Title: Safe Sliding Mode Control in Position for Double Integrator Systems Show Chinese title

Title: 双积分器系统的安全滑动模式控制

Abstract: We address the problem of robust safety control design for double integrator systems. We show that, when the constraints are defined only on position states, it is possible to construct a safe sliding domain from the dynamic of a simple integrator that is already safe. On this domain, the closed-loop trajectories remain robust and safe against uncertainties and disturbances. Furthermore, we design a controller gain that guarantees convergence to the safe sliding domain while avoiding the given unsafe set. The concept is initially developed for first-order sliding mode and is subsequently generalized to an adaptive framework, ensuring that trajectories remain confined to a predefined vicinity of the sliding domain, outside the unsafe region. Show Chinese abstract

Abstract: 我们解决双积分器系统的鲁棒安全控制设计问题。 我们表明，当约束仅定义在位置状态上时，可以从一个已经安全的简单积分器的动力学中构造出一个安全滑动域。 在这个域上，闭环轨迹对不确定性和干扰具有鲁棒性并保持安全。 此外，我们设计了一个控制器增益，确保收敛到安全滑动域的同时避免给定的不安全集合。 该概念最初是为一阶滑模设计的，并随后推广到自适应框架，确保轨迹保持在滑动域的预定义附近，且不在不安全区域内。