Certificate-Carrying Distributed Model Predictive Control on Product Manifolds with SO(3)
Abstract
This paper studies constraint certification in synchronous distributed model predictive control (DMPC) when neighboring predictions change between sampling instants. Before the parallel local solves, each agent communicates a shifted prediction and an announced update budget. A hard trajectory trust region makes that budget enforceable, while an edge-wise feasibility cap computed from the shifted packets keeps the fallback feasible without using any current optimizer output. Distance and relative-attitude constraints are tightened with explicit Lipschitz constants and two budget layers: one accounts for the simultaneous neighbor update and the other retains a checkable shift reserve. We prove hard pairwise constraint satisfaction and recursive feasibility under stated nominal-execution and terminal assumptions, give the additional residual caused by execution error, and derive a local practical value-decrease bound. A spacecraft formation example uses hard terminal and pairwise constraints, a geodesic relative- attitude constraint on SO, and reproducible terminal-set checks. Comparisons with fixed, trajectory-only, and windowed online margins show that the proposed budget reduces conservatism while preserving a positive shifted-feasibility margin.
Related
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- Distributed Formation Model Predictive Control Under Communication Denial: An Edge-Splitting ADMM with Centralized-Equivalence Gating and Confidence-Decayed Coupling
- Distributed electricity–carbon co-optimization of hydrogen energy storage microgrids with dynamic laplace perturbation and model predictive control
- Trajectory Manifolds for Nonlinear Data-Enabled Predictive Control
BibTeX
@misc{zhang2026certificatecarrying,
title = {{Certificate-Carrying Distributed Model Predictive Control on Product Manifolds with $\mathrmSO(3)$}},
author = {Shengjun Zhang and Tingyi Liu and Lei Xu and Tao Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30655},
eprint = {2609.30655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30655},
}
RIS
TY - UNPB
TI - Certificate-Carrying Distributed Model Predictive Control on Product Manifolds with SO(3)
AU - Shengjun Zhang
AU - Tingyi Liu
AU - Lei Xu
AU - Tao Yang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30655
UR - https://arxiv.org/abs/2609.30655
AB - This paper studies constraint certification in synchronous distributed model predictive control (DMPC) when neighboring predictions change between sampling instants. Before the parallel local solves, each agent communicates a shifted prediction and an announced update budget. A hard trajectory trust region makes that budget enforceable, while an edge-wise feasibility cap computed from the shifted packets keeps the fallback feasible without using any current optimizer output. Distance and relative-attitude constraints are tightened with explicit Lipschitz constants and two budget layers: one accounts for the simultaneous neighbor update and the other retains a checkable shift reserve. We prove hard pairwise constraint satisfaction and recursive feasibility under stated nominal-execution and terminal assumptions, give the additional residual caused by execution error, and derive a local practical value-decrease bound. A spacecraft formation example uses hard terminal and pairwise constraints, a geodesic relative- attitude constraint on SO, and reproducible terminal-set checks. Comparisons with fixed, trajectory-only, and windowed online margins show that the proposed budget reduces conservatism while preserving a positive shifted-feasibility margin.
ER -