Verifying performance, stability, and feasibility of inexact non-linear model predictive controllers
Abstract
We introduce a verification framework to numerically analyze inexact model predictive controllers (MPCs) in the constrained non-linear discrete-time setting. Rather than modifying the controller so that guarantees hold by construction, we treat the controller as given. In particular, we focus on two types of inexact controllers: (a) one whose input is extracted from a primal-dual point satisfying the Karush-Kuhn-Tucker (KKT) conditions of the non-convex MPC problem, and (b) one whose input is obtained by linearizing the dynamics and solving a convex quadratic program. The main idea of our verification framework is to formulate an optimization problem that searches over the worst-case initial state within a given set and control inputs consistent with the inexact controller to maximize a carefully-chosen performance metric. Using this framework, we show how to certify (i) the worst-case suboptimality gap of a single MPC problem, (ii) the worst-case closed-loop suboptimality gap over a given number of dynamical system iterations, (iii) closed-loop stability, and (iv) feasibility of the closed-loop system. Through numerical examples, we showcase the ability of our framework to precisely quantify both types of suboptimality, and to test the stability and feasibility of the inexact controllers.
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BibTeX
@misc{sambharya2026verifying,
title = {{Verifying performance, stability, and feasibility of inexact non-linear model predictive controllers}},
author = {Rajiv Sambharya and Sribalaji C. Anand and George Pappas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14920},
eprint = {2609.14920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14920},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Verifying performance, stability, and feasibility of inexact non-linear model predictive controllers
AU - Rajiv Sambharya
AU - Sribalaji C. Anand
AU - George Pappas
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14920
UR - https://arxiv.org/abs/2609.14920
AB - We introduce a verification framework to numerically analyze inexact model predictive controllers (MPCs) in the constrained non-linear discrete-time setting. Rather than modifying the controller so that guarantees hold by construction, we treat the controller as given. In particular, we focus on two types of inexact controllers: (a) one whose input is extracted from a primal-dual point satisfying the Karush-Kuhn-Tucker (KKT) conditions of the non-convex MPC problem, and (b) one whose input is obtained by linearizing the dynamics and solving a convex quadratic program. The main idea of our verification framework is to formulate an optimization problem that searches over the worst-case initial state within a given set and control inputs consistent with the inexact controller to maximize a carefully-chosen performance metric. Using this framework, we show how to certify (i) the worst-case suboptimality gap of a single MPC problem, (ii) the worst-case closed-loop suboptimality gap over a given number of dynamical system iterations, (iii) closed-loop stability, and (iv) feasibility of the closed-loop system. Through numerical examples, we showcase the ability of our framework to precisely quantify both types of suboptimality, and to test the stability and feasibility of the inexact controllers.
ER -