Related papers: Minimal Reachability Problems
In the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system $w_t=w_{xx}$, $w(0,\cdot)=u$, $x>0$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a control.…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Given a conjunctive Boolean network (CBN) with $n$ state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is…
We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. In this work, we use the deployment strategy for diagonal guards…
This paper considers the problem of reachability analysis of control systems with optimal controllers, as a first step towards verifying the safety and correctness of such systems. Despite their appeal in guaranteeing task satisfaction…
We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an…
Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to…
This article treats three problems of sparse and optimal multiplexing a finite ensemble of linear control systems. Given an ensemble of linear control systems, multiplexing of the controllers consists of an algorithm that selects, at each…
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…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
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…
We consider the problem of proving that each point in a given set of states ("target set") can indeed be reached by a given nondeterministic continuous-time dynamical system from some initial state. We consider this problem for abstract…
In this paper, we present an empirical balanced truncation method for nonlinear systems with linear time-invariant input vector field components. First, we define differential reachability and observability Gramians. They are matrix valued…
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
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…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
A standard model that arises in several applications in sequential decision making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in such…