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This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Numerical Analysis · Mathematics 2019-11-28 N. Benjamin Erichson , Lionel Mathelin , Steven L. Brunton , J. Nathan Kutz

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…

Optimization and Control · Mathematics 2014-12-11 Martin Rasmussen , Janosch Rieger , Kevin Webster

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…

Systems and Control · Computer Science 2018-01-30 John Maidens , Murat Arcak

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…

Systems and Control · Electrical Eng. & Systems 2020-07-14 Alex Devonport , Mahmoud Khaled , Murat Arcak , Majid Zamani

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…

Systems and Control · Electrical Eng. & Systems 2021-03-22 Matthew Abate , Samuel Coogan

Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…

Systems and Control · Electrical Eng. & Systems 2025-09-12 Elizabeth Dietrich , Rosalyn Devonport , Stephen Tu , Murat Arcak

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,…

Optimization and Control · Mathematics 2026-03-18 Steven Nguyen , Jorge Cortés , Boris Kramer

We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Sergiy Bogomolov , Marcelo Forets , Goran Frehse , Kostiantyn Potomkin , Christian Schilling

Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…

Systems and Control · Electrical Eng. & Systems 2024-12-30 Taha Shafa , Melkior Ornik

One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…

Numerical Analysis · Mathematics 2020-08-06 Matthias Althoff

The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…

Optimization and Control · Mathematics 2020-12-29 Melkior Ornik

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

Systems and Control · Electrical Eng. & Systems 2022-04-15 Thomas Lew , Lucas Janson , Riccardo Bonalli , Marco Pavone

In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…

Systems and Control · Electrical Eng. & Systems 2024-06-18 Yushen Huang , Ertai Luo , Stanley Bak , Yifan Sun

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…

Numerical Analysis · Mathematics 2023-07-24 Janosch Rieger , Kyria Wawryk

A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this…

Systems and Control · Computer Science 2017-05-02 Francesca Parise , Maria Elena Valcher , John Lygeros

We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission…

Optimization and Control · Mathematics 2023-09-11 Yaodong Li , Michelle S. Chong

The reachable set of controlled dynamical systems consist of the set of all possible reachable states from an initial condition, over a certain period of time under various control and operation constraints and exogenous disturbances. For…

Optimization and Control · Mathematics 2023-12-14 Sean R. Bowerfind , Ehsan Taheri

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…

Systems and Control · Electrical Eng. & Systems 2023-09-11 Taha Shafa , Roy Dong , Melkior Ornik

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…

Systems and Control · Electrical Eng. & Systems 2023-05-15 Mohamed Serry , Jun Liu

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…

Systems and Control · Electrical Eng. & Systems 2023-09-29 Laura Lützow , Matthias Althoff