Related papers: On the Completeness and Ordering of Path-Complete …
The barrier function method for safety control typically assumes the availability of full state information. Unfortunately, in many scenarios involving uncertain dynamical systems, full state information is often unavailable. In this paper,…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing set invariance. While a…
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…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
We build on our recent work on formalization of responsibility-sensitive safety (RSS) and present the first formal framework that enables mathematical proofs of the safety of control strategies in intersection scenarios. Intersection…
Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has 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…
In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$.…
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…
Collision-free motion is a fundamental requirement for many autonomous systems. This paper develops a safety-critical control approach for the collision-free navigation of polytope-shaped agents in polytope-shaped environments. A systematic…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
This paper presents a switched model reference admittance control framework to achieve safe and compliant human-robot collaboration through reference trajectory shaping. The proposed method generates variable admittance parameters according…
We consider a class of partially observable Markov decision processes (POMDPs) with uncertain transition and/or observation probabilities. The uncertainty takes the form of probability intervals. Such uncertain POMDPs can be used, for…
We consider the problem of verifying safety for continuous-time dynamical systems. Developing upon recent advancements in data-driven verification, we use only a finite number of sampled trajectories to learn a barrier certificate, namely a…
This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system…
This paper presents a method for the simultaneous synthesis of a barrier certificate and a safe controller for discrete-time nonlinear stochastic systems. Our approach, based on piecewise stochastic control barrier functions, reduces the…
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…
For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant…