标题： 面向更新的非线性系统的鲁棒最优预测控制研究 显示英文标题

标题： Update-Aware Robust Optimal Model Predictive Control for Nonlinear Systems

摘要： 鲁棒最优或min-max模型预测控制（MPC）方法旨在确保在已知且有界的不确定性集上满足约束条件的同时最小化最坏情况下的性能界限。 传统上，这些方法计算一条在固定预测时域内满足期望特性的轨迹，应用部分由此产生的输入，然后在下一时间步使用新获得的测量值重新求解MPC问题。 然而，这种方法未能考虑到未来将更新控制轨迹的事实，这可能导致保守的设计。 在本文中，我们提出了一种新颖的更新感知鲁棒最优MPC算法，用于非线性系统上的递减时域问题，并明确考虑了未来的控制轨迹更新。 这种额外的见解使我们的方法能够证明扩大可行解集，并与现有技术相比保证更优的最坏情况性能界限。 我们的方法将轨迹生成问题表述为一系列嵌套的存在约束半无限规划（SIP），这些问题可以高效地使用局部约简技术解决。 为了验证其有效性，我们在平面四旋翼问题上评估了我们的方法，结果显示它明显优于一种等效方法，尽管后者由于增加了计算时间而未考虑未来的更新。 显示英文摘要

摘要： Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a trajectory that meets the desired properties over a fixed prediction horizon, apply a portion of the resulting input, and then re-solve the MPC problem using newly obtained measurements at the next time step. However, this approach fails to account for the fact that the control trajectory will be updated in the future, potentially leading to conservative designs. In this paper, we present a novel update-aware robust optimal MPC algorithm for decreasing horizon problems on nonlinear systems that explicitly accounts for future control trajectory updates. This additional insight allows our method to provably expand the feasible solution set and guarantee improved worst-case performance bounds compared to existing techniques. Our approach formulates the trajectory generation problem as a sequence of nested existence-constrained semi-infinite programs (SIPs), which can be efficiently solved using local reduction techniques. To demonstrate its effectiveness, we evaluate our approach on a planar quadrotor problem, where it clearly outperforms an equivalent method that does not account for future updates at the cost of increased computation time.