In simulations, a proposed distributed control method tied for the fewest reported consensus steps in both 50-robot and 100-robot networks, while recording the lowest listed performance cost. The result comes from an arXiv preprint that tests modeled multi-agent systems. The method jointly optimizes control inputs and a common equilibrium, but that equilibrium must be admissible for every agent. The paper’s guarantees are conditional, and the closed-loop theorem assumes the optimization is solved exactly at every update.
The target has to work for every agent
Model predictive control, or MPC, is used here as a way to plan control inputs over a prediction horizon while choosing the common equilibrium at the same time. The target is not a fixed point imposed in advance. It is selected from the equilibrium options allowed by each agent’s constraints. The modeled agents have constant but potentially different discrete-time linear dynamics. Their state sets are convex and closed, their input sets are convex and compact, and their input matrices have full column rank. For a general reader, the practical meaning is straightforward: the controller looks for one shared operating point that the different agents can all support under the model.
The calculation is distributed, but the proof is conditional
That shared choice is calculated in a distributed way. Algorithm 2 solves the local control and equilibrium subproblems in parallel, then uses a distributed stopping condition that involves all agents across the network. Theorem 1 states that these iterations converge to the optimal solution when the optimization problem is feasible, the paper’s common-relative-interior assumption holds, and its listed local conditions are met. The claim is therefore a conditional result about the solver, not a promise that every network will converge under any settings.
Corollary 1 adds a convergence-rate estimate. It links the objective and the consensus residual to the iterations when the norm of an optimal Lagrange multiplier is bounded by a positive constant, called gamma in the analysis. The estimate depends on that bound and on the algorithmic assumptions, so it should be read as a conditional analytical measure rather than a universal performance figure.
Small simulations set the stage
The first numerical example used five heterogeneous linear agents, a prediction horizon of eight steps, and a control period set to two. In the reported run, the agents reached consensus while keeping state variables and control inputs within their prescribed constraints. The inputs converged to distinct nonzero values.
A second simulation used five robots whose actual masses varied around a nominal mass. The paper reports that the formation task was completed. Together, the examples illustrate the proposed calculation in two modeled settings, one framed as heterogeneous linear agents and one as a robot formation.
The larger tests favored the proposed method
The larger comparison used robot networks of 50 and 100 robots and compared the proposed method with STBC, AFGC, STMPC and OCMPC. In the 50-robot case, the proposed method and OCMPC each reached consensus in 26 steps, the shortest reported result. The proposed method had the lowest listed cost at 3.6616 × 104, compared with 3.6648 × 104 for OCMPC. STMPC took 68 steps and had a cost of 3.5440 × 105; STBC took 87 and 3.3821 × 105; AFGC took 143 and 5.1211 × 105.
At 100 robots, the proposed method and OCMPC again tied at 27 consensus steps. The proposed method’s listed cost was 4.6292 × 104, below OCMPC’s 4.6309 × 104. STMPC required 87 steps and 4.0371 × 105; STBC required 127 and 3.5506 × 105; AFGC required 169 and 5.7765 × 105. The proposed method therefore retained the lowest listed cost in the larger test.
The key qualification is finite solver accuracy
The numbers favor the proposed method in these reported simulations, but the closed-loop proof carries an important qualification. Theorem 2 assumes an exact optimal MPC solution at every prediction time. The algorithm’s finite stopping rule generally produces only an approximate solution, and the authors say the effect of that error on closed-loop feasibility, constraint satisfaction and consensus is beyond the paper’s scope. The simulations show reported behavior under the tested settings, while the theorem does not characterize finite-iteration error.
The document is an arXiv version 1 preprint dated 28 Aug 2026. It reports support from the National Natural Science Foundation of China, the Beijing Municipal Science & Technology Commission and Administrative Commission of Zhongguancun Science Park, and the Fundamental Research Funds for the Central Universities.
Paper data and sources
Original title: Distributed Model Predictive Control for Optimal Consensus of Constrained Heterogeneous Multi-agent Systems
Authors: Nan Bai, Tao Liu, Qishao Wang, Zhisheng Duan
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text