In large-scale networks of uncertain dynamical systems, where communication is limited and there is a strong interaction among subsystems, learning local models and control policies offers great potential for designing high-performance controllers. At the same time, the lack of safety guarantees, here considered in the form of constraint satisfaction, prevents the use of data-driven techniques to safety-critical distributed systems. This paper presents a safety framework that guarantees constraint satisfaction for uncertain distributed systems while learning. The framework considers linear systems with coupling in the dynamics and subject to bounded parametric uncertainty, and makes use of robust invariance to guarantee safety. In particular, a robust non-convex invariant set, given by the union of multiple ellipsoidal invariant sets, and a nonlinear backup control law, given by the combination of multiple stabilizing linear feedbacks, are computed offline. In presence of unsafe inputs, the safety framework applies the backup control law, preventing the system to violate the constraints. As the robust invariant set and the backup stabilizing controller are computed offline, the online operations reduce to simple function evaluations, which enables the use of the proposed framework on systems with limited computational resources. The capabilities of the safety framework are illustrated by three numerical examples.
Inverse Safety Filtering: Inferring Constraints from Safety Filters for Decentralized Coordination
Department of Electrical Engineering and Computer Sciences, University of California Berkeley（加州大学伯克利分校电气与计算机科学与工程系）；Oden Institute, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登研究所）
Risk-Aware Safety Filters with Poisson Safety Functions and Laplace Guidance Fields
Department of Mechanical and Civil Engineering, Caltech（加州理工学院机械与土木工程系）；Department of Computing and Mathematical Sciences, Caltech（加州理工学院计算与数学科学系）；Department of Mechanical Engineering, Tufts University（塔夫茨大学机械工程系）
Cooptimizing Safety and Performance Using Safety Value-Constrained Model Predictive Control
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明希德电气与计算机工程系）；Department of Aeronautics and Astronautics, Stanford University（斯坦福大学航空与航天系）；Electrical and Computer Engineering Department, New York University（纽约大学电气与计算机工程系）
Predictive Safety Shield for Dyna-Q Reinforcement Learning
Departement U2IS, ENSTA Paris, Institut Polytechnique de Paris（ENSTA巴黎大学U2IS部门，巴黎理工学院）；Department of Electrical Engineering and Computer Science, University of California, Berkeley, USA（加州大学伯克利分校电气工程与计算机科学系）
