PreprintCC BY-NC-SA 4.0arXiv
On the suboptimality of stochastic MPC with varying constraint horizon
Abstract
Enforcing stochastic state constraints over the full prediction horizon in Model Predictive Control (MPC) can be computationally demanding. Here we study stochastic MPC without terminal ingredients in which chance constraints are enforced only over a shorter constraint horizon. Using stochastic relaxed dynamic programming, we derive an explicit upper bound on the average expected closed-loop cost that depends on both prediction and constraint horizons. For linear quadratic problems with affine chance constraints and bounded uniform disturbances, we provide a deterministic reformulation via coordinate transformation and constraint tightening. Simulations illustrate the trade-off between computational effort and performance.
Related
- Stochastic Sequential Feedback Optimization for Wind Farm Control under Time-Varying Inflow
- Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations: Spectral Contraction and Infinite-Horizon Maximum Principle
- On the Limits of Stochastic Push-Pull over Time-Varying Digraphs
- Optimal Resource Extraction under Distribution Learning and Infinite-Horizon Stochastic Hamilton--Jacobi Equations
- Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games
BibTeX
@misc{nascimento2026suboptimality,
title = {{On the suboptimality of stochastic MPC with varying constraint horizon}},
author = {Allan Andre Do Nascimento and Andre Bertolace and Antonis Papachristodoulou and Kostas Margellos},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30017},
eprint = {2608.30017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30017},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - On the suboptimality of stochastic MPC with varying constraint horizon
AU - Allan Andre Do Nascimento
AU - Andre Bertolace
AU - Antonis Papachristodoulou
AU - Kostas Margellos
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.30017
UR - https://arxiv.org/abs/2608.30017
AB - Enforcing stochastic state constraints over the full prediction horizon in Model Predictive Control (MPC) can be computationally demanding. Here we study stochastic MPC without terminal ingredients in which chance constraints are enforced only over a shorter constraint horizon. Using stochastic relaxed dynamic programming, we derive an explicit upper bound on the average expected closed-loop cost that depends on both prediction and constraint horizons. For linear quadratic problems with affine chance constraints and bounded uniform disturbances, we provide a deterministic reformulation via coordinate transformation and constraint tightening. Simulations illustrate the trade-off between computational effort and performance.
ER -