In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

中文翻译：

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不确定非线性系统的计算高效鲁棒模型预测控制框架


在本文中，我们提出了一个针对一般（状态和输入相关）扰动的非线性鲁棒模型预测控制（MPC）框架。该方法使用在线构造的管来收紧标称（状态和输入）约束。为了促进高效的在线实施，管的形状基于离线计算的增量李亚普诺夫函数以及相应的（非线性）增量稳定反馈。至关重要的是，在线优化仅隐式地包含标量边界方面的这些非线性函数，从而实现了高效的实现。此外，为了有效评估最坏情况干扰，离线构建了一个简单的函数，该函数限制了开环轨迹给定点邻域中可能的干扰实现的上限。由此产生的 MPC 方案确保了鲁棒的约束满足和实际渐近稳定性，与名义 MPC 相比，在线计算需求略有增加。我们通过非线性基准示例证明了所提出的框架与最先进的稳健 MPC 方法的适用性。