Predictive Monitoring of Black-Box Dynamical Systems

We study the problem of predictive runtime monitoring of black-box dynamical systems with quantitative safety properties. The black-box setting stipulates that the exact semantics of the dynamical system and the controller are unknown, and that we are only able to observe the state of the controlled (aka, closed-loop) system at finitely many time points. We present a novel framework for predicting future states of the system based on the states observed in the past. The numbers of past states and of predicted future states are parameters provided by the user. Our method is based on a combination of Taylor's expansion and the backward difference operator for numerical differentiation. We also derive an upper bound on the prediction error under the assumption that the system dynamics and the controller are smooth. The predicted states are then used to predict safety violations ahead in time. Our experiments demonstrate practical applicability of our method for complex black-box systems, showing that it is computationally lightweight and yet significantly more accurate than the state-of-the-art predictive safety monitoring techniques.

Neural Control and Certificate Repair via Runtime Monitoring

Learning-based methods provide a promising approach to solving highly non-linear control tasks that are often challenging for classical control methods. To ensure the satisfaction of a safety property, learning-based methods jointly learn a control policy together with a certificate function for the property. Popular examples include barrier functions for safety and Lyapunov functions for asymptotic stability. While there has been significant progress on learning-based control with certificate functions in the white-box setting, where the correctness of the certificate function can be formally verified, there has been little work on ensuring their reliability in the black-box setting where the system dynamics are unknown. In this work, we consider the problems of certifying and repairing neural network control policies and certificate functions in the black-box setting. We propose a novel framework that utilizes runtime monitoring to detect system behaviors that violate the property of interest under some initially trained neural network policy and certificate. These violating behaviors are used to extract new training data, that is used to re-train the neural network policy and the certificate function and to ultimately repair them. We demonstrate the effectiveness of our approach empirically by using it to repair and to boost the safety rate of neural network policies learned by a state-of-the-art method for learning-based control on two autonomous system control tasks.