Configuration-Constrained Tube MPC for Difference-of-Convex Nonlinear Systems
Abstract
This paper develops a convex tube model predictive control formulation for constrained nonlinear systems. We consider dynamics described by a discrete-time state-space model with parametric and additive uncertainty that admits a difference-of-convex decomposition. Convex directional bounds of the nonlinear dynamics are combined with configuration-constrained polytopic tubes, whose predefined combinatorial structure yields an affine parameterization of their vertices. The resulting finite-dimensional sufficient conditions certify robust one-step tube propagation under parametric uncertainty and additive disturbances, while allowing the tube geometry and an associated vertex control law to be optimized jointly in a single convex program. An implicit terminal condition guarantees recursive feasibility and convergence of the predicted tube to a target robust control invariant set. Numerical results illustrate the closed-loop properties and the trade-off between geometric flexibility and computational complexity.
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BibTeX
@misc{badalamenti2026configurationconstrained,
title = {{Configuration-Constrained Tube MPC for Difference-of-Convex Nonlinear Systems}},
author = {Filippo Badalamenti and Jose A. Borja-Conde and Filiberto Fele and Teodoro Alamo and Daniel Limon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07809},
eprint = {2609.07809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07809},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Configuration-Constrained Tube MPC for Difference-of-Convex Nonlinear Systems
AU - Filippo Badalamenti
AU - Jose A. Borja-Conde
AU - Filiberto Fele
AU - Teodoro Alamo
AU - Daniel Limon
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07809
UR - https://arxiv.org/abs/2609.07809
AB - This paper develops a convex tube model predictive control formulation for constrained nonlinear systems. We consider dynamics described by a discrete-time state-space model with parametric and additive uncertainty that admits a difference-of-convex decomposition. Convex directional bounds of the nonlinear dynamics are combined with configuration-constrained polytopic tubes, whose predefined combinatorial structure yields an affine parameterization of their vertices. The resulting finite-dimensional sufficient conditions certify robust one-step tube propagation under parametric uncertainty and additive disturbances, while allowing the tube geometry and an associated vertex control law to be optimized jointly in a single convex program. An implicit terminal condition guarantees recursive feasibility and convergence of the predicted tube to a target robust control invariant set. Numerical results illustrate the closed-loop properties and the trade-off between geometric flexibility and computational complexity.
ER -