用时空管控制未知非线性系统,满足复杂时序逻辑任务。
Learning Spatiotemporal Tubes for Full Class of Signal Temporal Logic Tasks for Control of Unknown Systems under Input Constraints

- 用物理信息神经网络建模随时间变化的时空管,联合参数化中心与半径。
- 将时序逻辑鲁棒性作为损失函数,学习到的管能自动满足任务时序要求。
- 支持多智能体且防碰撞,适用于带输入约束的复杂控制场景。
本文提出一种基于时空管(STT)的控制框架,用于满足输入受限条件下未知非线性欧拉-拉格朗日(EL)系统的信号时序逻辑(STL)规范。每个智能体的STT被建模为时变球体,其中心与半径由物理信息神经网络(PINN)联合参数化。将对应于各智能体的STL鲁棒性度量引入训练过程作为损失函数,使学习得到的时空管能够编码任务级时序需求。在多智能体场景中,引入全局任务的鲁棒性度量,确保各时空管之间不发生碰撞。为保证系统轨迹始终位于学习到的时空管内,从而满足局部与全局的STL规范,提出一种显式考虑输入约束的控制策略。特别地,设计了闭式控制律,在调节时空管演化的同时,根据系统输入约束对管的运动施加边界限制。所提方法已在多个案例研究中验证有效。
原文摘要 · Abstract (English)
This paper presents a Spatiotemporal Tube (STT)-based control framework for general unknown nonlinear Euler-Lagrange (EL) systems subject to input constraints, with the objective of satisfying Signal Temporal Logic (STL) specifications, where confinement of the system trajectory within the STT guarantees the satisfaction of the corresponding STL task. For both single and multi-agent scenarios, the STT corresponding to each agent is modeled as a time-varying ball, whose center and radius are jointly parameterized using a physics-informed neural network (PINN). The robustness metric associated with the STL specification corresponding to the agents is incorporated into the training process as a loss function, enabling the learned tube to encode task-level temporal requirements. For a multi-agent scenario, we introduce an additional robustness metric corresponding to the global task, which, when satisfied, ensures the tubes do not collide with each other. To ensure that the system trajectory remains within the learned STT and thereby satisfies the local and global STL specifications, we propose a control strategy that explicitly accounts for input constraints. In particular, a closed-form control law is developed to keep the trajectory inside the tube while regulating the motion of the tube by enforcing bounds on its evolution depending on the input constraints of the system. The proposed approach has been validated over several case studies.
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