Related papers: Safety Verification for Distributed Parameter Syst…
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our…
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…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that certifies both asymptotic stability and safety. This…
This paper considers the general problem of transitioning theoretically safe controllers to hardware. Concretely, we explore the application of control barrier functions (CBFs) to sampled-data systems: systems that evolve continuously but…
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined…
Discrete-time Control Barrier Functions (DTCBFs) form a powerful control theoretic tool to guarantee safety and synthesize safe controllers for discrete-time dynamical systems. In this paper, we provide an optimization-based algorithm,…
In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that…
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…
Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human…
As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific…
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…
Control systems often must satisfy strict safety requirements over an extended operating lifetime. Control Barrier Functions (CBFs) are a promising recent approach to constructing simple and safe control policies. This paper proposes a…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
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…
Partially observable Markov decision processes (POMDPs) provide a modeling framework for a variety of sequential decision making under uncertainty scenarios in artificial intelligence (AI). Since the states are not directly observable in a…