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Discrete-time Control Barrier Functions (DTCBFs) have recently attracted interest for guaranteeing safety and synthesizing safe controllers for discrete-time dynamical systems. This paper addresses the open challenges of verifying candidate…
We provide certificates for almost sure reachability of continuous-time stochastic systems governed by stochastic differential equations (SDEs). We first show that a standard Euler-Maruyama discretization may fail to preserve almost sure…
Due to their expressive power, neural networks (NNs) are promising templates for functional optimization problems, particularly for reach-avoid certificate generation for systems governed by stochastic differential equations (SDEs).…
We study black-box testing for stochastic systems and arbitrary $\omega$-regular specifications, explicitly including liveness properties. We are given a finite-state probabilistic system that we can only execute from the initial state. We…
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,…
Probabilistic pushdown automata (pPDA) are a standard model for discrete probabilistic programs with procedures and recursion. In pPDA, many quantitative properties are characterized as least fixpoints of polynomial equation systems. In…
We construct an aggregated version of the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs). The results…
We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only…
This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are…
Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time,…
We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum…
This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
In this paper, we study the control properties of a new class of stochastic ensemble systems that consists of families of random variables. These random variables provide an increasingly good approximation of an unknown discrete,…
This work is concerned with a formal approach for safety controller synthesis of stochastic control systems with both process and measurement noises while considering wireless communication networks between sensors, controllers, and…
This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing…
In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…
Providing guarantees on the safe operation of robots against edge cases is challenging as testing methods such as traditional Monte-Carlo require too many samples to provide reasonable statistics. Built upon recent advancements in…
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has…