标题： 集合理论直接数据驱动预测控制 显示英文标题

标题： Set-Theoretic Direct Data-driven Predictive Control

摘要： 设计直接数据驱动预测控制的终端成分带来了挑战，因为它依赖于一种隐式的、非最小化的输入-输出数据驱动表示。 通过考虑一类具有未知时延的约束线性时不变（LTI）系统，我们提出了一种集合论的直接数据驱动预测控制器，该控制器无需终端成本即可提供闭环保证。 具体而言，首先，从输入/输出数据序列出发，我们提出了一种基于采样的方法来构建N步输入输出向后可达集。 然后，我们利用构造的向后可达集族推导出一种数据驱动的控制律。 所提出的方法保证了有限时间收敛性和递归可行性，且与目标函数的调整无关。 它既不需要显式的状态估计，也不需要显式的预测模型，仅依赖于输入-输出测量；因此可以避免未建模的动力学。 最后，一个数值例子展示了所提出方法在稳定系统方面的有效性，而没有终端成分的直接数据驱动预测控制在相同条件下会失败。 显示英文摘要

摘要： Designing the terminal ingredients of direct data-driven predictive control presents challenges due to its reliance on an implicit, non-minimal input-output data-driven representation. By considering the class of constrained LTI systems with unknown time delays, we propose a set-theoretic direct data-driven predictive controller that does not require a terminal cost to provide closed-loop guarantees. In particular, first, starting from input/output data series, we propose a sample-based method to build N-step input output backward reachable sets. Then, we leverage the constructed family of backward reachable sets to derive a data-driven control law. The proposed method guarantees finite-time convergence and recursive feasibility, independent of objective function tuning. It requires neither explicit state estimation nor an explicit prediction model, relying solely on input-output measurements; therefore, unmodeled dynamics can be avoided. Finally, a numerical example highlights the effectiveness of the proposed method in stabilizing the system, whereas direct data-driven predictive control without terminal ingredients fails under the same conditions.