Related papers: Stochastic Omega-Regular Verification and Control …
A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by…
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…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of…
This paper focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system…
We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic optimal control problem interpretation of the time…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
This paper presents a novel data-driven framework for the robust safety verification and safe control synthesis of unknown monotone discrete-time systems. While existing data-driven safety analysis approaches are often either heuristic in…
Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications. One promising solution to address this problem…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite-time horizon. We use stochastic control barrier functions as a means to quantify the probability that a system exits a given safe region of…
In this paper, we study two kinds of singular optimal controls (SOCs for short) problems where the systems governed by forward-backward stochastic differential equations (FBSDEs for short), in which the control has two components: the…
When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the…
A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel's martingales. The multidimensional Teugel's martingales are constructed by orthogonalizing the multidimensional L\'{e}vy…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
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).…
Given a random sample from a random variable $T$ which is bounded from above, $T\le\tau$ a.s., we define processes that are positive supermartingales if $E(T)\ge\mu$. Such processes are called test martingales. Tests of the supermartingale…
We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae…
A barrier certificate, defined over the states of a dynamical system, is a real-valued function whose zero level set characterizes an inductively verifiable state invariant separating reachable states from unsafe ones. When combined with…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…