Related papers: Reachability Analysis of Nonlinear Discrete-Time S…
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…
Weighted timed automata have been defined in the early 2000's for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm…
Artificial neural networks have recently been utilized in many feedback control systems and introduced new challenges regarding the safety of such systems. This paper considers the safe verification problem for a dynamical system with a…
This paper presents novel polytopic and interval observer designs for uncertain linear continuous-time (CT) and discrete-time (DT) systems subjected to bounded disturbances and noise. Our approach guarantees enclosure of the true state and…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to…
In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a $C^{\infty}$-partition of unity method in time and a conventional boundary element method for the spatial…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
This contribution proposes a recursive, computationally efficient, ready-to-use, online method for the ellipsoidal state characterization for linear discrete-time models with additive unknown disturbances vectors (bounded by known possibly…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et al. have devised the distributed PCP framework for sub-quadratic time inapproximability. We show that the distributed PCP theorem can be…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
A popular method for solving reachability in timed automata proceeds by enumerating reachable sets of valuations represented as zones. A na\"ive enumeration of zones does not terminate. Various termination mechanisms have been studied over…
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…
A novel explicit method to model Lorentz linear dispersive media with finite difference method are presented. The method shows an explicit method without any modification to the Leap-Frogging scheme. The polarizations of the Lorentz media…
In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et al. have devised the distributed PCP framework for proving sub-quadratic time inapproximability. Here we try to go further in this direction.…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
Backwards reachability is an efficient zone-based approach for model checking probabilistic timed automata w.r.t. PTCTL properties. Current implementations, however, are restricted to maximum probabilities of reachability properties. In…
We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…
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…