Myopically Verifiable Probabilistic Certificates for Safe Control and Learning

TL;DR

This paper introduces probabilistic invariance techniques for designing safety certificates in stochastic systems, enabling real-time safe control and learning with long-term safety guarantees using short-term outlooks.

Contribution

It proposes a novel probabilistic invariance method that ensures long-term safety through myopic controllers and learning algorithms, balancing safety and computational efficiency.

Findings

Efficient safety assurance using neural networks and MPC with short horizons

Guarantees of long-term safety during and after training

Validated performance in numerical simulations

Abstract

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.