PaperlayerView exact revision on arXiv

Source-linked AI summary

Consensus-Aware Co-design of Wireless Multi-Agent Control and Communication Systems

Atefeh Termehchi, Sajedeh Soleimani, Shiva Kazemi Taskooh, Mehdi Rasti, Ekram Hossain

arXiv:2610.30141v1math.OCcs.MA

TL;DR

Conventional MACS and wireless designs do not jointly account for how control and communication affect one another, leaving consensus requirements and scarce bandwidth to be handled separately. This paper co-optimizes consensus topology and wireless resource allocation, using an optimality property to obtain a sequential solution. In a smart-grid case study, it saves 24.1% and 27.0% bandwidth against the two baselines while maintaining consensus and QoS.

  • Problem

    Conventional MACS designs abstract communication, while wireless systems provision resources for worst-case requirements, despite their two-way coupling and shared bandwidth constraints.

    Source: §I · p. 2, C. Numerical Results · p. 12

  • Method

    The approach jointly optimizes time-varying consensus topology and bandwidth allocation for D2D links sharing spectrum with cellular users, using a structural property to solve the problem in two sequential stages.

    Source: §I · p. 2, §II · p. 3, §VI · p. 13

  • Results

    24.1% and 27.0% bandwidth savings versus event-triggered and fully-connected schemes, respectively, with co-design maintaining consensus and QoS.

    Source: C. Numerical Results · pp. 11–12

  • Takeaways & Limitations

    The smart-grid case study shows that jointly selecting topology and bandwidth can reduce consumption while maintaining consensus and communication requirements.

    Source: C. Numerical Results · pp. 11–12, §VI · p. 12

Abstract

from arXiv · show

Autonomous multi-agent control systems (MACSs) enable distributed coordination in emerging applications such as smart power grids and autonomous vehicle or drone networks. In many of these applications, inter-agent communication relies on wireless networks. However, conventional MACS designs neglect the interaction between the communication and control subsystems. At the same time, conventional wireless designs reserve communication resources based on worst-case MACS requirements. Consequently, control performance is degraded and wireless resources are utilized inefficiently. To address these challenges, we propose a consensus-aware co-design approach for MACSs and wireless communication systems. We introduce a system model in which agents achieve consensus by exchanging information through device-to-device (D2D) links that share spectrum with cellular users under limited bandwidth resources. Based on this model, we formulate a joint optimization problem for consensus-topology selection and wireless resource allocation to minimize bandwidth consumption while guaranteeing consensus and satisfying the quality-of-service (QoS) requirements of both MACSs and cellular users. Although the resulting problem is a mixed-integer nonlinear program (NP-hard in general), a structural property of the optimal solution enables a sequential two-stage optimization algorithm with polynomial complexity. Simulations on a smart power grid case study demonstrate that the proposed approach achieves 24-27% bandwidth savings compared with the two baselines while maintaining consensus and satisfying all QoS requirements of the control agents and the communication users.

I. INTRODUCTION

Wireless MACSs couple control performance to communication design, yet conventional abstractions hide wireless resource needs and worst-case provisioning wastes bandwidth. The paper proposes joint topology and resource design for consensus and QoS, supported by a model of wireless inter-agent dynamics.

I. INTRODUCTION

  • Wireless MACSs make control performance depend on communication design, while abstract communication requirements hide resource needs and worst-case provisioning wastes bandwidth.Without joint design, insufficient resources can compromise consensus and erase potential savings from time-varying connectivity.Source: §I · pp. 1–2

A. Related Work

  • Prior work spans control-aware wireless design, wireless-aware control, and co-design, but wireless-enabled MACSs lack prior control-aware design or co-design.The identified gap is a model capturing bidirectional coupling and joint optimization of multi-agent control and wireless communication.Source: A. Related Work · p. 2

B. Contributions

  • The paper develops a coupled control–wireless model and jointly selects consensus topology and resource allocation to meet consensus and QoS requirements.The stated contributions also include smart-grid simulations showing bandwidth savings while maintaining consensus and QoS.Source: B. Contributions · pp. 2–3
  • A structural property reduces the feasible search space without loss of optimality, enabling two sequential stages with polynomial complexity per slot.The approach addresses an otherwise NP-hard mixed-integer nonlinear problem.Source: B. Contributions · pp. 2–3

II. SYSTEM MODEL AND ASSUMPTIONS

  • The system model allocates disjoint portions of shared bandwidth to control agents and cellular users, with resource allocation and communication graphs varying by slot.The base station allocates bandwidth subject to consensus, minimum QoS, and total-bandwidth constraints.Source: §II · p. 3

A. Multi-Agent Control System Dynamics and Network Cou-

  • In the stacked agent dynamics, the graph-Laplacian coupling term drives connected agents’ states toward agreement, while disconnected pairs receive no direct coupling in that slot.The model assumes each agent is internally stable.Source: A. Multi-Agent Control System Dynamics… · p. 3

B. Consensus in Multi-Agent Control System

Consensus is measured through the agents’ disagreement from their common average state. Under the stated stability, coupling, and windowed-connectivity conditions, disagreement vanishes exponentially, including when individual slot graphs are disconnected.

B. Consensus in Multi-Agent Control System

  • Consensus is the vanishing of the disagreement component; the average component evolves separately and is unaffected by the consensus coupling.The disagreement component measures deviations from the average, while the coupling drives agents toward a common network trajectory.Source: B. Consensus in Multi-Agent Control… · pp. 3–4
  • Under the theorem’s conditions, disagreement converges exponentially to zero and all agents’ states approach the common average trajectory.The conditions include connected union graphs over consecutive-slot windows, rather than requiring every slot graph to be connected.Source: B. Consensus in Multi-Agent Control… · p. 4
  • With bounded disturbances, disagreement remains bounded and can be made arbitrarily small by increasing coupling strength or windowed connectivity.This is the stated input-to-state stability property.Source: B. Consensus in Multi-Agent Control… · p. 4
  • Stronger coupling and better connectivity over time increase the approximate exponential decay rate of disagreement.The rate also increases when the window horizon is smaller.Source: B. Consensus in Multi-Agent Control… · p. 4
  • Joint connectivity requires the union graph over every K-slot window to be connected, even if individual slot graphs are disconnected.For an undirected graph, positive algebraic connectivity of the union Laplacian is equivalent to union-graph connectivity.Source: B. Consensus in Multi-Agent Control… · p. 4

C. Wireless Communication Subsystem

The wireless subsystem shares system bandwidth among D2D agent links and cellular-user links, with allocations constrained by rate, delay, and bandwidth requirements. Channel models determine link quality and the resources needed for communication.

C. Wireless Communication Subsystem

  • Total system bandwidth is shared by D2D links between control agents and base-station–cellular-user links, with normalized bandwidth shares assigned to each.Allocated sub-bands are orthogonal, and total use must remain within the per-slot bandwidth budget.Source: C. Wireless Communication Subsystem · pp. 4–5
  • Rayleigh fading models describe the channels between control agents and between the base station and cellular users, with distance-dependent path loss and small-scale fading.Control-agent D2D links use symmetric channel gains and half-duplex, equal-time exchanges over the same allocated bandwidth in both directions.Source: C. Wireless Communication Subsystem · p. 5
  • A minimum rate requirement on every active D2D link keeps its transmission delay below the admissible margin, preventing delay from destabilizing consensus dynamics.The admissible delay margin depends on the largest eigenvalue of the graph Laplacian.Source: C. Wireless Communication Subsystem · p. 5

III. PROBLEM FORMULATION

The formulation minimizes per-slot bandwidth consumption by jointly choosing the control-agent communication topology and bandwidth allocations. It enforces windowed connectivity for consensus, link-rate and cellular-user QoS requirements, and the total bandwidth budget.

III. PROBLEM FORMULATION

  • The optimization jointly selects D2D topology and bandwidth allocations across control-agent and cellular links to minimize total bandwidth consumption per slot.The constraints include windowed algebraic connectivity, minimum communication rates, and a per-slot bandwidth budget.Source: §III · p. 6
  • The formulation requires minimum rates for active agent links and cellular-user uplink and downlink QoS while keeping total allocations within the bandwidth budget.The agent-link rate requirement also bounds transmission delay within the admissible margin.Source: §III · p. 6
  • Constraint C1 enforces windowed algebraic connectivity over every specified consecutive-slot window, guaranteeing consensus among control agents.A smaller window requires stronger per-slot connectivity and faster consensus convergence; a window of one requires a connected graph in every slot.Source: §III · p. 6

IV. PROPOSED SOLUTION APPROACH

The proposed solution approach exploits a structural property of the optimization problem to reduce its computational complexity. This addresses the general difficulty of solving its mixed-integer nonlinear formulation.

IV. PROPOSED SOLUTION APPROACH

  • A structural property of the mixed-integer nonlinear problem enables solution methods with substantially lower complexity.Mixed-integer nonlinear programs are generally NP-hard and may require prohibitively large search trees.Source: §IV · p. 6

A. Structural Properties and Solution Approach

The structural result reduces the joint optimization to selecting a minimum-edge topology that meets windowed connectivity, followed by bandwidth allocation. Channel-aware edge weights favor topologies with lower bandwidth costs, and the fixed-topology allocation stage is convex.

A. Structural Properties and Solution Approach

  • Every optimal solution uses the minimum number of active D2D edges that satisfies the windowed connectivity constraint, enabling sequential optimization without loss of optimality.The first stage selects a topology; the second solves the resulting convex bandwidth-allocation problem.Source: A. Structural Properties and Solution… · pp. 6–7
  • The topology-selection stage uses channel quality as edge weights, while the bandwidth-allocation stage assigns minimum resources to cellular users and selected control-agent links according to their SNRs.Topology selection uses a spectral linear matrix inequality for windowed algebraic connectivity; allocation is convex for a fixed topology.Source: A. Structural Properties and Solution… · p. 7
  • Channel-aware edge weights favor minimum-edge topologies whose links require less bandwidth, reducing the total bandwidth cost of the subsequent allocation stage.The choice among topologies with the same minimum edge count affects bandwidth cost.Source: A. Structural Properties and Solution… · p. 7

B. Minimal-Edge Graph Subproblem via Spectral LMI

The minimal-edge graph subproblem enforces windowed spectral connectivity through an LMI, then uses relaxation, rounding, and pruning to obtain a feasible binary topology.

B. Minimal-Edge Graph Subproblem via Spectral LMI

  • The joint connectivity condition C1 is represented by an LMI affine in the adjacency variables through the windowed Laplacian, enabling continuous relaxation of the binary edges.Relaxing each aij(Tk) from {0, 1} to [0, 1] yields a convex SDP.Source: B. Minimal-Edge Graph Subproblem via… · p. 7
  • The proposed procedure organizes the per-slot co-design into sequential steps, including SDP relaxation, rounding and certification, and convex bandwidth allocation.Algorithm 1 takes channel information and system parameters as inputs and returns adjacency and bandwidth variables.Source: B. Minimal-Edge Graph Subproblem via… · p. 8
  • Rounding selects edges by threshold or top-κ relaxed weights, then greedily prunes edges while restoring any whose removal violates the connectivity condition.The resulting binary solution is minimal or near-minimal and feasible for C1.Source: B. Minimal-Edge Graph Subproblem via… · p. 8

C. Bandwidth Allocation Subproblem

For a fixed feasible topology, bandwidth allocation is a convex subproblem whose linear objective minimizes total bandwidth while enforcing control-agent and cellular-user QoS.

C. Bandwidth Allocation Subproblem

  • With adjacency variables fixed, minimizing total bandwidth is linear in the bandwidth variables, and the rate-based QoS constraints are convex.The control-agent and cellular-user rate functions are concave in bandwidth, while constraints C4–C6 are affine.Source: C. Bandwidth Allocation Subproblem · p. 8
  • The bandwidth-allocation subproblem therefore has a global optimum obtainable with standard convex optimization tools.The passage gives CVX/CVXPY with MOSEK as example solvers.Source: C. Bandwidth Allocation Subproblem · p. 8

D. Overall Procedure of the Proposed Approach

The proposed procedure is summarized in Algorithms 1–4, with per-slot complexity dominated by the SDP relaxation and stated to be polynomial in the numbers of control agents and cellular users.

D. Overall Procedure of the Proposed Approach

E. Analysis of Computational Complexity

  • The SDP relaxation dominates per-slot computation, with stated complexity O(Nc^6.5), so total per-slot complexity is polynomial in Nc and Nm.The SDP uses an Nc × Nc LMI and interior-point iterations.Source: E. Analysis of Computational Complexity · p. 8
  • Rounding sorts O(Nc^2) edges, and pruning attempts at most κ removals, each requiring an O(Nc^3) Laplacian eigenvalue check.An edge is retained if its removal would violate the connectivity condition.Source: E. Analysis of Computational Complexity · p. 8
  • For a fixed topology, bandwidth allocation is formulated as a convex program over nonnegative bandwidths for active D2D edges and cellular users.The program minimizes total bandwidth subject to the specified QoS and other constraints.Source: E. Analysis of Computational Complexity · p. 9

V. PERFORMANCE EVALUATION

The evaluation models a 20-control-agent, 40-cellular-user load-frequency-control system. It tracks consensus and frequency behavior alongside connectivity and bandwidth consumption.

A. Simulated Multi-agent Control and Communication Model

  • The case study uses 20 control agents for a 20-area load-frequency-control system and 40 cellular users sharing licensed spectrum with D2D links.The agents exchange ACE integral states to achieve consensus, supporting secondary frequency regulation and tie-line power balance.Source: A. Simulated Multi-agent Control and… · p. 9
  • Each control area is one agent with frequency deviation and ACE states, and the ACE integral state accumulates frequency deviations and neighboring discrepancies.The agent state also includes turbine, governor, and tie-line power deviations.Source: A. Simulated Multi-agent Control and… · p. 9
  • The model distinguishes physical coupling through the power-network tie-line Laplacian from information coupling through a time-varying D2D communication Laplacian.Performance measures include ACE disagreement, frequency deviations, windowed algebraic connectivity, and normalized total bandwidth consumption.Source: A. Simulated Multi-agent Control and… · p. 9

B. Wireless Communication System

The wireless model shares spectrum between control-agent D2D links and cellular users, and the numerical study tests consensus, communication QoS, and bandwidth use. In the 20-area case, the co-design reduces bandwidth consumption while maintaining consensus and service requirements.

B. Wireless Communication System

  • The study models 20 control agents and 40 cellular users in an 80 m × 80 m microgrid, with 0.5 s slots and Rayleigh block fading for cellular links.Each slot contains about 11 independent fading realizations; the simulation runs for 50 s with continuous dynamics integrated at 0.01 s.Source: B. Wireless Communication System · p. 10, C. Numerical Results · p. 10

C. Numerical Results

  • ACE disagreement falls below 10^-4 by about 10 s, while windowed connectivity stays above 0.15 despite temporarily disconnected single-slot graphs.The reported window spans five slots and satisfies the joint-connectivity condition.Source: C. Numerical Results · p. 10, Figure 2 · p. 11
  • Cellular uplink and downlink rates remain close to or above their QoS targets throughout the horizon despite random fading.The figures show rates for two groups of 20 cellular users against their corresponding thresholds.Source: C. Numerical Results · p. 10, Figure 3 · p. 11, Figure 4 · p. 11
  • Average CA–CA D2D rate stays above the 10 kbps target, and the selected topology averages 11.5 active links per slot.The 11.5 links are reported as the minimum number required for feasibility under the chosen windowed-connectivity constraint.Source: Figure 5 · p. 11, C. Numerical Results · p. 11
  • The event-triggered baseline alternates complementary subgraphs and reserves bandwidth using worst-case channel SNR; fully-connected activates all 190 D2D links with the same conservative allocation.The event-triggered allocation is reserved for scheduled edges, including links whose endpoints do not trigger.Source: C. Numerical Results · pp. 11–12
  • 59.1% normalized bandwidth consumption is 24.1% below event-triggered (83.2%) and 27.0% below fully-connected (86.1%).The proposed scheme maintains consensus while the baselines provision bandwidth conservatively.Source: C. Numerical Results · p. 12
  • The co-design reaches 1.4×10^-5 ACE disagreement in about 15 s; fully-connected reaches 5.5×10^-7, while event-triggered stalls at 3.9×10^-4.The event-triggered residual is reported as 28 times the co-design residual.Source: Figure 7 · p. 12, C. Numerical Results · p. 12

VI. CONCLUSION

The conclusion presents joint topology and bandwidth optimization as a way to reduce wireless resource use while maintaining consensus and QoS. In a smart-grid case study, it reports 24–27% bandwidth savings over two baselines.

VI. CONCLUSION

  • The approach jointly optimizes the MACS communication topology and wireless resource allocation to minimize bandwidth while maintaining communication and consensus requirements.Source: §VI · pp. 12–13
  • 24–27% bandwidth savings over two baselines were achieved while maintaining consensus and satisfying all QoS requirements.The case study comprises 20 control agents and 40 cellular users.Source: §VI · p. 13, Figure 9 · p. 13
  • A structural property reduces the feasible search space without excluding a globally optimal solution, enabling two sequential stages with polynomial complexity per slot.Source: §VI · p. 13
Loading 2610.30141v1…