Myopically Verifiable Probabilistic Certificates for Safe Control and Learning
It addresses safety-critical applications in robotics or autonomous systems by providing efficient methods to balance long-term safety with computational feasibility, though it appears incremental in building on existing invariance and reachability approaches.
This paper tackles the challenge of ensuring long-term safety in stochastic control systems by introducing a 'probabilistic invariance' technique that allows for fast real-time control while maintaining safety guarantees, demonstrated through numerical simulations.
This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed `probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.