Related papers: Under-Approximate Reachability Analysis for a Clas…
In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…
We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses…
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…
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…
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…
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…
Inner-approximate reachability analysis involves calculating subsets of reachable sets, known as inner-approximations. This analysis is crucial in the fields of dynamic systems analysis and control theory as it provides a reliable…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
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…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…
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,…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
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,…