Gaussian Process-Based Prescribed-Time Input-to-State Safety for Unknown System Control

Abstract

In dynamic systems, safety is typically guaranteed through control barrier functions that keep states within a designated safe set throughout the entire evolution of the system. However, in certain scenarios where states are initially unsafe, it is necessary for system states to enter the safe set within a specified time and subsequently remain there. To address this safety control challenge, the concept of Gaussian process-based prescribed-time input-to-state safety is developed for systems experiencing unknown input disturbances. This approach ensures that the states remain either inside or very close to a slightly larger safe set after initially entering the safe set within the prescribed timeframe. The larger safe set is determined by the prediction error of disturbances, modeled using Gaussian processes (GP), which can be established by collecting a sufficiently large dataset. Furthermore, a prescribed-time input-to-state control barrier function (PT-ISSf-CBF) is proposed to secure safety for systems with a relative degree of one. Additionally, the concept is expanded to develop a prescribed-time input-to-state high-order control barrier function (PT-ISSf-HOCBF) applicable to systems with arbitrary relative degrees, detailing the relationship between the new larger safe set and the parameters defined in the PT-ISSf-CBF condition. Finally, the proposed method’s effectiveness is validated through simulations and a physical experiment conducted on the Franka Emika robot.