Safe Controller Synthesis With Tunable Input-to-State Safe Control Barrier Functions

Abstract

To bring complex systems into real world environments in a safe manner, they will have to be robust to uncertainties-both in the environment and the system. This paper investigates the safety of control systems under input disturbances, wherein the disturbances can capture uncertainties in the system. Safety, framed as forward invariance of sets in the state space, is ensured with the framework of control barrier functions (CBFs). Concretely, the definition of input to state safety (ISSf) is generalized to allow the synthesis of non-conservative, tunable controllers that are provably safe under varying disturbances. This is achieved by formulating the concept of tunable input to state safe control barrier functions (TISSf-CBFs) which guarantee safety for disturbances that vary with state and, therefore, provide less conservative means of accommodating uncertainty. The theoretical results are demonstrated with a simple control system with input disturbance and also applied to design a safe connected cruise controller for a heavy duty truck.

Input-to-State Safety with Input Delay in Longitudinal Vehicle Control

“…Below we outline a method that enables us to make this neighborhood as small as desired and keep safety violations arbitrarily small in the presence of disturbance. We achieve this by using tunable input-to-state safe control barrier functions (TISSf-CBFs) from Alan et al (2022). Definition 3.…”

“…Definition 3. (Alan et al (2022)). Function h : R n → R is a tunable input-to-state safe control barrier function (TISSf-CBF) for ( 20) with a continuously differentiable function σ : R → R >0 if there exists α ∈ K e ∞ such that ∀t ≥ 0 and ∀x ∈ R n : sup…”

“…Recently, safety-critical control with input delay has been addressed in discrete time (Liu et al, 2020;Singletary et al, 2020) and in continuous time for linear systems (Jankovic, 2018a;Abel et al, 2019) and nonlinear systems (Molnar et al, 2021), including multiple and time-varying input delays (Abel et al, 2020(Abel et al, , 2021. Furthermore, the safety of delayfree systems with input disturbance have been investigated by robust control barrier functions (Jankovic, 2018b) and using the notion of input-to-state safety (Kolathaya and Ames, 2019;Alan et al, 2022). While real-life control The contribution of our work is twofold.…”

“…First, we propose a safety-critical control method using CBFs that handles both input delay and input disturbance. We achieve this by integrating the approaches of Molnar et al (2021) and Alan et al (2022) that separately address delay and disturbance by relying on the concepts of predictor feedback (Michiels and Niculescu, 2007;Bekiaris-Liberis and Krstic, 2013;Karafyllis and Krstic, 2017) and input-tostate safety (Kolathaya and Ames, 2019), respectively. Second, we apply the proposed method to safely control a connected automated truck in the presence of a significant response time (input delay) and uncertainties in its dynamics (input disturbance).…”

Data-driven design of safe control for polynomial systems

“…In this setting, the controller depends critically on the model used for design and recent studies [20,16,25] focus on finding robust safe controllers to account for possibly inaccurate models. In [3], unmodeled dynamics are taken into account by adding a bounded disturbance on the input to find a robust control barrier function, in an input-to-state-safety fashion.…”