Towards the Graceful Control of Dynamic System Safety

Abstract

This dissertation introduces a novel framework for the ``graceful” control of dynamic system safety. The dissertation is motivated by the need for rigorous safety control guarantees in numerous application domains, including the biomedical, energy, and transportation domains. The literature typically defines a dynamic system’s safety in terms of its ability to always remain within a user-defined safe set if initialized within this set: a property known as forward invariance. Moreover, the literature presents different algorithms, including control barrier function (CBF) methods, for guaranteeing forward invariance. Unfortunately, these established methods from the literature only provide a single-layer definition of safety. This creates a need for controllers that provide more graceful, multi-layered safety assurances, where “grace” is defined in terms of the ability to achieve a “failsafe” operating mode even when a primary safety layer is breached. The main goal of this dissertation is to develop a framework for addressing this need for multi-layered, graceful dynamic system safety control. Toward the above goal, this dissertation provides six novel contributions to the literature. The first and second contributions present the development and the experimental validation of a retained volume estimator for peritoneal perfusion applications. This estimator is based on extended Kalman filtering, which is useful for the monitoring of perfusion safety by medical professionals. The third contribution demonstrates the development of a CBF-based safe perfusion controller. In contrast to the two previous contributions, this contribution represents a migration towards the active control-based, as opposed to human-centric, pursuit of safety. The fourth contribution presents a method of creating a graceful safety controller using a non-monotonic CBF. The proposed controller is applied to a battery pack thermal management problem, which represents a situation where the desirable primary safety is permanently compromised. In contrast to a baseline CBF controller from the literature, the proposed graceful algorithm prevents thermal runaway propagation within the battery pack. In the fifth contribution, a different notion of a graceful safety control method is explored using a nonlinear first- and second-order CBF. The proposed controller is used to avoid road vehicle collision when the desirable inter-vehicle distance is significantly violated, a situation where the primary safety is temporarily breached. Once again, unlike the baseline CBF controller, the graceful controller successfully avoids a frontal collision. Finally, the sixth contribution analyzes the above nonlinear graceful safety control framework to provide rigorous mathematical safety guarantees. Collectively, these six contributions represent a journey towards the graceful control of dynamic system safety.