Yicheng Lin

Yicheng Lin, Zhisheng Duan, Tianzhi Li et al.

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.

Yicheng Lin, Bingxian Wu, Nan Bai et al.

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This raises a distinct and fundamental question on optimality robustness, specifically, how uncertainties affect the optimal solution itself. To address this problem, we adopt a unified analysis-to-design perspective for systematically quantifying and improving optimality robustness. At the analysis level, we derive explicit upper bounds on the deviations of both the value function and the optimal controller, where uncertainties from multiple sources are systematically integrated into a unified norm-bounded representation. At the design level, we develop a robustness-aware optimal control methodology that provably reduces such optimality deviations, thereby enhancing robustness while explicitly revealing a quantitative trade-off between nominal optimality and robustness. As for practical implementation aspect, we further propose a tractable policy iteration algorithm, whose well-posedness and convergence are established via vanishing viscosity regularization and elliptic partial differential equation (PDE) techniques. Numerical examples validate the theoretical findings and demonstrate the effectiveness of proposed methodology.