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Mission Efficiency Optimization in Low-Altitude Economy: Adaptive Power Allocation for Coordinating Heterogeneous Aircraft Swarms

Jiarui Zhang, Wei Feng, Chao Dong, Ning Ge, Qihui Wu

arXiv:2609.39776v1cs.ITcs.SYeess.SYmath.IT

TL;DR

Coordinating heterogeneous low-altitude aircraft depends on delivering commands through constrained EIH downlinks while respecting each aircraft’s capabilities. The paper proposes OCE-aware adaptive power allocation to minimize LQR cost, and reports lower cost than traditional schemes, especially when power is constrained.

  • Problem

    Complex multi-aircraft missions require coordinated command delivery, while the downlink is critical to mission performance and individual aircraft have limited capability.

    Source: §I · p. 1

  • Method

    The paper defines OCE and jointly accounts for aircraft OCE and channel conditions in an LQR-cost-minimizing power allocation, solved through two convex subproblems iteratively.

    Source: §I · p. 1, §III · p. 3

  • Results

    The proposed scheme achieves the lowest LQR cost for a given power budget and significantly outperforms traditional approaches, with schemes converging as power increases toward the OCE-imposed performance bound.

    Source: §IV · pp. 4–5, §V · p. 5

  • Takeaways & Limitations

    Balancing OCE with channel conditions can improve use of limited power, while increasing power alone cannot overcome the OCE performance bottleneck.

    Source: §IV · p. 5

    Jointly allocating power and bandwidth to optimize SC3 control performance remains an open direction.

    Source: §IV · p. 5

Abstract

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With the rapid development of the low-altitude economy, low-altitude operations are booming, where complex missions require collaborative efforts among multiple heterogeneous low-altitude aircrafts (LAAs). Specifically, different LAAs assume distinct roles: some for sensing, some for communication, some for computing, and others for mission execution, together forming a sensing-communication-computing-control (SC3) closed loop, akin to a reflex arc. To enable efficient coordination in such multi-LAA swarms, we introduce the concept of operational-capability entropy (OCE) to quantify the effective work capability of operational LAAs. Accordingly, by jointly considering heterogeneous OCE and channel conditions among LAAs, we formulate the power allocation problem with the goal of minimizing the linear quadratic regulator (LQR) cost, which serves as a metric for mission efficiency. The resulting complex optimization problem is decomposed into two convex subproblems that are solved iteratively, with closed-form solutions derived for each. Simulation results demonstrate that the proposed mission-oriented adaptive power allocation scheme significantly outperforms traditional ones.

I. INTRODUCTION

Heterogeneous low-altitude aircraft coordinate through a sensing-communication-computing-control (SC3) loop, but constrained EIH downlinks and aircraft capabilities complicate mission-oriented resource allocation. The paper introduces OCE and an adaptive power-allocation approach that accounts for OCE and channel conditions while minimizing LQR cost.

I. INTRODUCTION

  • The SC3 loop connects sensing aircraft, computing aircraft acting as edge information hubs, and operational aircraft that execute control commands.The computing aircraft bridge the sensing and operational aircraft by processing collected data and transmitting commands.Source: §I · p. 1
  • Command delivery from the EIH to operational aircraft is critical, yet limited EIH resources must serve aircraft with heterogeneous capabilities and channel conditions under a strict power budget.These conditions make efficient swarm-wide resource allocation challenging.Source: §I · p. 1
  • Prior resource-allocation work often focuses on communication metrics or models coordinated actuators as independent loops with unlimited operational capability.Commands beyond an aircraft’s processing, caching, or decoding limits may arrive too late, wasting resources and adding control delay or instability risk.Source: §I · p. 1
  • OCE quantifies the effective work capability of an aircraft, capturing how much control information it can receive, decode, and use in one SC3 cycle.The paper combines heterogeneous OCE and channel conditions in a mission-oriented power-allocation formulation.Source: §I · p. 1
  • The proposed OCE-aware, channel-aware power allocation minimizes LQR cost and significantly outperforms traditional approaches in simulations.The optimization is transformed into two convex subproblems with closed-form solutions and an iterative algorithm with guaranteed convergence.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model allocates EIH downlink power across operational aircraft in a cooperative SC3 mission, accounting for wireless-channel capacity and each aircraft’s operational-capability entropy. The formulation uses LQR cost to represent control performance and imposes rate, capability, and power constraints.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The EIH sends commands to K operational aircraft over orthogonal downlink channels, with total transmit power limited by Pmax.The model assumes single antennas on the operational aircraft and the EIH’s user-facing communication module.Source: §II · p. 1
  • Each aircraft’s downlink capability depends on its channel gain, modeled using small-scale Rayleigh fading and large-scale gain with distance-dependent path loss and shadow fading.The model describes ergodic channel capability for the EIH-to-aircraft links.Source: §II · p. 2
  • OCE Ek bounds the control-command rate an aircraft can effectively execute in one SC3 cycle; rates above Ek cannot be processed in time.The model constrains each aircraft’s rate by its OCE.Source: §II · p. 2
  • The cooperative mission’s control process is modeled as a discrete linear time-invariant system with state and control inputs.The total control action combines the individual aircraft actions.Source: §II · p. 2
  • LQR cost measures control performance as a weighted sum of state deviation and control input.The formulation states that this cost has a lower bound.Source: §II · p. 2
  • Stability requires the mission-related data rate per cycle to exceed the system’s intrinsic entropy rate; otherwise, LQR cost is infinite.The stated condition is R > log2 |det A|.Source: §II · p. 2
  • The non-convex power-allocation problem uses Shannon-capability and OCE rate constraints, alongside nonnegative power and auxiliary variables.The formulation jointly optimizes the power vector and an auxiliary vector.Source: §II · p. 3

III. MISSION-ORIENTED ADAPTIVE POWER ALLOCATION

The section converts LQR-cost minimization into maximizing mission-related data rate, then solves the resulting allocation problem through two convex subproblems in an iterative scheme.

III. MISSION-ORIENTED ADAPTIVE POWER ALLOCATION

  • Because the LQR-cost expression decreases with R, minimizing LQR cost is equivalent to maximizing R; maximizing mission-related data rate also requires Shannon-capability equalities.These transformations yield the max-min problem P2.Source: §III · p. 3
  • Strong concavity in power and strong convexity in the auxiliary variables let the max-min problem split into two convex subproblems solved iteratively.The paper states that the subproblems can be solved with an iterative algorithm.Source: §III · p. 3
  • With p fixed, the auxiliary-variable block separates into K single-variable convex problems minimizing each Rk, and its OCE constraint can be omitted because the power block enforces it.During alternating optimization, satisfying the OCE constraint in P3 means P4 inherently satisfies it as well.Source: §III · p. 3
  • For the power block, each subchannel reaches its OCE limit when the stated power condition holds, while insufficient total power requires full transmit-power use.At the OCE limit, increasing power yields no further performance improvement.Source: §III · p. 3
  • The iteration uses F(w) and G(p) as optimal responses for fixed counterpart variables, blends them with current iterates, and applies backward-feedback updates.F returns the optimal p for fixed w; G returns the optimal w for fixed p.Source: §III · p. 4
  • The initial iterate must lie in the feasible region, or the iteration may not proceed.The stability condition is checked after solving P2; if it fails, the system cannot be stabilized and its LQR cost is infinite.Source: §III · pp. 3–4

IV. SIMULATION RESULTS AND DISCUSSION

Simulations show the proposed scheme achieves the lowest LQR cost across power budgets and converges quickly. Its advantage is strongest under constrained power or bandwidth, while performance eventually approaches an OCE-imposed ceiling.

IV. SIMULATION RESULTS AND DISCUSSION

  • Unless otherwise specified, simulations use five operational LAAs distributed within a 5 km-radius, 1 km-altitude area, with 5 kHz subchannels and 49.8 ms latency.The control-noise variables are independent zero-mean Gaussians with variance 0.01; the algorithm terminates at δ = 10^-6.Source: §IV · p. 4
  • The iterative algorithm converges within 18 iterations across 100 independent simulations.The simulations randomly selected 5–20 operational LAAs and maximum transmit power of 6–24 dBW.Source: Figure 3 · p. 4, §IV · p. 4
  • The proposed scheme achieves the lowest LQR cost for every Pmax; below 7 dBW, conventional schemes approach instability and infinite cost.At sufficiently high power, scheme performance converges as the OCE-imposed upper bound becomes dominant.Source: Figure 4 · p. 4, §IV · pp. 4–5
  • The proposed allocation balances OCE and channel gain, avoiding resource waste on low-OCE channels through OCE-constrained water-filling.The control-oriented baseline can overallocate power to LAAs with favorable channels but low OCE.Source: Figure 5 · p. 5, §IV · p. 5
  • At Pmax = 10 dBW, the proposed scheme has the lowest LQR cost across subchannel bandwidths, with a larger advantage when bandwidth is limited.Increasing bandwidth lowers LQR cost across schemes, but their performance converges as the bottleneck shifts from bandwidth to OCE; joint power-and-bandwidth allocation remains open.Source: Figure 6 · p. 5, §IV · p. 5

V. CONCLUSIONS

The conclusion presents OCE-aware adaptive power allocation for multi-LAA SC3 control, with LQR cost as the mission-efficiency objective. The scheme jointly accounts for OCE and channel heterogeneity and outperforms traditional approaches in simulations.

V. CONCLUSIONS

  • The proposed mission-oriented adaptive power allocation minimizes LQR cost while jointly accounting for OCE and channel heterogeneity.OCE quantifies LAAs’ work capability during mission execution.Source: §V · p. 5
  • The original non-convex problem is decoupled into two convex subproblems with closed-form solutions, and an iterative algorithm is developed.Source: §V · p. 5
  • Simulations show the scheme exploits limited resources and significantly outperforms traditional approaches.Source: §V · p. 5
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