AI 中文总结
该研究针对受仿射状态约束的连续时间线性控制系统，提出了一种结构化采样方法计算容许集的内部多面体近似，避免状态空间大区域离散化，可扩展至高维系统。
AI 中文摘要
本文提出了一种用于计算受仿射状态约束的连续时间线性控制系统的容许集的内部多面体近似的方法。基于障碍理论和线性系统的显式解，开发了一种结构化采样程序以直接生成容许集的边界样本，从而避免了许多可行性和可达性方法所需的对状态空间大区域的离散化。所提出的框架分别计算各个状态约束的容许集，并通过交集组合得到的内部近似，避免了同时处理主动约束。边界样本被转换为半空间表示，并推导了采样和多面体重构算法的运行时复杂度分析。还提出了将该框架扩展到Hammerstein系统的方案。该方法在三重积分器和更高维的质量-弹簧-阻尼链系统上进行了验证，展示了容许集近似的几何构造，并证明了其对更高维系统的可扩展性。
英文摘要
This paper presents a method for computing inner polytopic approximations of admissible sets for continuous-time linear control systems subject to multiple affine state constraints, with a particular concern on computational tractability for large dimensional problems. In place of globally computing the admissible set and the part of its boundary called the barrier, we compute the so-called individual admissible sets and the corresponding barriers for each single constraint. We then use the exact sampling of linear systems and generate polytopes in half-space representation that provide an approximation of the individual admissible sets, to finally intersect them. We provide a complexity analysis of the whole procedure to evaluate its efficiency. The approach is illustrated by two examples -a triple integrator and a mass-spring-damper chain considered in 4, 6, 8, and 10 dimensions- with corresponding runtimes evaluated for both.
Comments35 pages, 11 figures
