AI 中文总结
研究数据驱动非线性控制中模型不匹配对最优性的影响，通过理论分析表明标称最优值函数可保持闭环鲁棒稳定性，明确最优性偏差特征，给出统一计算形式和迭代算法，数值例子验证了理论及其实践可计算性。
AI 中文摘要
在数据驱动的非线性控制中，基于学习模型设计的最优控制器在实际系统中部署时不可避免地会存在模型不匹配问题，这可能损害闭环稳定性和最优性。本文研究模型不匹配如何通过最优控制结构传播并改变最优性。首先表明在可量化准则下，标称最优值函数仍是李雅普诺夫函数，保持闭环鲁棒稳定性。在此基础上，明确了模型不匹配在闭环性能和最优控制器中引起的最优性偏差特征，揭示其与经典线性二次结果的一致性。此外，所提分析有统一计算形式和收敛迭代算法，能定量评估非线性最优控制中的最优性鲁棒性。数值例子验证了理论分析，揭示其与经典结果的内在联系并证明其实际可计算性。
英文摘要
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.
