Related papers: Quantitative Verification of Constrained Occupatio…
We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
In this paper, a method to achieve smooth transitions between sequential reachability tasks for a continuous time mobile robotic system is presented. Control barrier functions provide formal guarantees of forward invariance of safe sets and…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
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…
Reach-avoid analysis is fundamental to reasoning about the safety and goal-reaching behavior of dynamical systems, and serves as a foundation for specifying and verifying more complex control objectives. This paper introduces a reach-avoid…
In this paper, we present a novel data-driven approach to quantify safety for non-linear, discrete-time stochastic systems with unknown noise distribution. We define safety as the probability that the system remains in a given region of the…
We study exit times from time-dependent domains under joint perturbations of the trajectory and the domain. Representing a moving domain by a continuous barrier $\Phi$ on space-time, we reduce the exit problem to a one-dimensional…
We study the problem of co-designing control barrier functions and linear state feedback controllers for discrete-time linear systems affected by additive disturbances. For disturbances of bounded magnitude, we provide a semi-definite…
This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety…
We introduce a general methodology for quantitative model checking and control synthesis with supermartingale certificates. We show that every specification that is invariant to time shifts admits a stochastic invariant that bounds its…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic…
In this paper, we study Stochastic Control Barrier Functions (SCBFs) to enable the design of probabilistic safe real-time controllers in presence of uncertainties and based on noisy measurements. Our goal is to design controllers that bound…
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a…
This paper presents a safe controller synthesis of discrete-time stochastic systems using Control Barrier Functions (CBFs). The proposed condition allows the design of a safe controller synthesis that ensures system safety while avoiding…
This work is concerned with the safety controller synthesis of stochastic hybrid systems, in which continuous evolutions are described by stochastic differential equations with both Brownian motions and Poisson processes, and instantaneous…
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs…
We propose distributed iterative algorithms for safe control design and safety verification for networked multi-agent systems. These algorithms rely on distributing a control barrier function (CBF) related quadratic programming (QP) problem…
Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and…