From 2D system to 1D system via restriction to a vertical strip: applications to time-controllability and zero-time-controllability

Abstract

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.

arXiv commentAccepted at the 12th Indian Control Conference (ICC-12), IIT Kharagpur, India, 2027