The paper considers the controller synthesis problem for general MIMO systems with unknown dynamics, aiming to fulfill the temporal reach-avoid-stay task, where the unsafe regions are time-dependent, and the target must be reached within a specified time frame. The primary aim of the paper is to construct the spatiotemporal tube (STT) using a sampling-based approach and thereby devise a closed-form approximation-free control strategy to ensure that system trajectory reaches the target set while avoiding time-dependent unsafe sets. The proposed scheme utilizes a novel method involving STTs to provide controllers that guarantee both system safety and reachability. In our sampling-based framework, we translate the requirements of STTs into a Robust optimization program (ROP). To address the infeasibility of ROP caused by infinite constraints, we utilize the sampling-based Scenario optimization program (SOP). Subsequently, we solve the SOP to generate the tube and closed-form controller for an unknown system, ensuring the temporal reach-avoid-stay specification. Finally, the effectiveness of the proposed approach is demonstrated through three case studies: an omnidirectional robot, a SCARA manipulator, and a magnetic levitation system.

翻译：本文研究了具有未知动力学的一般多输入多输出系统的控制器综合问题，旨在实现时空可达-避障-驻留任务，其中不安全区域是时变的，且目标必须在指定时间范围内到达。论文的主要目标是通过基于采样的方法构建时空管道，并由此设计一种无需近似的闭式控制策略，以确保系统轨迹在避开时变不安全集的同时到达目标集。所提出的方案利用一种涉及时空管道的新颖方法，提供能同时保证系统安全性与可达性的控制器。在我们的基于采样的框架中，我们将时空管道的要求转化为一个鲁棒优化规划。为了解决由无限约束导致的鲁棒优化规划不可行问题，我们采用了基于采样的场景优化规划。随后，我们求解该场景优化规划，为未知系统生成管道和闭式控制器，从而确保满足时空可达-避障-驻留任务规范。最后，通过三个案例研究验证了所提方法的有效性：全向移动机器人、SCARA机械臂和磁悬浮系统。