Related papers: Minimal Reachability Problems
We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical…
This paper looks at two problems, minimum constrained input selection and minimum cost constrained input selection for state space structured systems. The input matrix is constrained in the sense that the set of states that each input can…
This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical…
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…
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
This paper addresses two fundamental problems in the context of jump linear systems (JLS). The first problem is concerned with characterizing the minimal state space dimension solely from input-output pairs and without any knowledge of the…
Interval Markov chains extend classical Markov chains with the possibility to describe transition probabilities using intervals, rather than exact values. While the standard formulation of interval Markov chains features closed intervals,…
The problem of controlling a finite state Markov chain in the presence of an adversary so as to ensure desired performance levels for a vector of objectives is cast in the framework of Blackwell approachability. Relying on an elementary two…
Neural networks (NNs) have been shown to learn complex control laws successfully, often with performance advantages or decreased computational cost compared to alternative methods. Neural network controllers (NNCs) are, however, highly…
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…
Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
Determining the distance between a controllable system to the set of uncontrollable systems, namely, the controllability radius problem, has been extensively studied in the past. However, the opposite direction, that is, determining the…
Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…
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…
Given a linear system $\dot{x} = Ax$, where $A$ is an $n \times n$ matrix with $m$ nonzero entries, we consider the problem of finding the smallest set of state variables to affect with an input so that the resulting system is structurally…
We propose a solution to a time-varying variant of Markov Decision Processes which can be used to address decision-theoretic planning problems for autonomous systems operating in unstructured outdoor environments. We explore the time…
In this paper, we provide optimal solutions to two different (but related) input/output design problems involving large-scale linear dynamical systems, where the cost associated to each directly actuated/measured state variable can take…
It is shown that for two large subclasses of discrete-time nonlinear systems - analytic systems defined on a compact state space and rational systems - the minimum length $r^*$ for input sequences, called here accessibility index of the…