Adaptive Safety with Control Barrier Functions

Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation

Adaptive Safety with Control Barrier Functions

Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation

Deadzone-Adapted Disturbance Suppression Control for Global Practical IOS and Zero Asymptotic Gain to Matched Uncertainties

In this paper we study a special class of systems: time-invariant control systems that satisfy the matching condition for which no bounds for the disturbance and the unknown parameters are known. For this class of systems, we provide a simple, direct, adaptive control scheme that combines three elements: (a) nonlinear damping, (b) single-gain adjustment, and (c) deadzone in the update law. It is the first time that these three tools are combined and the proposed controller is called a Deadzone-Adapted Disturbance Suppression (DADS) Controller. The proposed adaptive control scheme achieves for the first time an attenuation of the plant state to an assignable small level, despite the presence of disturbances and unknown parameters of arbitrary and unknown bounds. Moreover, the DADS Controller prevents gain and state drift regardless of the size of the disturbance and unknown parameter.Comment: 26 pages, 3 figure

Deadzone-Adapted Disturbance Suppression Control for Strict-Feedback Systems

In this paper we extend our recently proposed Deadzone-Adapted Disturbance Suppression (DADS) Control approach from systems with matched uncertainties to general systems in parametric strict feedback form. The DADS approach prevents gain and state drift regardless of the size of the disturbance and unknown parameter and achieves an attenuation of the plant output to an assignable small level, despite the presence of persistent disturbances and unknown parameters of arbitrary and unknown bounds. The controller is designed by means of a step-by-step backstepping procedure which can be applied in an algorithmic fashion. Examples are provided which illustrate the efficiency of the DADS controller compared to existing adaptive control schemes.Comment: 32 pages, 6 figures. arXiv admin note: text overlap with arXiv:2311.0793

Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules

SUMMARY It is a fundamental and important problem whether or not a metabolic network can admit multiple equilibria in a living organism. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoints. In this paper, a structure-oriented modularization research framework is proposed to analyze the multi-stability of metabolic networks. We first decompose a metabolic network into four types of basic building blocks (called metabolic modules) according to the particularity of its structure, and then focus on one type of these basic building blocksthe single substrate and single product with no inhibition (SSN) module, by deriving a nonlinear ordinary differential equation (ODE) model based on the Hill kinetics. We show that the injectivity of the vector field of the ODE model is equivalent to the nonsingularity of its Jacobian matrix, which enables us equivalently to convert an unverifiable sufficient condition for the absence of multiple equilibria of an SSN module into a verifiable one. Moreover, we prove that this sufficient condition holds for the SSN module in a living organism. Such a theoretical result not only provides a general framework for modeling metabolic networks, but also shows that the SSN module in a living organism cannot be multi-stable