arXiv subjects

Max H. Cohen

Publications and source records attributed to Max H. Cohen.

23 records · Page 2Linked to original sources

arXiv2024

Uncertainty Quantification for Recursive Estimation in Adaptive Safety-Critical Control

In this paper, we present a framework for online parameter estimation and uncertainty quantification in the context of adaptive safety-critical control. The key insight enabling our approach is that the parameter estimate generated by the continuous-time recursive least squares (RLS) algorithm at any point in time is an affine transformation of the initial parameter estimate. This property allows for parameterizing such estimates using objects that are closed under affine transformation, such as zonotopes, and enables the efficient propagation of such set-based estimates as time progresses. We illustrate how such an approach facilitates the synthesis of safety-critical controllers for systems with parametric uncertainty and additive disturbances using control barrier functions, and demonstrate the utility of our approach through illustrative examples.

eess.SY↗

arXiv2023

Characterizing Smooth Safety Filters via the Implicit Function Theorem

Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but are generally not smooth, let alone continuously differentiable. In this paper, we present a general characterization of smooth safety filters -- smooth controllers that guarantee safety in a minimally invasive fashion -- based on the Implicit Function Theorem. This characterization leads to families of smooth universal formulas for safety-critical controllers that quantify the conservatism of the resulting safety filter, the utility of which is demonstrated through illustrative examples.

eess.SY↗

arXiv2022

Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functions

This paper develops a model-based reinforcement learning (MBRL) framework for learning online the value function of an infinite-horizon optimal control problem while obeying safety constraints expressed as control barrier functions (CBFs). Our approach is facilitated by the development of a novel class of CBFs, termed Lyapunov-like CBFs (LCBFs), that retain the beneficial properties of CBFs for developing minimally-invasive safe control policies while also possessing desirable Lyapunov-like qualities such as positive semi-definiteness. We show how these LCBFs can be used to augment a learning-based control policy to guarantee safety and then leverage this approach to develop a safe exploration framework in a MBRL setting. We demonstrate that our approach can handle more general safety constraints than comparative methods via numerical examples.

cs.LG↗

arXiv2022

Robust Control Barrier Functions for Nonlinear Control Systems with Uncertainty: A Duality-based Approach

This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-output data collected online. In particular, we leverage an integral set-membership identification algorithm that iteratively shrinks the set of possible system parameters online and guarantees stability and safety during learning. The efficacy of the developed approach is illustrated on two numerical examples.

math.OC↗

arXiv2022

High Order Robust Adaptive Control Barrier Functions and Exponentially Stabilizing Adaptive Control Lyapunov Functions

This paper studies the problem of utilizing data-driven adaptive control techniques to guarantee stability and safety of uncertain nonlinear systems with high relative degree. We first introduce the notion of a High Order Robust Adaptive Control Barrier Function (HO-RaCBF) as a means to compute control policies guaranteeing satisfaction of high relative degree safety constraints in the face of parametric model uncertainty. The developed approach guarantees safety by initially accounting for all possible parameter realizations but adaptively reduces uncertainty in the parameter estimates leveraging data recorded online. We then introduce the notion of an Exponentially Stabilizing Adaptive Control Lyapunov Function (ES-aCLF) that leverages the same data as the HO-RaCBF controller to guarantee exponential convergence of the system trajectory. The developed HO-RaCBF and ES-aCLF are unified in a quadratic programming framework, whose efficacy is showcased via two numerical examples that, to our knowledge, cannot be addressed by existing adaptive control barrier function techniques.

eess.SY↗