Characterizing Robustness in Nonlinear Optimal Control: From Stability to Optimality
arXiv:2607.07570
The paper studies how errors between learned models and real nonlinear systems affect the stability and performance of data‑driven optimal controllers, providing Lyapunov‑based robustness guarantees and explicit formulas for optimality loss, along with a convergent algorithm to quantify these effects.
Abstract
In nonlinear optimal control, uncertainties in system dynamics may affect not only closed-loop stability but also the achieved optimality properties of the resulting solutions. This paper develops a systematic robustness analysis for nonlinear optimal control beyond the conventional focus on stability in robust control theory. First, we demonstrate that the optimal value function retains its Lyapunov property under a quantifiable criterion, thereby guaranteeing the preservation of closed-loop 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 further reveal their consistency with classical linear-quadratic regulator (LQR) results. In addition, the robustness analysis admits a unified computational formulation that gives rise to an iterative scheme with guaranteed convergence, enabling quantitative assessment of optimality robustness in nonlinear control systems. Numerical examples validate the theoretical analysis.