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

Yicheng Lin, Zhisheng Duan, Tianzhi Li, Bingxian Wu, Zhiyong Sun

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.