线性差分包含的最大鲁棒正不变集

中文摘要 AI 辅助

本文针对受硬状态约束的线性差分包含，建立了最大鲁棒正不变集的系统性刻画与精确计算框架。该集合被刻画为鲁棒前驱算子的最大不动点，由此引出三种等价的递减集合迭代——标准迭代、自限制迭代与增量迭代——以及精确的停止检验。在矩阵族一致指数稳定且有界扰动的条件下，刻画了极限扰动可达集，并据此推导了集合非空性与有限确定性的条件。当状态约束集为多面体时，三种迭代对有界扰动以及有限或凸多面体矩阵族均可实现精确的半空间实现。尽管这些实现生成相同的集合序列，但计算负担的分配方式不同。复杂度分析与数值研究使这些差异明确化，并揭示了底层问题结构如何指导实现方案的选择。

英文摘要

This article develops a systematic characterization and exact computational framework for the maximal robust positively invariant set of linear difference inclusions subject to hard state constraints. The set is characterized as the greatest fixed point of the robust predecessor operator, leading to three equivalent decreasing set iterations---the standard, self-restricted, and incremental iterations---and exact stopping tests. Under uniform exponential stability of the matrix family and bounded disturbances, the limiting disturbance-reachable set is characterized and used to derive conditions for nonemptiness and finite determination. When the state constraint set is polyhedral, the three iterations admit exact half-space implementations for bounded disturbances and finite or polytopic matrix families. Although these implementations generate the same set sequence, they distribute computational effort differently. The complexity analysis and numerical study make these differences explicit and reveal how the underlying problem structure informs the choice of implementation.

发表机构

• Linköping University（林雪平大学）

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