Control barrier functions (CBFs) have become popular as a safety filter to guarantee the safety of nonlinear dynamical systems for arbitrary inputs. However, it is difficult to construct functions that satisfy the CBF constraints for high relative degree systems with input constraints. To address these challenges, recent work has explored learning CBFs using neural networks via neural CBFs (NCBFs). However, such methods face difficulties when scaling to higher dimensional systems under input constraints. In this work, we first identify challenges that NCBFs face during training. Next, to address these challenges, we propose policy neural CBFs (PNCBFs), a method of constructing CBFs by learning the value function of a nominal policy, and show that the value function of the maximum-over-time cost is a CBF. We demonstrate the effectiveness of our method in simulation on a variety of systems ranging from toy linear systems to a jet aircraft with a 16-dimensional state space. Finally, we validate our approach on a two-agent quadcopter system on hardware under tight input constraints.

This paper addresses the problem of controlling an unknown dynamical system to safely reach a target set. We assume we have a priori access to a finite set of uncertain linear systems, to which the unknown system belongs to. This set can contain models for different failure or operational modes or potential environmental conditions. Given a desired exploration-exploitation profile, we provide a bilinear optimization based solution to this control synthesis problem. Our approach provides a family of controllers that enable adaptation based on data observed at run-time to automatically trade off model detection and reachability objectives while maintaining safety. We demonstrate the approach with several examples.

In this paper, we present a compositional condition for ensuring safety of a collection of interacting systems modeled by inter-triggering hybrid automata (ITHA). ITHA is a modeling formalism for representing multi-agent systems in which each agent is governed by individual dynamics but can also interact with other agents through triggering actions. These triggering actions result in a jump/reset in the state of other agents according to a global resolution function. A sufficient condition for safety of the collection, inspired by responsibility-sensitive safety, is developed in two parts: self-safety relating to the individual dynamics, and responsibility relating to the triggering actions. The condition relies on having an over-approximation method for the resolution function. We further show how such over-approximations can be obtained and improved via communication. We use two examples, a job scheduling task on parallel processors and a highway driving example, throughout the paper to illustrate the concepts. Finally, we provide a comprehensive evaluation on how the proposed condition can be leveraged for several multi-agent control and supervision examples.

When deployed into real environments, control systems need to be able to operate when their sensor data can become 'missing' (e.g., a vehicle's radar system may incorrectly detect a falling leaf as a vehicle on the road, or a distributed control system may lose sensor data packets while attempting to transmit). Guaranteeing safety of such systems can be handled by enforcing boundedness of the state or the estimated state of a system during operation. The form of boundedness that we use within this work is called equalized recovery and the goal of this work is to find controllers or estimators that satisfy equalized recovery in the presence of missing data. Equalized recovery relaxes the notion of invariance and allows the system states to be in a larger set during missing data events as long as the states can be steered back to the original set. Prefix-based controllers and estimators are introduced to solve this problem and methods to synthesize them are presented.

This paper employs correct-by-construction control synthesis, in particular controlled invariant set computations, for falsification. Our hypothesis is that if it is possible to compute a “large enough” controlled invariant set either for the actual system model or some simplification of the system model, interesting corner cases for other control designs can be generated by sampling initial conditions from the boundary of this controlled invariant set. Moreover, if falsifying trajectories for a given control design can be found through such sampling, then the controlled invariant set can be used as a supervisor to ensure safe operation of the control design under consideration. In addition to interesting initial conditions, which are mostly related to safety violations in transients, we use solutions from a dual game, a reachability game for the safety specification, to find falsifying inputs. We also propose optimization-based heuristics for input generation for cases when the state is outside the winning set of the dual game. To demonstrate the proposed ideas, we consider case studies from basic autonomous driving functionality, in particular, adaptive cruise control and lane keeping. We show how the proposed technique can be used to find interesting falsifying trajectories for classical control designs like proportional controllers, proportional integral controllers and model predictive controllers, as well as an open source real-world autonomous driving package.