A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability

The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis

A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability

The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis

A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety

In this letter we seek to quantify the ability of learning to improve safety guarantees endowed by Control Barrier Functions (CBFs). In particular, we investigate how model uncertainty in the time derivative of a CBF can be reduced via learning, and how this leads to stronger statements on the safe behavior of a system. To this end, we build upon the idea of Input-to-State Safety (ISSf) to define Projection-to-State Safety (PSSf), which characterizes degradation in safety in terms of a projected disturbance. This enables the direct quantification of both how learning can improve safety guarantees, and how bounds on learning error translate to bounds on degradation in safety. We demonstrate that a practical episodic learning approach can use PSSf to reduce uncertainty and improve safety guarantees in simulation and experimentally

A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety

In this paper we seek to quantify the ability of learning to improve safety guarantees endowed by Control Barrier Functions (CBFs). In particular, we investigate how model uncertainty in the time derivative of a CBF can be reduced via learning, and how this leads to stronger statements on the safe behavior of a system. To this end, we build upon the idea of Input-to-State Safety (ISSf) to define Projection-to-State Safety (PSSf), which characterizes degradation in safety in terms of a projected disturbance. This enables the direct quantification of both how learning can improve safety guarantees, and how bounds on learning error translate to bounds on degradation in safety. We demonstrate that a practical episodic learning approach can use PSSf to reduce uncertainty and improve safety guarantees in simulation and experimentally.Comment: 6 pages, 2 figures, submitted to L-CSS + CDC 202

Bayesian Learning-Based Adaptive Control for Safety Critical Systems

Deep learning has enjoyed much recent success, and applying state-of-the-art model learning methods to controls is an exciting prospect. However, there is a strong reluctance to use these methods on safety-critical systems, which have constraints on safety, stability, and real-time performance. We propose a framework which satisfies these constraints while allowing the use of deep neural networks for learning model uncertainties. Central to our method is the use of Bayesian model learning, which provides an avenue for maintaining appropriate degrees of caution in the face of the unknown. In the proposed approach, we develop an adaptive control framework leveraging the theory of stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control Barrier Functions) along with tractable Bayesian model learning via Gaussian Processes or Bayesian neural networks. Under reasonable assumptions, we guarantee stability and safety while adapting to unknown dynamics with probability 1. We demonstrate this architecture for high-speed terrestrial mobility targeting potential applications in safety-critical high-speed Mars rover missions.Comment: Corrected an error in section II, where previously the problem was introduced in a non-stochastic setting and wrongly assumed the solution to an ODE with Gaussian distributed parametric uncertainty was equivalent to an SDE with a learned diffusion term. See Lew, T et al. "On the Problem of Reformulating Systems with Uncertain Dynamics as a Stochastic Differential Equation

Safe Robot Planning and Control Using Uncertainty-Aware Deep Learning

In order for robots to autonomously operate in novel environments over extended periods of time, they must learn and adapt to changes in the dynamics of their motion and the environment. Neural networks have been shown to be a versatile and powerful tool for learning dynamics and semantic information. However, there is reluctance to deploy these methods on safety-critical or high-risk applications, since neural networks tend to be black-box function approximators. Therefore, there is a need for investigation into how these machine learning methods can be safely leveraged for learning-based controls, planning, and traversability. The aim of this thesis is to explore methods for both establishing safety guarantees as well as accurately quantifying risks when using deep neural networks for robot planning, especially in high-risk environments. First, we consider uncertainty-aware Bayesian Neural Networks for adaptive control, and introduce a method for guaranteeing safety under certain assumptions. Second, we investigate deep quantile regression learning methods for learning time-and-state varying uncertainties, which we use to perform trajectory optimization with Model Predictive Control. Third, we introduce a complete framework for risk-aware traversability and planning, which we use to enable safe exploration of extreme environments. Fourth, we again leverage deep quantile regression and establish a method for accurately learning the distribution of traversability risks in these environments, which can be used to create safety constraints for planning and control.Ph.D