On the Robustness in Data-Driven Nonlinear Optimal Control: From Stability to Optimality

Jul 16, 2026

Data-driven nonlinear control often relies on controllers synthesized from learned surrogate models, yet deployment on real systems introduces inevitable model mismatch that can harm both closed-loop stability and achieved optimality. This paper studies how mismatch propagates through the optimal control structure and changes the resulting optimal value. The nominal optimal value function is proved to remain a Lyapunov function under a quantifiable criterion. Explicit characterizations quantify optimality deviations in performance and controllers, consistent with linear-quadratic results, supported by a convergent iterative algorithm and numerical validation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

Introduction

Data-driven nonlinear control and learned surrogate models

Existing robustness work and the optimality gap

Contributions and unified robustness framework

On the Robustness in Data-Driven Nonlinear Optimal Control: From Stability to Optimality Yicheng Lin, Zhisheng Duan, Senior Member, IEEE , Tianzhi Li, Bingxian Wu and Zhiyong Sun, Member, IEEE arXiv :2607 .07570v1 [math .OC] 8 Jul 2026 Abstract—In data-driven nonlinear control, optimal controllers designed from learned models are inevitably subject to model mismatch when deployed on actual systems, potentially compromising both closed-loop stability and optimality. This paper investigates how the model mismatch propagates through the optimal control structure and alters the resulting optimality. First, we show that the nominal optimal value function remains a Lyapunov function under a quantifiable criterion, thereby preserving closed-loop robust stability. Building upon this foundation, we establish explicit characterizations for optimality deviations induced by model mismatch in both closed-loop performance and optimal controllers, and then reveal their consistency with classical linear-quadratic results. In addition, the proposed analysis admits a unified computational formulation with a provably convergent iterative algorithm, enabling quantitative assessment of optimality robustness in nonlinear optimal control. Numerical examples validate the theoretical analysis, reveal its intrinsic connection with classical results, and demonstrate its practical computability. Index Terms—Robustness analysis, nonlinear systems, data-driven control, robust optimal control. I. INTRODUCTION DATA-DRIVEN control has been reshaping how we ap proach nonlinear dynamical systems. Rather than laboriously deriving first-principles models, researchers increasingly learn surrogate dynamics from experimental or simulation data and then synthesize controllers based on these learned models. This paradigm has evolved into a vibrant research direction in modern nonlinear control research [1] . Representative techniques range from neural network (NN) approximation [2] and Gaussian process regression (GPR) [3] to sparse identification of nonlinear dynamics (SINDy) [4] and operator theoretic representations [5], each offering a distinct route toward constructing control-oriented surrogate models directly from data. Despite these technical advances, a fundamental issue persisting across different data-driven control techniques is that the learned model is inherently imperfect. Besides accuracy limits of specific techniques, inevitable discrepancy between data-driven surrogate model and the actual system arises from multiple sources [6]–[8], including modeling error, data This work was supported by the National Natural Science Foundation of China (NSFC) under grants T2121002, U24A20266 and 62173006 . Yicheng Lin, Zhisheng Duan, Tianzhi Li, Bingxian Wu and Zhiyong Sun are with the School of Advanced Manufacturing and Robotics, Peking University, Beijing, 100871 China (email: [linyc020709@stu.pku.edu.cn](linyc020709@stu.pku.edu.cn), [duanzs@pku.edu.cn](duanzs@pku.edu.cn), {tlee, [davidwu2003](davidwu2003}@stu.pku.edu.cn)[}](davidwu2003}@stu.pku.edu.cn)[@stu.pku.edu.cn](davidwu2003}@stu.pku.edu.cn), [zhiyong.sun@pku.edu.cn](zhiyong.sun@pku.edu.cn)). limitation, external disturbance, etc. In typical practice of datadriven control, the optimal controller is often designed based on the surrogate model and then directly applied to the actual system. This naturally leads to the critical problem of how the model mismatch fundamentally alters the stability and optimality properties of the resulting closed-loop system. Existing works have tried to address the robustness issues in data-driven nonlinear control from different perspectives. On the one hand, the robustness of stability has been extensively studied within specific methodological frameworks [8]–[10] . These results often exploit structural properties oriented to the adopted learning method, and therefore provide robustness guarantees whose applicability is often tied to particular mod

FAQs

Why does model mismatch matter in data-driven nonlinear optimal control?

Controllers designed from learned models are applied to real systems where the surrogate model is imperfect. This discrepancy can degrade closed-loop stability and alter the achieved optimality.

How does the paper preserve closed-loop robust stability under mismatch?

It shows that the nominal optimal value function can remain a Lyapunov function under a criterion that is quantifiable. This establishes robust stability despite model mismatch.

How is optimality degradation characterized and related to classical results?

The framework explicitly characterizes deviations in closed-loop performance and in the resulting controllers caused by model mismatch. The derived optimality behavior is shown to be consistent with classical linear-quadratic (LQR) results.

Jul 16, 2026

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