Distributed Model Predictive Control for Dynamic Cooperation of Multi-Agent Systems

We propose a distributed model predictive control (MPC) framework for coordinating heterogeneous, nonlinear multi-agent systems under individual and coupling constraints. The cooperative task is encoded as a shared objective function minimized collectively by the agents. Each agent optimizes an artificial reference as an intermediate step towards the cooperative objective, along with a control input to track it. We establish recursive feasibility, asymptotic stability, and transient performance bounds under suitable assumptions. The solution to the cooperative task is not predetermined but emerges from the optimized interactions of the agents. We demonstrate the framework on numerical examples inspired by satellite constellation control, collision-free narrow-passage traversal, and coordinated quadrotor flight.

💡 Research Summary

This paper introduces a novel distributed model predictive control (DMPC) framework designed to coordinate heterogeneous, nonlinear multi‑agent systems under both individual and coupling constraints, without requiring a pre‑specified cooperative trajectory. The central idea is to embed an artificial reference as a decision variable for each agent, allowing the agents to generate intermediate “cooperation outputs” that serve as locally tracked targets while simultaneously minimizing a global cooperation objective.

The authors first formalize the cooperative task as a compact set of admissible periodic output trajectories, (Y_c^T). Each agent selects a cooperation output (y_{T,i}) from a locally admissible set (Y_{T,i}) and, through Lipschitz‑continuous injective mappings (g_{x,i}) and (g_{u,i}), obtains a corresponding periodic state‑input reference ((x_{T,i},u_{T,i})). This reference is used in a standard tracking cost (\ell_i’) that measures the minimal stage cost required to drive the current state toward the reference.

The global cost consists of two parts: (1) a tracking component that penalizes deviation of each agent’s state from its chosen reference, and (2) a cooperation objective (W_c) that quantifies the distance of the collection of cooperation outputs from the set (Y_c^T). Crucially, (W_c) is separable with respect to the communication graph, i.e., (W_c = \sum_i W_{c,i}(y_{T,i},y_{T,N_i})), which enables fully distributed optimization using only neighbor information.

To guarantee closed‑loop properties, the paper adopts standard MPC‑for‑tracking terminal ingredients: a terminal control law (k_{f,i}), a terminal cost (V_{f,i}), and a terminal set (X_{f,i}) that are defined for any admissible periodic reference. Under a set of technical assumptions (compactness of admissible reference sets, Lipschitz continuity of the reference mappings, existence of suitable terminal ingredients, etc.), the authors prove three main theoretical results:

1. Recursive Feasibility – If the initial state satisfies the individual and coupling constraints, the DMPC problem remains feasible at every subsequent sampling instant. This follows from the fact that the artificial reference can always be chosen inside the interior of the constraint set.

2. Asymptotic Stability – A Lyapunov‑like function (V = \sum_i V_{f,i} + W_c) is shown to be non‑increasing along the closed‑loop trajectory, implying that the collective output converges to the cooperation set (Y_c^T).

3. Transient Performance Bounds – The authors derive explicit bounds showing that the closed‑loop cost improves as the prediction horizon (N) grows, extending known results for single‑agent MPC‑for‑tracking to the multi‑agent setting.

The framework is illustrated through three numerical case studies:

• Satellite Constellation Control – Multiple satellites autonomously achieve a periodic relative formation without a centrally prescribed trajectory.

• Collision‑Free Narrow‑Passage Traversal – Ground robots navigate a tight corridor while respecting inter‑robot distance constraints, demonstrating the emergence of a safe traversal order.

• Coordinated Quadrotor Flight – A fleet of quadrotors maintains a complex formation and avoids collisions, highlighting the method’s ability to handle fast, highly nonlinear dynamics.

In all scenarios, the distributed scheme achieves the cooperative goal with relatively short prediction horizons (as low as 5–10 steps) and without any central coordination. The authors emphasize the modularity of the design: dynamics, constraints, terminal ingredients, and the cooperation objective can be designed independently, facilitating easy adaptation to changes in topology or task specifications.

The paper concludes by suggesting future extensions such as handling asynchronous updates, communication delays, stochastic constraints, and experimental validation on hardware platforms. Overall, the work provides a powerful and flexible tool for achieving emergent cooperative behavior in complex, constrained, nonlinear multi‑agent systems.