Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs

Recent advancements in the areas of stochastic optimal control theory and machine learning create new opportunities towards the development of scalable algorithms for stochastic dynamic optimization. Despite the progress, there is a scarcity of methodologies that have the characteristics of being solidly grounded in first principles, have the flexibility of deep learning algorithms in terms of representational power, and can be deployed on systems operating in safety critical scenarios. Safety plays a major role in designing any engineering system in various industries ranging from automobiles and aviation to energy and medicine. With the rapid emergence of various advanced autonomous systems, the control system community has investigated various techniques such as barrier methods [1], reachable sets [2], and discrete approximation [3] to ensure safety certifications. However with the recent introduction of Control Barrier Functions (CBFs) [4, 5, 6], there has been a growing research interest in the community in designing controllers with verifiable safety bounds. CBFs provide a measure of safety to a system given its current state. As the system approaches the boundaries of its safe operating region, the CBFs tend to infinity, leading to the name "barrier".