165,809 research outputs found
Input-to-State Safety With Control Barrier Functions
This letter presents a new notion of input-to-state safe control barrier
functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under
input disturbances. Similar to how safety conditions are specified in terms of
forward invariance of a set, input-to-state safety (ISSf) conditions are
specified in terms of forward invariance of a slightly larger set. In this
context, invariance of the larger set implies that the states stay either
inside or very close to the smaller safe set; and this closeness is bounded by
the magnitude of the disturbances. The main contribution of the letter is the
methodology used for obtaining a valid ISSf-CBF, given a control barrier
function (CBF). The associated universal control law will also be provided.
Towards the end, we will study unified quadratic programs (QPs) that combine
control Lyapunov functions (CLFs) and ISSf-CBFs in order to obtain a single
control law that ensures both safety and stability in systems with input
disturbances.Comment: 7 pages, 7 figures; Final submitted versio
Input-to-State Safety with Control Barrier Functions
This letter presents a new notion of input-to-state safe control barrier functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances. Similar to how safety conditions are specified in terms of forward invariance of a set, input-to-state safety (ISSf) conditions are specified in terms of forward invariance of a slightly larger set. In this context, invariance of the larger set implies that the states stay either inside or very close to the smaller safe set; and this closeness is bounded by the magnitude of the disturbances. The main contribution of the letter is the methodology used for obtaining a valid ISSf-CBF, given a control barrier function (CBF). The associated universal control law will also be provided. Towards the end, we will study unified quadratic programs (QPs) that combine control Lyapunov functions (CLFs) and ISSf-CBFs in order to obtain a single control law that ensures both safety and stability in systems with input disturbances
Violation-Free Inter-Sampling Safety: from Control Barrier Functions to Tunable Controllers with Input-to-State Safety Guarantees
A common assumption on the deployment of safeguarding controllers on the
digital platform is that high sampling frequency translates to a small
violation of safety. This paper investigates and formalizes this assumption
through the lens of Input-to-State Safety. From this perspective, we propose an
alternative solution for maintaining safety of sample-and-hold controlled
systems without any violation to the original safe set. Our approach centers
around modulating the sampled control input in order to guarantee a more robust
safety condition. We analyze both the time-triggered and the event-triggered
sample-and-hold implementations, including the characterization of sampling
frequency requirements and trigger conditions. We demonstrate the effectiveness
of our approach in the context of adaptive cruise control through simulations.Comment: Submitted to IEEE Conference on Decision and Control 202
Safe Control of Euler-Lagrange Systems with Limited Model Information
This paper presents a new safe control framework for Euler-Lagrange (EL)
systems with limited model information, external disturbances, and measurement
uncertainties. The EL system is decomposed into two subsystems called the proxy
subsystem and the virtual tracking subsystem. An adaptive safe controller based
on barrier Lyapunov functions is designed for the virtual tracking subsystem to
ensure the boundedness of the safe velocity tracking error, and a safe
controller based on control barrier functions is designed for the proxy
subsystem to ensure controlled invariance of the safe set defined either in the
joint space or task space. Theorems that guarantee the safety of the proposed
controllers are provided. In contrast to existing safe control strategies for
EL systems, the proposed method requires much less model information and can
ensure safety rather than input-to-state safety. Simulation results are
provided to illustrate the effectiveness of the proposed method.Comment: Accepted to IEEE CDC 2023 and this is the extended versio
Neural Differentiable Integral Control Barrier Functions for Unknown Nonlinear Systems with Input Constraints
In this paper, we propose a deep learning based control synthesis framework
for fast and online computation of controllers that guarantees the safety of
general nonlinear control systems with unknown dynamics in the presence of
input constraints. Towards this goal, we propose a framework for simultaneously
learning the unknown system dynamics, which can change with time due to
external disturbances, and an integral control law for trajectory tracking
based on imitation learning. Simultaneously, we learn corresponding safety
certificates, which we refer to as Neural Integral Control Barrier Functions
(Neural ICBF's), that automatically encode both the state and input constraints
into a single scalar-valued function and enable the design of controllers that
can guarantee that the state of the unknown system will never leave a safe
subset of the state space. Finally, we provide numerical simulations that
validate our proposed approach and compare it with classical as well as recent
learning based methods from the relevant literature.Comment: 15 pages, 4 figure
Advanced safety filter based on SOS Control Barrier and Lyapunov Functions
This paper presents a novel safety filter framework based on Control Barrier
Functions (CBFs) and Control Lyapunov-like Functions (CLFs). The CBF guarantees
forward invariance of the safe set, constraining system trajectories within
state constraints, while the CLF guides the system away from unsafe states
towards a nominal region, preserving the performance of a nominal controller.
The first part of this work focuses on determining compatible CBF and CLF in
the presence of linear or quadratic input constraints. This is achieved by
formulating the CBF and CLF conditions, along with the input constraints, as
Sum of Squares (SOS) constraints using Putinar's Positivstellensatz. For
solving the resulting SOS optimization problem, we employ an alternating
algorithm that simultaneously searches for a feasible controller in the class
of rational functions of the state. The second part of this work details the
implementation of the safety filter as a Quadratically Constrained Quadratic
Program (QCQP), whose constraints encode the CBF and CLF conditions as well as
the input constraints. To avoid the chattering effect and guarantee the
uniqueness and Lipschitz continuity of solutions, the state-dependent
inequality constraints of the QCQP are selected to be sufficiently regular.
Finally, we demonstrate the method on a detailed case study involving the
control of a three-phase ac/dc power converter connected to an infinite bus.Comment: 15 pages, 11 figures, submitted to IEEE Transactions on Control
Systems Technolog
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