发表机构
Indian Institute of Technology Bombay（印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过将二维系统限制到垂直条带构造一维系统，提出基于Gröbner基的算法测试时间可控性与零时间可控性，并证明一维系统可生成全部可行轨迹，降低轨迹生成复杂度。
AI 中文摘要
受有限时间限制在一维（1D）系统中作用的启发，我们研究了定义在$\mathbb{N}^2$上的二维（2D）系统限制到垂直条带的问题。我们给出了一个构造性证明，表明这种限制会导出一个一维系统。随后，我们开发了一种基于Gröbner基的算法，用于从给定的二维系统计算这个受限的一维系统。该框架随后被应用于开发一种算法，用于测试标量自治二维系统的时间可控性和零时间可控性；已知这些性质等价于死区时间控制器（deadbeat controller）的存在。最后，我们证明，对于时间可控或零时间可控的标量自治二维系统，导出的一维系统生成原始二维系统的所有可行轨迹，从而降低了轨迹生成的复杂性。
英文摘要
Motivated by the role of finite-time restriction in one-dimensional (1D) systems, we investigate the restriction of two-dimensional (2D) systems defined over $\mathbb{N}^2$ to a vertical strip. We give a constructive proof that such a restriction induces a 1D system. A Gröbner basis-based algorithm is then developed to compute this restricted 1D system from a given 2D system. The framework is then applied to develop an algorithm for testing the time-controllability and zero-time-controllability of scalar autonomous 2D systems; these properties are known to be equivalent to the existence of a deadbeat controller. Finally, we show that, for time-controllable or zero-time-controllable scalar autonomous 2D systems, the induced 1D system generates all the admissible trajectories of the original 2D system, thereby reducing the complexity of trajectory generation.
CommentsAccepted at the 12th Indian Control Conference (ICC-12), IIT Kharagpur, India, 2027
