统一直接与间接学习以实现线性系统的安全控制
Unifying Direct and Indirect Learning for Safe Control of Linear Systems
AI总结：
针对不确定线性系统，本文用CMZ统一开环与闭环集合隶属学习以降低保守性，并通过线性规划学习保证多面体安全集λ收缩的自适应安全控制器。
摘要：
本文针对受系统不确定性和有界扰动影响的线性系统，开发了具备学习能力的安全控制器。给定扰动zonotope（全对称多胞体），首先利用matrix zonotope（MZ，矩阵全对称多胞体）刻画基于数据的闭环动力学（CLDs），并通过若干步骤进行精化，得到constrained matrix zonotope（CMZ，受约束矩阵全对称多胞体）。该精化通过引入共形等式约束来实现，这些约束消除了不相容的扰动实现。更具体地，先验知识和观测数据被分别用于构建同时符合数据与先验知识的扰动序列CMZ表示，并与扰动序列的初始MZ相交，从而产生精化后的CMZ。该方法降低了保守性。为进一步降低保守性，本文通过提出一种新颖的集合隶属辨识方法，将开环动力学建模为CMZ，从而统一开环学习与闭环学习。先验知识充当该CMZ的初始可行开环模型集（FOLMS），每当获得新的信息性在线数据时，该集合便被精化为后验集合。随后，该后验FOLMS自适应地替换闭环学习过程的扰动消除中所采用的先验知识集。由此得到的精化参数化CLD集合随后被用于直接且自适应地学习一个可鲁棒保证安全的控制器。为实现这一目标，本文构建了一个线性规划问题，以保证多面体安全集的λ收缩性。文中提供了一个仿真示例，用于验证所提方法的有效性并支持理论结果。
英文摘要：
This paper develops learning-enabled safe controllers for linear systems subject to system uncertainties and bounded disturbances. Given the disturbance zonotope, the databased closed-loop dynamics (CLDs) are first characterized using a matrix zonotope (MZ), and refined through several steps to yield a constrained matrix zonotope (CMZ). This refinement is achieved by introducing conformal equality constraints that eliminate incompatible disturbance realizations. More precisely, prior knowledge and observed data are used separately to construct CMZ representations of disturbance sequences that conform to both data and prior knowledge, and are intersected by the initial MZ of the disturbance sequence, producing a refined CMZ. This approach reduces conservatism. To further reduce the conservativeness, we unify open-loop learning with closed-loop learning by presenting a novel set-membership identification method that models open-loop dynamics as a CMZ. The prior knowledge serves as an initial feasible open-loop model set (FOLMS) of this CMZ, which is refined into a posterior set whenever new informative online data becomes available. This posterior FOLMS then adaptively replaces the prior knowledge set employed in the disturbance elimination of the closed-loop learning process. The resulting refined parameterized set of CLD is subsequently leveraged to directly and adaptively learn a controller that robustly enforces safety. Toward this goal, we formulate a linear programming problem that guarantees λcontractiveness of a polyhedral safe set. A simulation example is provided to validate the effectiveness of the proposed approach and support the theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
