标题： 无需参考的迭代学习模型预测控制与神经证书 显示英文标题

标题： Reference-Free Iterative Learning Model Predictive Control with Neural Certificates

摘要： 在本文中，我们提出了一种新颖的无参考迭代学习模型预测控制（MPC）。 在所提出的方法中，基于控制李雅普诺夫屏障函数（CLBF）的概念，使用从过去控制执行中收集的数据学习一个证书函数，并用于定义当前迭代中的MPC优化问题的终端集和成本。 此方案使得MPC的终端组件在连续迭代中逐步改进。 与依赖混合整数规划且存在数值困难的现有方法不同，所提出的方法将MPC优化问题表述为标准非线性规划，从而实现更高效的在线计算。 所提出的方法满足关键的MPC属性，包括递归可行性和渐近稳定性。 此外，我们证明了在一定假设下，性能成本随着迭代次数的增加而不会增加。 数值实验包括与PyBullet的仿真，证实我们的控制方案迭代地提高了控制性能，并且相比现有方法显著提高了在线计算效率。 显示英文摘要

摘要： In this paper, we propose a novel reference-free iterative learning model predictive control (MPC). In the proposed method, a certificate function based on the concept of Control Lyapunov Barrier Function (CLBF) is learned using data collected from past control executions and used to define the terminal set and cost in the MPC optimization problem at the current iteration. This scheme enables the progressive refinement of the MPC's terminal components over successive iterations. Unlike existing methods that rely on mixed-integer programming and suffer from numerical difficulties, the proposed approach formulates the MPC optimization problem as a standard nonlinear program, enabling more efficient online computation. The proposed method satisfies key MPC properties, including recursive feasibility and asymptotic stability. Additionally, we demonstrate that the performance cost is non-increasing with respect to the number of iterations, under certain assumptions. Numerical experiments including the simulation with PyBullet confirm that our control scheme iteratively enhances control performance and significantly improves online computational efficiency compared to the existing methods.