Distributed MPC and Decentralized MPC

The core distinction lies in the level of subsystem coordination. Distributed MPC involves iterative, cooperative optimization where subsystems solve local problems but exchange information (e.g., predicted states or inputs) to converge on a globally consistent solution. Decentralized MPC employs fully independent local controllers that operate based only on local measurements and models, with no explicit coordination loop. Distributed MPC seeks a Nash equilibrium or Pareto optimum through negotiation, while decentralized controllers often assume weak coupling between subsystems.

Communication patterns define feasibility. Distributed MPC requires a reliable, often synchronous, communication network to support multiple rounds of message passing (iterations) within each control sampling period. Bandwidth and latency are critical. Decentralized MPC is designed for minimal or no communication; it is the preferred choice when communication is unreliable, expensive, or introduces security risks. Decentralized schemes may use implicit coordination via the physical coupling of the plant itself.

This defines how the global system model and objective are partitioned. In Distributed MPC, the global optimization problem is decomposed into smaller subproblems. Subsystems are coupled through:

• State Coupling: Shared state variables.
• Input Coupling: Control inputs that affect multiple subsystems.
• Constraint Coupling: Constraints involving variables from multiple agents. Algorithms like Dual Decomposition or the Alternating Direction Method of Multipliers (ADMM) are used to handle these couplings. Decentralized MPC ignores these couplings in the optimization, treating other subsystems' actions as unmeasured disturbances, which requires robustness to this approximation.

Theoretical guarantees differ significantly. Distributed MPC, with sufficient communication and convergence of its iterative algorithm, can approach the performance of a centralized controller, offering near-optimal solutions and formal guarantees of closed-loop stability and constraint satisfaction for the overall system. Decentralized MPC generally provides no global optimality guarantees. Stability is analyzed by considering the interconnected system as a set of perturbed subsystems, often using small-gain theorem or ISS (Input-to-State Stability) arguments, leading to potentially more conservative performance.

Complexity shifts from online computation to offline design. Distributed MPC moves the computational burden of a large centralized problem onto parallel solvers across subsystems, but introduces complexity in designing the coordination protocol, ensuring convergence, and managing communication. Decentralized MPC has very low online computational cost per agent, as each solves a small, local problem. The design complexity lies in ensuring the independent controllers are robust to interactions, often requiring extensive offline analysis and possibly conservative tuning.

The choice is driven by physical and infrastructural constraints.

Distributed MPC is applied in:

• Power Grids: For economic dispatch and voltage control across interconnected areas.
• Large-Scale Chemical Processes: With tightly integrated unit operations.
• Formations of UAVs/UGVs: Where coordinated trajectory planning is essential.

Decentralized MPC is applied in:

• Building Temperature Control: Where rooms are loosely coupled.
• Large-Scale Irrigation Networks: With limited communication infrastructure.
• Automated Highway Systems: Where vehicles act primarily on local sensor data.

The baseline architecture where a single, monolithic controller has access to all sensor data from the entire system and computes all control inputs by solving one large optimization problem.

• Key Characteristic: Full system observability and centralized decision-making.
• Limitation: Computational complexity scales poorly with system size, creating a single point of failure and high communication bandwidth requirements to a central node.
• Use Case: Small-scale processes like a single chemical reactor or a drone where a single processor can manage the entire model and optimization in real-time.

An architecture where the overall system is partitioned into fully independent subsystems. Each local controller uses a local model of its own subsystem, measures only local states, and computes its local control actions with no explicit communication or coordination with other controllers.

• Key Characteristic: No communication between controllers. Stability and constraint satisfaction rely on careful offline design to ensure the decoupled or weakly coupled subsystems do not destabilize each other.
• Advantage: Simple, robust to communication failures, and highly scalable.
• Use Case: Large-scale systems with naturally weak dynamic coupling, such as temperature control in separate rooms of a building or independent vehicles on a highway with large headways.

A coordinated architecture where the global system is decomposed into subsystems with local controllers. These controllers solve local optimization problems but communicate iteratively with neighbors to share predicted trajectories. Through this negotiation, they converge toward a solution that approximates the global optimum.

• Key Characteristic: Iterative, cooperative computation with communication. Employs consensus algorithms or decomposition methods like Dual Decomposition or the Alternating Direction Method of Multipliers (ADMM).
• Advantage: More scalable than centralized MPC and can achieve near-optimal performance for coupled systems.
• Use Case: Tightly coupled networks like power grids, formation flying of drones, or multi-zone heating, ventilation, and air conditioning systems where actions in one zone affect others.

A multi-layer control architecture that separates decision-making by timescale or objective. A supervisory MPC operates at a slower timescale with a coarse model to set economic targets or trajectory references. One or more lower-layer MPC (which may be distributed or decentralized) operate at a faster timescale to achieve these setpoints while handling detailed dynamics and constraints.

• Key Characteristic: Vertical decomposition with different optimization horizons and models.
• Advantage: Manages complexity by separating strategic planning from tactical control.
• Use Case: Plant-wide process optimization in chemical industries, where an economic MPC sets production targets for unit operations controlled by faster regulatory MPCs.

This distinction defines the objective of the local controllers in a multi-agent setting.

• Cooperative MPC: All agents share a common global objective (e.g., minimize total fleet energy consumption). In Distributed MPC, agents cooperate through communication to achieve this shared goal.
• Non-Cooperative MPC: Each agent acts in its own self-interest, optimizing a local objective that may conflict with others (e.g., competing autonomous vehicles minimizing their own travel time). This leads to a game-theoretic formulation like Nash equilibrium, where stability is not guaranteed without careful design.

Most industrial Distributed MPC is cooperative, while non-cooperative approaches are studied for economic or adversarial multi-agent scenarios.

A specific application domain for Distributed and Decentralized MPC where the subsystems are autonomous agents (e.g., robots, vehicles). The focus is on enabling collaborative task completion (like payload transport) or independent goal achievement while avoiding collisions.

• Key Techniques: Incorporates collision avoidance constraints (often as coupled constraints requiring communication in Distributed MPC) and may use consensus on a shared plan.
• Communication Topology: Defines which agents talk to each other (e.g., mesh, star, or limited peer-to-peer networks).
• Challenge: Must handle dynamically changing network connectivity and real-time computation. Frameworks often integrate MPC with higher-level task allocation and path planning.