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We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

Optimization and Control · Mathematics 2026-04-16 Thomas Lew , Riccardo Bonalli , Marco Pavone

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…

Systems and Control · Computer Science 2022-05-03 Sergiy Bogomolov , Marcelo Forets , Goran Frehse , Andreas Podelski , Christian Schilling , Frédéric Viry

Reachability analysis is a fundamental program analysis with a wide variety of applications. We present FlowCFL, a framework for type-based reachability analysis in the presence of mutable data. Interestingly, the underlying semantics of…

Programming Languages · Computer Science 2020-05-15 Ana Milanova

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…

Systems and Control · Electrical Eng. & Systems 2020-05-18 He Yin , Andrew Packard , Murat Arcak , Peter Seiler

In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set…

Systems and Control · Electrical Eng. & Systems 2024-06-21 Ahmad Hafez , Frank J. Jiang , Karl H. Johansson , Amr Alanwar

Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…

Systems and Control · Electrical Eng. & Systems 2023-05-17 Taha Entesari , Mahyar Fazlyab

This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to…

Systems and Control · Electrical Eng. & Systems 2025-04-17 Brenner S. Rego , Guilherme V. Raffo , Marco H. Terra , Joseph K. Scott

This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and diminished control authority, given an a priori computed reachable set for…

Optimization and Control · Mathematics 2022-03-22 Hamza El-Kebir , Ani Pirosmanishvili , Melkior Ornik

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…

Systems and Control · Computer Science 2022-05-03 Sergiy Bogomolov , Marcelo Forets , Goran Frehse , Kostiantyn Potomkin , Christian Schilling

Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…

Machine Learning · Statistics 2025-08-11 Ben Adcock

The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…

Systems and Control · Electrical Eng. & Systems 2023-06-16 Ivan Perez Avellaneda , Luis A. Duffaut Espinosa

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 consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a…

Systems and Control · Electrical Eng. & Systems 2023-09-19 Navid Hashemi , Xin Qin , Lars Lindemann , Jyotirmoy V. Deshmukh

We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…

Optimization and Control · Mathematics 2021-04-09 Swann Marx , Edouard Pauwels , Tillmann Weisser , Didier Henrion , Jean Lasserre

Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment…

Optimization and Control · Mathematics 2025-09-03 Yuhao Zhang , Xiangru Xu

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable…

Systems and Control · Electrical Eng. & Systems 2025-12-23 Zhen Zhang , M. Umar B. Niazi , Michelle S. Chong , Karl H. Johansson , Amr Alanwar

We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial…

Numerical Analysis · Mathematics 2021-05-04 Akil Narayan , John D. Jakeman , Tao Zhou

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…

Systems and Control · Electrical Eng. & Systems 2024-09-04 Saber Jafarpour , Zishun Liu , Yongxin Chen

Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…

Artificial Intelligence · Computer Science 2026-01-14 Samuel I. Akinwande , Sydney M. Katz , Mykel J. Kochenderfer , Clark Barrett

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

Optimization and Control · Mathematics 2014-04-24 Kendra Lesser , Meeko Oishi