Related papers: Reachability of Linear Uncertain Systems: Sampling…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
We study finite horizon reachable set estimation for unknown discrete-time dynamical systems using only sampled state trajectories. Rather than treating scenario optimization as a black-box tool, we show how it can be tailored to reachable…
Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable…
A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study…
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…
In this work, we consider how preference models in interactive recommendation systems determine the availability of content and users' opportunities for discovery. We propose an evaluation procedure based on stochastic reachability to…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…