AI 中文总结
研究基于学习的MPC用于离散时间线性系统约束镇定，通过非渐近正则化最小二乘估计生成参数置信集，嵌入鲁棒管传播等，证明了高概率递归可行性等，数值例子验证了有效性和理论保证。
AI 中文摘要
本文研究了基于学习的MPC，用于具有未知系统参数和加性有界干扰的离散时间线性系统的约束镇定。我们开发了一种易于处理的相似管MPC方案，其中通过非渐近正则化最小二乘估计生成高概率参数置信集，而非先验假设。所得不确定性集被嵌入到鲁棒管传播和约束收紧中，产生具有线性和二阶锥约束的凸公式。我们证明了高概率递归可行性、鲁棒约束满足和输入到状态稳定性，以及明确的非渐近状态界。一个数值例子说明了有效性和理论保证。
英文摘要
This paper studies learning-based MPC for constrained stabilization of discrete-time linear systems with unknown system parameters and additive bounded disturbances. We develop a tractable homothetic-tube MPC scheme in which a high-probability parameter confidence set is generated from non-asymptotic regularized least-squares estimation, rather than assumed a priori. The resulting uncertainty set is embedded into robust tube propagation and constraint tightening, yielding a convex formulation with linear and second-order-cone constraints. We prove high-probability recursive feasibility, robust constraint satisfaction, and input-to-state stability, together with explicit non-asymptotic state bounds. A numerical example illustrates the effectiveness and theoretical guarantees.
Comments16 pages, 2 figures
