Related papers: Characterizing Safety: Minimal Barrier Functions f…
We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…
This paper studies set invariance and contractivity in hybrid systems modeled by hybrid inclusions using barrier functions. After introducing the notion of a multiple barrier functions, we investigate the tightest possible sufficient…
This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the…
Control barrier functions (CBFs) provide a rigorous framework for designing controllers enforcing safety constraints. While CBF theory is well-developed for a finite number of safety constraints, certain applications, e.g., backup CBFs,…
This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite the presence of unmatched parametric uncertainties. The approach combines two ideas. The first is to construct a…
In this brief paper we introduce a robust-safety notion for differential inclusions, and we propose a general framework to certify such a notion in terms of barrier functions. While existing literature studied only what we designate by…
This paper presents converse theorems for safety in terms of barrier functions for unconstrained continuous-time systems modeled as differential inclusions. Via a counterexample, we show the lack of existence of autonomous and continuous…
This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine…
This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and…
The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…
Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety…
Barrier functions (BFs) characterize safe sets of dynamical systems, where hard constraints are never violated as the system evolves over time. Computing a valid safe set and BF for a nonlinear (and potentially unmodeled), non-autonomous…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…
Industrial control applications require high performance under strict constraints. Control barrier functions (CBFs) provide principled safety mechanisms, but constructing CBF-based safety filters for large-scale systems is challenging. We…
Accurate quantification of safety is essential for the design of autonomous systems. In this paper, we present a methodology to characterize the exact probabilities associated with invariance and recovery in safe control. We consider a…
Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe…
In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a…
We study feasibility guarantees for safety filters developed using Control Barrier Functions (CBFs) when a safe set is defined using the pointwise minimum of continuously differentiable functions, a construction that is common for the…
Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for…