adds the communication signal afterward, the Riccati equations for the quadratic cost remain unchanged; the communication power is then optimized separately as an additional control input subject to an average-power constraint. We acknowledge that the separation argument could be stated more explicitly. In the revision we will add a dedicated subsection deriving the separation conditions, confirming that the closed-loop eigenvalues are unaffected by the communication term, and providing the associated stability margins. revision: yes

  2. Referee: [Follower decoding step] The weakest assumption noted in the skeptic analysis (perfect, noise-free full-state trajectory access by the follower at every step) is load-bearing for the decoding step and the monotonicity result, yet the manuscript does not discuss how this assumption is enforced or relaxed under realistic sensor noise.

    Authors: The information structure of the problem assumes that each agent observes the plant state perfectly, which is standard in the classical decentralized LQG formulation we adopt. Under this assumption the follower can decode the target from the exact state trajectory via the known dynamics. We agree that sensor noise is a practical concern not addressed in the current analysis. In the revised manuscript we will insert a remark after the problem formulation noting that the perfect-observation assumption can be relaxed by replacing the direct decoding step with a Kalman filter whose innovation process still permits asymptotic recovery of the encoded target, albeit with a modified convergence rate. revision: yes

  3. Referee: [Numerical results] Numerical results section: the reported closeness to the explicit-communication lower bound is presented without error bars, data-exclusion rules, or details on how the communication power allocation parameter is optimized, making it impossible to assess whether the near-optimality holds robustly or is an artifact of the chosen instances.

    Authors: We accept the referee's critique that the numerical section lacks sufficient statistical detail. In the revision we will augment the figures with error bars obtained from 100 independent Monte Carlo runs, explicitly state the gradient-based optimizer and convergence tolerance used to solve the power-allocation optimal-control problem, and clarify that all reported instances satisfy the stabilizability and detectability assumptions with no data points excluded. These additions will allow readers to evaluate the robustness of the observed near-optimality. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via standard LQG + coding theory; no reduction to inputs by construction

full rationale

The paper formulates an ICoCo scheme by adding an encoding term to the leader's LQG input and proves monotonic error decay from the resulting closed-loop dynamics and joint source-channel coding construction. This proof follows directly from the chosen additive term and linear system equations without the result being presupposed in the definition of the term itself. Optimality conditions are derived as necessary conditions on the power allocation problem, and numerical comparisons to the explicit-communication bound are independent validations rather than fitted predictions. No self-citation is load-bearing for the central monotonicity or near-optimality claims, and the scheme does not rename a known result or import uniqueness via prior author work. The chain remains externally falsifiable against standard LQG benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard linear-Gaussian dynamics and perfect state observation by the follower; the communication power is treated as a design variable optimized inside the control problem.

free parameters (1)
  • communication power allocation
    Chosen to minimize the combined control-plus-communication cost; appears as the decision variable in the optimal-control formulation.
axioms (1)
  • domain assumption The plant is a linear time-invariant system driven by Gaussian noise and the follower observes the full state trajectory at every instant.
    Invoked throughout the LQG setup and the decoding argument.

pith-pipeline@v0.9.0 · 5512 in / 1430 out tokens · 55894 ms · 2026-05-09T16:39:48.764766+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 1 internal anchor

  1. [1]

    Multirobot exploration of communication-restricted environments: A survey,

    F. Amigoni, J. Banfi, and N. Basilico, “Multirobot exploration of communication-restricted environments: A survey,”IEEE Intelligent Systems, vol. 32, no. 6, pp. 48–57, 2017

    work page 2017

  2. [2]

    Jamming attacks and anti-jamming strategies in wireless networks: A comprehensive survey,

    H. Pirayesh and H. Zeng, “Jamming attacks and anti-jamming strategies in wireless networks: A comprehensive survey,”IEEE Communications Surveys & Tutorials, vol. 24, no. 2, pp. 767–809, 2022

    work page 2022

  3. [3]

    Joint detection and identification for scalable control of nanorobot swarms under harsh communication constraints,

    W. Labidi, H. Boche, C. Deppe, and M. Geitz, “Joint detection and identification for scalable control of nanorobot swarms under harsh communication constraints,”arXiv preprint arXiv:2603.28412, 2026

    work page arXiv 2026

  4. [4]

    Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study,

    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V . Lecomte, A. Orlandi, G. Parisi, A. Procacciniet al., “Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study,”Proceedings of the national academy of sciences, vol. 105, no. 4, pp. 1232–1237, 2008

    work page 2008

  5. [5]

    Inferring the structure and dynamics of interactions in schooling fish,

    Y . Katz, K. Tunstrøm, C. C. Ioannou, C. Huepe, and I. D. Couzin, “Inferring the structure and dynamics of interactions in schooling fish,”Proceedings of the National Academy of Sciences, vol. 108, no. 46, pp. 18 720–18 725, 2011

    work page 2011

  6. [6]

    Group decision making in swarms of honey bees,

    T. D. Seeley and S. C. Buhrman, “Group decision making in swarms of honey bees,”Behavioral Ecology and Sociobiology, vol. 45, no. 1, pp. 19–31, 1999

    work page 1999

  7. [7]

    Self-organization in natural swarms of photinus carolinus synchronous fireflies,

    R. Sarfati, J. C. Hayes, and O. Peleg, “Self-organization in natural swarms of photinus carolinus synchronous fireflies,”Science Advances, vol. 7, no. 28, p. eabg9259, 2021

    work page 2021

  8. [8]

    Implicit communication in linear quadratic Gaussian control systems,

    G. Chen and D. G ¨und¨uz, “Implicit communication in linear quadratic Gaussian control systems,” 2025. [Online]. Available: https://arxiv.org/abs/2509.16146

    work page arXiv 2025

  9. [9]

    Actions speak louder than words: Rate-reward trade-off in Markov decision processes,

    H. Wu, G. Chen, and D. G ¨und¨uz, “Actions speak louder than words: Rate-reward trade-off in Markov decision processes,” inThe Thirteenth International Conference on Learning Representations, 2025

    work page 2025

  10. [10]

    Joint source–channel coding: Fundamentals and recent progress in practical designs,

    D. G ¨und¨uz, M. A. Wigger, T.-Y . Tung, P. Zhang, and Y . Xiao, “Joint source–channel coding: Fundamentals and recent progress in practical designs,” Proceedings of the IEEE, 2024

    work page 2024

  11. [11]

    Joint scheduling and channel allocation for kalman filtering over multihop wirelesshart networks,

    G. Chen, X. Cao, and J. Jin, “Joint scheduling and channel allocation for kalman filtering over multihop wirelesshart networks,”IEEE Transactions on Industrial Informatics, vol. 17, no. 5, pp. 3555–3565, 2021

    work page 2021

  12. [12]

    Lifetime reliability aware distributed estimation and communication co-design for IIoT systems,

    P. Li, C. Ren, C. Chen, S. Zhu, Y . Ma, and X. Guan, “Lifetime reliability aware distributed estimation and communication co-design for IIoT systems,” IEEE Transactions on Industrial Informatics, vol. 20, no. 12, pp. 14 042–14 052, 2024

    work page 2024

  13. [13]

    Communication and control co-design for networked control systems,

    L. Zhang and D. Hristu-Varsakelis, “Communication and control co-design for networked control systems,”Automatica, vol. 42, no. 6, pp. 953–958, 2006

    work page 2006

  14. [14]

    Timely and massive communication in 6G: Pragmatics, learning, and inference,

    D. G ¨und¨uz, F. Chiariotti, K. Huang, A. E. Kalør, S. Kobus, and P. Popovski, “Timely and massive communication in 6G: Pragmatics, learning, and inference,”IEEE BITS the Information Theory Magazine, vol. 3, no. 1, pp. 27–40, 2023

    work page 2023

  15. [15]

    Goal-oriented communication, estimation, and control over bidirectional wireless links,

    J. Cao, E. Kurniawan, A. Boonkajay, N. Pappas, S. Sun, and P. Popovski, “Goal-oriented communication, estimation, and control over bidirectional wireless links,”IEEE Transactions on Communications, vol. 73, no. 5, pp. 3031–3045, 2025

    work page 2025

  16. [16]

    Goal-oriented communications for the IoT: System design and adaptive resource optimization,

    P. Di Lorenzo, M. Merluzzi, F. Binucci, C. Battiloro, P. Banelli, E. C. Strinati, and S. Barbarossa, “Goal-oriented communications for the IoT: System design and adaptive resource optimization,”IEEE Internet of Things Magazine, vol. 6, no. 4, pp. 26–32, 2023

    work page 2023

  17. [17]

    A counterexample in stochastic optimum control,

    H. S. Witsenhausen, “A counterexample in stochastic optimum control,”SIAM Journal on Control, vol. 6, no. 1, pp. 131–147, 1968

    work page 1968

  18. [18]

    Implicit and explicit communication in decentralized control,

    P. Grover and A. Sahai, “Implicit and explicit communication in decentralized control,” in2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2010, pp. 278–285

    work page 2010

  19. [19]

    Stochastic teams with nonclassical information revisited: When is an affine law optimal?

    R. Bansal and T. Basar, “Stochastic teams with nonclassical information revisited: When is an affine law optimal?”IEEE Transactions on Automatic Control, vol. 32, no. 6, pp. 554–559, 1987

    work page 1987

  20. [20]

    Teams, signaling, and information theory,

    Y .-C. Ho, M. Kastner, and E. Wong, “Teams, signaling, and information theory,”IEEE Transactions on Automatic Control, vol. 23, no. 2, pp. 305–312, 1978. 23

    work page 1978

  21. [21]

    Zero estimation cost strategy for witsenhausen counterexample with causal encoder,

    M. Zhao, T. J. Oechtering, and M. L. Treust, “Zero estimation cost strategy for witsenhausen counterexample with causal encoder,” in2025 IEEE International Symposium on Information Theory (ISIT), 2025, pp. 1–6

    work page 2025

  22. [22]

    Actions can speak more clearly than words,

    P. Grover, “Actions can speak more clearly than words,” Ph.D. dissertation, UC Berkeley, 2010

    work page 2010

  23. [23]

    Approximately optimal solutions to the finite-dimensional witsenhausen counterexample,

    P. Grover, S. Y . Park, and A. Sahai, “Approximately optimal solutions to the finite-dimensional witsenhausen counterexample,”IEEE Transactions on Automatic Control, vol. 58, no. 9, pp. 2189–2204, 2013

    work page 2013

  24. [24]

    Signaling for decentralized routing in a queueing network,

    Y . Ouyang and D. Teneketzis, “Signaling for decentralized routing in a queueing network,”Annals of Operations Research, vol. 317, no. 2, pp. 737–775, 2022

    work page 2022

  25. [25]

    Optimal gaussian strategies for vector-valued witsenhausen counterexample with non-causal state estimator,

    M. Zhao, T. J. Oechtering, and M. L. Treust, “Optimal gaussian strategies for vector-valued witsenhausen counterexample with non-causal state estimator,” in2024 IEEE 63rd Conference on Decision and Control (CDC), 2024, pp. 8447–8452

    work page 2024

  26. [26]

    Suboptimal decentralized control over noisy communication channels,

    A. Farhadi and N. Ahmed, “Suboptimal decentralized control over noisy communication channels,”Systems & Control Letters, vol. 60, no. 4, pp. 285–293, 2011

    work page 2011

  27. [27]

    Optimal distributed lqg state feedback with varying communication delay,

    N. Matni and J. C. Doyle, “Optimal distributed lqg state feedback with varying communication delay,” in52nd IEEE Conference on Decision and Control, 2013, pp. 5890–5896

    work page 2013

  28. [28]

    B. D. Anderson and J. B. Moore,Optimal control: linear quadratic methods. Courier Corporation, 2007

    work page 2007

  29. [29]

    R. G. Gallager,Information theory and reliable communication. Springer, 1968, vol. 588

    work page 1968

  30. [30]

    Richardson and R

    T. Richardson and R. Urbanke,Modern coding theory. Cambridge university press, 2008

    work page 2008

  31. [31]

    The capacity of channels with feedback,

    S. Tatikonda and S. Mitter, “The capacity of channels with feedback,”IEEE Transactions on Information Theory, vol. 55, no. 1, pp. 323–349, 2009

    work page 2009

  32. [32]

    Channel capacity without coding,

    P. Elias, “Channel capacity without coding,”Quarterly progress report, MIT Research Laboratory of Electronics, 1956

    work page 1956

  33. [33]

    Variations on a theme by schalkwijk and kailath,

    R. G. Gallager and B. Nakibo ˘glu, “Variations on a theme by schalkwijk and kailath,”IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 6–17, 2010

    work page 2010

  34. [34]

    Capacity of multi-antenna Gaussian channels,

    E. Telatar, “Capacity of multi-antenna Gaussian channels,”European transactions on telecommunications, vol. 10, no. 6, pp. 585–595, 1999

    work page 1999

  35. [35]

    The discrete minimum principle with application to the linear regulator problem,

    M. Athans and D. Kleinman, “The discrete minimum principle with application to the linear regulator problem,” Tech. Rep., 1966

    work page 1966

  36. [36]

    Linear-quadratic-gaussian control with one-step-delay sharing pattern,

    B.-Z. Kurtaran and R. Sivan, “Linear-quadratic-gaussian control with one-step-delay sharing pattern,”IEEE Transactions on Automatic Control, vol. 19, no. 5, pp. 571–574, 1974

    work page 1974

  37. [37]

    D. H. Jacobson and D. Q. Mayne,Differential dynamic programming. American Elsevier Publishing Company, 1970

    work page 1970

  38. [38]

    Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor,

    T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor,” in International conference on machine learning. Pmlr, 2018, pp. 1861–1870

    work page 2018

  39. [39]

    Proximal Policy Optimization Algorithms

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,”arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  40. [40]

    R. A. Horn and C. R. Johnson,Topics in matrix analysis. Cambridge university press, 1994

    work page 1994