Coordinated Mobility & Power Control

• Coordinated mobility and power control is the joint optimization of movement and energy allocation in multi-agent systems, enhancing throughput, reliability, and cost efficiency.
• Techniques such as approximate dynamic programming, mixed-integer convex programming, and Lyapunov-based control are employed to solve large-scale, nonconvex problems in real time.
• Application areas include robotic relays, vehicular networks, and MEC systems, where coordinated strategies deliver measurable gains in performance and energy savings.

Coordinated mobility and power control concerns the joint optimization of motion (mobility, trajectory, dispatch) and transmission/charging power in distributed multi-agent, vehicular, robotic, and networked systems. The core objective is to maximize global utility—such as throughput, reliability, energy efficiency, connectivity, or system cost—by exploiting the interplay between agents’ spatiotemporal decisions and their power budgets under practical network, energy, or interference constraints. The field covers foundational dynamic programming, network utility maximization, graph-theoretic models, mixed-integer convex programming, Lyapunov-based online control, and a variety of distributed or decentralized algorithmic paradigms for both information-centric and infrastructural scenarios across wireless, transportation, and cyber-physical systems.

1. Fundamental Problem Formulations

Coordinated mobility and power control problems are naturally formulated as large-scale, often nonconvex, constrained optimization problems that jointly capture agent dynamics (physical motion or routing), communication (or energy transfer) models, and power/resource allocation.

In robotic relay or mobile networking, the canonical framework considers a set of $N$ mobile agents (relays) and, typically, two fixed base stations. The system state is a stacked vector $z_k\in\mathbb{R}^{2(N+2)}$ of all positions at time step $k$; agent actions are velocity vectors $u_k\in\mathbb{R}^{2N}$. The per-stage cost is decomposed as

$$C(z_k, u_k) = J_{\rm comm}(z_k) + J_{\rm mob}(u_k),$$

where $J_{\rm comm}$ penalizes link quality (e.g., squared distances, modeling communication or power transfer cost) and $J_{\rm mob}$ penalizes motion energy. The problem is to minimize the expected discounted total cost via an admissible policy, leading to a dynamic programming (DP) formulation with Bellman recursion: $$V^*(z) = \min_{u} \left[ C(z, u) + \alpha V^*(z + B u) \right ].$$ Key research has produced approximate dynamic programming (ADP) policies with provable performance gaps (Jaleel et al., 2016), as well as distributed and decentralized algorithms for real-time implementation.

In networked vehicular systems and intelligent transportation-power systems, the OMTEPF (Optimal Multi-Modal Transportation and Electric Power Flow) model integrates vehicle dispatch, route selection, charging (wired, inductive, V2G), and power flow into a unified mixed-integer convex program (Qiu et al., 13 Oct 2025). The state includes individual EV state-of-charge (SOC), network queues, vehicle and power flow variables, and links multiple decision layers with coupling constraints between transportation and electrical networks.

In dynamic wireless or cyber-physical networks (e.g., multi-UAV, vehicular ad hoc networks), the system state generalizes to joint (possibly time-indexed) positions, velocities, transmit powers, and possibly task migration parameters, with constraints on motion, communication delay, link interference, or queue stability (Hou et al., 13 Dec 2025, Liang et al., 2022, Shen et al., 2018, Huang et al., 2019).

2. Algorithmic Paradigms and Solution Methods

The high dimensionality and nonconvexity associated with coupled mobility and power variables require scalable, structure-exploiting algorithms:

• Approximate Dynamic Programming: Policies are constructed by sparsity projection of the global Riccati solution or via one-step lookahead, yielding distributed update laws. The suboptimality can be explicitly bounded in terms of the cost-to-go norm error; for example, for projection-based policies EAP I/II, the gap is upper-bounded as $$\|J^{\hat\mu} - J^*\| \leq 2\alpha\varepsilon/(1-\alpha)$$, with $\varepsilon$ the worst-case approximation error (Jaleel et al., 2016).
• Hetero-Functional Graph and Mixed-Integer Programming: Complex MES are modeled as engineering nets with place-transition structure, capturing transportation, charging, electric flow, and SOC dynamics. Coordinated operation is achieved by solving a large-scale mixed-integer convex optimization, typically using commercial solvers (e.g., Gurobi, JuMP), leveraging block-diagonal or per-agent structure for scalability (Qiu et al., 13 Oct 2025).
• Lyapunov-Based Online Control: Dynamic reliability and energy trade-offs in computation offloading or networked migration are optimized using virtual-queue-based Lyapunov drift-plus-penalty methods. This yields two-timescale algorithms: large timescale for mobility/service migration; small timescale for per-slot power decisions, often resulting in adaptive threshold policies (Liang et al., 2022).
• Convexification and Successive Convex Approximation (SCA): In multi-UAV or UAV-cognitive radio scenarios, joint trajectory and power control (TPC) is performed via SCA or semidefinite relaxation. These methods iteratively linearize nonconvex rate and interference constraints, solving convex approximations at each step until convergence to a KKT point (Shen et al., 2018, Huang et al., 2019).
• Distributed/Parallel Algorithms: Primal gradient/projection methods decompose multi-node NUM problems over individual power and trajectory variables, enabling fully distributed synchronous or asynchronous execution subject to convexity (gradient projection, dual decomposition). Block Successive Upper-bound Minimization of Multipliers (BSUMM) and segment-by-segment decomposition further parallelize the solution and reduce per-iteration complexity (Hou et al., 13 Dec 2025, Shen et al., 2018).

3. Representative Application Domains

Coordinated mobility and power control underpins a wide range of emerging autonomy and cyber-physical infrastructure applications:

• Robotic and Relay Networks: Teams of mobile nodes (relays, swarms) can establish communication links with provable energy guarantees by jointly planning movement and transmission power, using distributed ADP schemes to ensure real-time feasibility and local information exchange only (Jaleel et al., 2016).
• Future Mobility-Energy Systems: With electrified transportation accounting for a major share of energy consumption, joint optimization of routing (dispatch, queueing), charging schedules, and grid dispatch is crucial. The OMTEPF model demonstrates that integrated operation yields up to 28% reductions in peak dispatchable generation cost, significant CO₂ emission reduction, and improved effective utilization compared to siloed management (Qiu et al., 13 Oct 2025).
• Edge Computing and Mobile Networks: Two-timescale frameworks address user mobility (migration of service between MEC servers) and instantaneous power control for task offloading, guaranteeing reliability and latency while minimizing mobile energy under fast-changing wireless channels and user trajectories (Liang et al., 2022).
• Vehicular and UAV Networks: In V2X or multi-UAV networks, coordinated trajectory and power control (NUM formulation, SCA-based TPC) enhance packet reception rates, manage interference, and achieve near-optimal connectivity, especially under dense, interference-limited conditions. The fly-hover-fly strategy is provably optimal under round-trip constraints, and coordination outperforms orthogonal access by up to 30% in sum throughput (Hou et al., 13 Dec 2025, Shen et al., 2018, Huang et al., 2019).

4. Performance Analysis, Scalability, and Implementation

The primary metrics are network utility (e.g., sum throughput, aggregate PRR), energy efficiency, reliability (e.g., task-failure rate), emission reduction, and system utilization. Algorithmic performance is quantified both via suboptimality gaps (with explicit bounds) and empirical evaluations.

A consolidated table from the ADP-based relay control scenario (Jaleel et al., 2016):

Policy	Discounted Cost	Gap to Optimum
Optimal	$2.62\times10^6$	--
EAP I	$3.94\times10^6$	$\approx$50%
EAP II	$2.91\times10^6$	$\approx$11%
EAP III	$2.88\times10^6$	$\approx$10%

In OMTEPF-controlled MES, coordinated operation improves the system objective by 3.6%, reduces generation costs by 28%, and yields an ~8% CO₂ reduction relative to uncoordinated baselines (Qiu et al., 13 Oct 2025).

Scalability is achieved via per-agent block-diagonalization, segmenting long horizons, and leveraging convex problem structure. For instance, BSUMM parallelizes TPC over $K$ UAVs, each solving a local QP per iteration, and segment-by-segment TPC achieves ~10× speedup with negligible throughput loss (Shen et al., 2018). Lyapunov-based MEC control exhibits explicit $[O(1/V),\,O(V)]$ energy-delay/reliability trade-off (Liang et al., 2022).

Distributed implementation is enabled by restricting required information exchange to local neighbors (e.g., one-hop consensus for power/position updates (Jaleel et al., 2016), peer-to-peer utility gradients for V2X (Hou et al., 13 Dec 2025)), and by adopting threshold-based local control rules whenever global communication is impractical.

5. Theoretical Insights and Guiding Principles

Several common principles emerge across domains:

• Convexity and Concavity: A key analytical insight is that utility functions, e.g., $\log(P_{i,j})$, maintain concavity in power and position variables, supporting distributed convex optimization with global optima (Hou et al., 13 Dec 2025). This property underpins the design of fully decentralized utility gradient-based update rules.
• Sparsity and Real-Time Feasibility: Imposing communication graph sparsity on global cost-to-go matrices (e.g., via Laplacian zeroing/projection in the Riccati solution) allows distributed approximate dynamic programming with bounded suboptimality and practical communication requirements (Jaleel et al., 2016).
• Separation of Timescales: Decoupling slow timescale mobility/migration from fast timescale power control exploits the inherent system dynamics and reduces decision complexity without significant utility loss; virtual queue–driven Lyapunov optimization ensures long-term constraints are met (Liang et al., 2022).
• Path/Trajectory Structural Results: The fly-hover-fly property in multi-UAV TPC scenarios is optimal under round-trip and symmetry constraints, dramatically reducing trajectory planning dimensionality (Shen et al., 2018). Joint 3D mobility and power control in cognitive UAV communication reveals that optimal altitude is at the minimum feasible for quasi-stationary operations, but must adapt dynamically in mobile or interference-limited regimes (Huang et al., 2019).

6. Extensions, Open Challenges, and Future Directions

Major ongoing directions include:

• Integration of Uncertainty and Stochastic Elements: Incorporating stochastic renewables, time-varying or unpredictable user demand and channel conditions, requires robust/stochastic optimization and real-time learning mechanisms.
• Large-Scale and Real-Time Deployment: Further scaling to hundreds or thousands of agents/vehicles in dense networks, or extending frameworks to accommodate interdependent critical infrastructure (transportation, power, communication), is actively studied, with emphasis on distributed and hierarchical architectures.
• Resource Market Mechanisms: Dynamic tariffs and joint pricing of mobility-power costs, as well as economic mechanisms for resource allocation, are proposed to align user incentives with societal optima in MES and networked transportation (Qiu et al., 13 Oct 2025).
• Cyber-Physical Security and Resilience: Maintaining coordination in the presence of adversarial interference, attacks, or failure, and designing control schemes robust to model misspecification or partial observability.
• Application to Emerging Domains: Extension of coordinated control to ride-sharing fleets, autonomous logistics, V2G ancillary service markets, and swarms of connected UAVs or ground robots is ongoing.

7. Key References and Comparative Summary

Reference	Primary Domain	Architecture/Method	Performance Highlights
(Jaleel et al., 2016)	Robotic relay/agents	Approx. DP (EAP I/II/III)	Suboptimality gap $<11\%$, local implementation
(Qiu et al., 13 Oct 2025)	Mobility-energy-infra	OMTEPF (mixed-integer convex)	28% gen. cost reduction, 8% CO₂ decrease
(Liang et al., 2022)	MEC mobile offloading	Two-timescale Lyapunov O.C.	30–50% energy savings, $O(1/V)$ optimality gap
(Hou et al., 13 Dec 2025)	V2X/UAV connectivity	NUM, distributed gradient	$+7\%$ PRR real-world, symmetry optimality
(Shen et al., 2018)	Multi-UAV interference	SCA-TPC, parallel & segmental	$>30\%$ sum-rate gain, provable fly-hover-fly
(Huang et al., 2019)	Cognitive UAV comm	SDP+SCA, trajectory-power	10–40% rate gains, dynamic altitude adaptation

Coordinated mobility and power control, across theoretical approaches and system contexts, demonstrates substantial utility gains, scalability, and resilience over separated designs, provided that algorithmic and structural insights into convexity, sparsity, and spatio-temporal coupling are fully leveraged.