Joint Control–Communication: Co-Design Principles

• Joint control–communication is the co-optimization of control actions and communication protocols in systems with interdependent dynamics.
• It employs models like linear state-space and techniques such as dynamic programming, convex optimization, and reinforcement learning to balance performance and resource use.
• This concept is vital in applications such as power networks, UAV systems, and vehicular platoons, highlighting trade-offs between convergence speed, stability, and communication cost.

The joint control–communication problem addresses how the design and operation of control systems and communication protocols must be inherently co-optimized in systems where physical processes and information exchange are tightly interdependent. This class of problems arises in distributed and networked systems—such as power networks, multi-agent automation, wireless vehicular systems, and cyber-physical environments—where the actions of controllers depend critically on timely and reliable communication, while communication requirements are dictated by system stability, optimality, or performance constraints. The mathematical and algorithmic frameworks for these problems integrate system-theoretic models, optimization, and information constraints, seeking to rigorously quantify and trade off performance, stability, efficiency, and communication resource usage.

1. Core Models and Problem Formalizations

The joint control–communication problem is unified by the explicit interplay between plant dynamics, control objectives, and communication constraints:

Linear/nonlinear state-space models: Distributed plants are modeled as either linear (e.g., discrete/continuous-time LTI systems) or nonlinear (possibly control-non-affine) dynamical systems with multiple agents, nodes, or actuators (Vijithasena et al., 2 Sep 2025).

Control objectives: Typical aims include stability (mean-square, Lyapunov, input-to-state), economic cost minimization (e.g., quadratic cost, economic dispatch), or LQG/LQR performance in the presence of communication uncertainties (Zhang et al., 2018, Liu et al., 19 Jan 2025, Klügel et al., 2019).

Communication architecture: The systems are embedded over networks (wired or wireless, static or mobile). Communication may be centralized, distributed, or hybrid; it may be deterministic, packet-switched, or event-triggered, with varying delays, outages, limited bandwidth, or communication costs.

Joint design variables: Problems couple plant control actions and communication policies. Design variables include local/varying control gains, scheduling or power allocation for network transmissions, communication topologies (who can talk to whom and when), or association/allocation of system elements to communication resources (Zeng et al., 2018, Liu et al., 19 Jan 2025).

Optimization paradigms: Approaches include dynamic programming (for finite-horizon or Markov decision process models), Lyapunov-based joint scheduling, co-design via alternating minimization (e.g., control given communication, and vice versa), and reinforcement learning for policy synthesis in cases where plant or network models are partially known (Vijithasena et al., 2 Sep 2025, Liu et al., 2023, Mason et al., 2023).

2. Foundational Examples and Theoretical Structures

Economic Dispatch with Frequency Regulation: The power grid context provides a canonical example. The network is viewed as a graph with buses and lines, and the swing equations model frequency and power flows. A decentralized integral controller integrates local frequency deviations to restore nominal frequency after disturbances, and controller gains are tuned to minimize generation cost. The trade-off emerges between the control cost gap (to the global optimum) and convergence time, both modulated by the communication policy between nodes (from none, to sparse, to full mesh) (Zhang et al., 2018).

Control-Communication Complexity: For two-agent distributed systems with bilinear input-output mappings, the minimum average control energy required to implement a matrix of target actions is analyzed as a function of information sharing. No-communication protocols (each agent acts with only its own choice) and full-communication protocols (all choices known) span extremes; intermediate protocols reveal the value of each bit of exchanged information in reducing control effort (Wong et al., 2012).

Discrete Event/Finite-State Synthesis: In distributed systems modeled by finite-state automata or Petri nets, coordination between local controllers can be trivial (with full synchronization) or undecidable (without communication). Intermediate schemes use minimal online communication (e.g., local supervisors consult semi-global supervisors only if their knowledge is insufficient to guarantee safety), yielding EXPTIME-complete synthesis but efficient online implementations that minimize communication acts while maintaining invariants (Peled et al., 2011).

3. Methodologies for Joint Design

Analytic and Convex Optimization: For linear/quadratic problems, analytic bounds and convex reformulations (e.g., via matrix inequalities or Lagrangian duality) are standard. In power and wireless networked control, convex approximations or decomposition (alternating minimization: fix control, optimize communication, then vice versa) are often deployed for computational tractability (Zhang et al., 2018, Liu et al., 19 Jan 2025, Hisham et al., 2019).

Successive Convex Approximation (SCA) in Non-Convex Problems: In non-convex joint designs (e.g., UAV communication where trajectory and power must be co-optimized under interference constraints), alternating between convex subproblems (fix one set of variables, optimize the other) and iterative linearization yields locally optimal policies (Huang et al., 2018, Huang et al., 2019).

Dynamic Programming and Coordinator POMDPs: In multi-agent setups with communication costs or constraints, optimal communication and control strategies can be synthesized via dynamic programming on a common-information Markov state (shared belief), which captures all relevant knowledge available to the coordination entity. These provide globally optimal policies and enable extensions such as erasure/packet-loss models and state-dependent costs (Sudhakara et al., 2021, Peled et al., 2011).

Lyapunov-Drift Quantification: In systems with nonlinear or non-affine dynamics, stability-ensuring joint control–communication policies can be constructed using virtual queues and Lyapunov drift-plus-penalty methodologies. Scheduling policies are derived that dynamically balance stabilization requirements and resource/battery constraints (Vijithasena et al., 2 Sep 2025).

Reinforcement Learning and Value-of-Information (VoI) Approaches: Sequential stochastic decision process (SSDP) frameworks and reinforcement learning (RL) algorithms enable model-free joint control–communication design. Key innovations include using estimated value-of-information metrics—quantifying the loss in control performance due to delayed, missing, or imperfect communication—as immediate rewards in DRL agents that drive communication scheduling, resource allocation, and control policies (Lei et al., 11 May 2025, Lei et al., 12 May 2025, Mason et al., 2023, Liu et al., 2023).

4. Trade-Offs and Performance Metrics

The joint control–communication problem is characterized by fundamental trade-offs:

• Performance vs. communication cost: Reducing communication (packet rate, bit rate, event triggers) generally leads to increased control cost (suboptimal convergence, stability margin loss, or regulation cost). Precise quantification is system-dependent but is often expressed in closed-form (see, e.g., bounds on cost gap scaling with communication gain parameter $h$ in economic dispatch (Zhang et al., 2018), or minimum energy formulas in distributed control (Wong et al., 2012)).
• Convergence vs. steady-state optimality: In many feedback-driven systems, increasing communication allows more aggressive (faster) control but may come at higher transient cost or less robustness. Rigorous upper bounds on the transient-to-steady-state cost gap can be given in terms of network algebraic connectivity, susceptibility, and communication topology (Zhang et al., 2018).
• Reliability and latency in networked control: System performance is determined by precise delay and reliability metrics, such as end-to-end latency, buffer state occupancy (used as a network “price” in thresholded sampling), and packet-drop probability. These are coupled to plant stability by explicit algebraic inequalities or Lyapunov mean-square stability conditions (Zeng et al., 2018, Liu et al., 19 Jan 2025, Klügel et al., 2019).
• Value of information: Explicit VoI quantification (expected regret, immediate advantage, or information-theoretic divergence) enables precise scheduling—transmitting only when the control benefit exceeds communication cost (Lei et al., 11 May 2025, Lei et al., 12 May 2025).

5. Application Domains and Representative Results

Power networks: Decentralized integral frequency control (without communication) achieves provable steady-state frequency recovery and nearly optimal dispatch; communication among generators further reduces convergence time and mitigates cost gap, up to full optimality if the communication graph remains connected. Loss of key (weak) communication links degrades performance most significantly (Zhang et al., 2018).

UAV-Aided Cognitive Networks: Joint trajectory and power control under interference-temperature constraints are solved via alternating optimization/SCA, achieving 30–50% rate improvements over single-parameter designs and enabling UAVs to avoid/hover to maximize rates while satisfying spectral coexistence (Huang et al., 2018, Huang et al., 2019).

Wireless Vehicular Networks and Platooning: String stability and delay margin are co-optimized with communication reliability; delay bounds derived from plant stability guide required network latency (including queuing and fading effects). Control gains are tuned to maximize wireless reliability, demonstrating up to 15% increase in reliability when co-optimized (Zeng et al., 2018).

Edge-controlled Networked Systems: In multi-BS/edge-controlled systems with multiple feedback loops, co-design of user association, MIMO resource allocation, and computation scheduling achieves 30–40% closed-loop latency reduction compared to heuristics, while ensuring mean-square stabilization of all subsystems despite hybrid HRLLC and computation constraints (Liu et al., 19 Jan 2025).

Distributed/Discrete-event systems: In Petri-net or automata-based systems, minimizing communication while satisfying global invariants is tractable via local knowledge plus supervisor consultation, with average online communication events per run nearly minimized without incurring deadlock or safety violations (Peled et al., 2011).

Reinforcement Learning and VoI: In complex, high-dimensional or uncertain systems, VoI-augmented DRL agents trained in end-to-end multitimescale fashion (control and communication DRL agents alternately trained with VoI metrics as coupling) yield empirical improvements in control cost, information efficiency, and system reliability—demonstrated in 6G V2X platooning and digital twin assisted vehicular networks (Lei et al., 11 May 2025, Lei et al., 12 May 2025).

6. Extensions, Limitations, and Ongoing Research

• Nonlinear, non-affine systems: Co-designs using deep Koopman embeddings generalize beyond linear/affine dynamics, with stability guarantees and robustness to prediction errors under communication loss (Vijithasena et al., 2 Sep 2025).
• Scalability and complexity: For large networks or multi-agent systems, state-space explosion and the curse of dimensionality remain challenges. Heuristic tables, (partial-)order policies, and model-free RL approaches have proven effective for select architectures (Peled et al., 2011, Mason et al., 2023).
• Dynamic and adversarial environments: Much of the theory assumes cooperative or static network settings. Extending to adversarial packet-loss, time-varying connectivity, or mixed-motive agents (stochastic games/safety games) is an open direction (Mason et al., 2023).
• Data-driven and digital-twin frameworks: Recent work leverages digital twins and data-driven modeling to simulate, co-design, and deploy joint control–communication in the IoV/6G context with real-time assess-and-adapt architecture (Lei et al., 12 May 2025).
• Value-of-information operationalization: Translating value-of-information computations into actionable communication scheduling policies, reward shaping, and multi-level communication-control agent interaction is an active area (Lei et al., 11 May 2025, Lei et al., 12 May 2025).

7. Summary Table of Representative Models and Trade-Offs

Domain	Control Obj. / Plant Model	Comm. Policy / Coupling	Design Outcome	Key Reference
Power networks	Frequency regulation + economic dispatch (swing eqs.)	Local integral + neighbor consensus	Cost gap vs. convergence time	(Zhang et al., 2018)
Two-agent control systems	Target matrix via bilinear functional	None vs. full info exchange	Energy required per scenario	(Wong et al., 2012)
Discrete-event systems	Petri-net/inv. safety model	Local, supervisor-based sparse comm.	Minimal comm. for safety	(Peled et al., 2011)
UAV comm. (spectrum share)	SR rate max., under interference temp. constraints	Trajectory + power alternation	30–50% rate uplift	(Huang et al., 2018)
Vehicular platoon	String stability/LQG under V2V net. delay	Joint gain/delay optimized	Improved rel./stability	(Zeng et al., 2018)
Edge-controlled plants	Mean-square stabilization, latency minimization	Joint assoc., comm., computation alloc.	30–40% latency reduction	(Liu et al., 19 Jan 2025)
Multi-agent RL	CP-task completion time, error rates	Goal-oriented comm. via MARL/CP-POMDP	Near-hardware performance	(Mason et al., 2023)
Digital twin IoV	VoI-driven MDP, interconnected control and comm. RL	CTDE iterative DRL with VoI reward	15–18% error reduction	(Lei et al., 12 May 2025)

This summary reflects the breadth and depth of the joint control–communication problem, highlighting the diversity of models, solution methodologies, and application domains, along with the universal presence of quantifiable trade-offs between system performance and information exchange.