Related papers: Reachability Analysis for Linear Systems with Unce…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
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…
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…
Reachability analysis for hybrid nonaffine systems remains computationally challenging, as existing set representations--including constrained, polynomial, and hybrid zonotopes--either lose tightness under high-order nonaffine maps or…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are…
In this paper, we propose a decision procedure of reachability for linear system {\xi}' = A{\xi} + u, where the matrix A's eigenvalues can be arbitrary algebraic numbers and the input u is a vector of trigonometric-exponential polynomials.…
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…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
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 article studies the distributed estimation problem of a multi-agent system with bounded absolute and relative range measurements. Parts of the agents are with high-accuracy absolute measurements, which are considered as anchors; the…
Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we…
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…