Related papers: Reachability Analysis Using Dissipation Inequaliti…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
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…
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…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…
This paper develops a robust control synthesis method for uncertain linear systems with input saturation in the framework of integral quadratic constraints (IQCs). The system is reformulated as a linear fractional representation (LFR) that…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…