Related papers: Multiple Reachability in Linear Dynamical Systems
In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…
We consider polyhedral versions of Kannan and Lipton's Orbit Problem (STOC '80 and JACM '86)---determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an…
We study a parametric version of the Kannan-Lipton Orbit Problem for linear dynamical systems. We show decidability in the case of one parameter and Skolem-hardness with two or more parameters. More precisely, consider a $d$-dimensional…
We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a…
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…
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…
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…
We study qualitative multi-objective reachability problems for Ordered Branching Markov Decision Processes (OBMDPs), or equivalently context-free MDPs, building on prior results for single-target reachability on Branching Markov Decision…
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…
We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching…
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…
Consider the problem of planning collision-free motion of $n$ objects in the plane movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of $m \leq n$ objects simultaneously. This…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
The \emph{Orbit Problem} consists of determining, given a linear transformation $A$ on $\mathbb{Q}^d$, together with vectors $x$ and $y$, whether the orbit of $x$ under repeated applications of $A$ can ever reach $y$. This problem was…
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…
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.…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
In this paper, we are interested in the synthesis of schedulers in double-weighted Markov decision processes, which satisfy both a percentile constraint over a weighted reachability condition, and a quantitative constraint on the expected…
Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets…