Related papers: Reachability problems for PAMs
These are lecture notes from a course in arithmetic dynamics given in Grenoble in June 2017. The main purpose of this text is to explain how arithmetic equidistribution theory can be used in the dynamics of rational maps on P^1. We first…
The aircraft routing problem is one of the most studied problems of operations research applied to aircraft management. It involves assigning flights to aircraft while ensuring regular visits to maintenance bases. This paper examines two…
Backward reachability (also termed controllability) has been extensively studied in control theory, and tools for a wide class of systems have been developed. Nevertheless, assessing a backward reachability analysis or synthesis remains…
This paper presents a real-time trajectory planning framework for Urban Air Mobility (UAM) that is both safe and scalable. The proposed framework employs a decentralized, free-flight concept of operation in which each aircraft independently…
Radio maps provide radio frequency metrics, such as the received signal strength, at every location of a geographic area. These maps, which are estimated using a set of measurements collected at multiple positions, find a wide range of…
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…
We study the reach control problem for affine systems on simplices, and the focus is on cases when it is known that the problem is not solvable by continuous state feedback. We examine from a geometric viewpoint the structural properties of…
We design the first polynomial time approximation schemes (PTASs) for the Minimum Betweenness problem in tournaments and some related higher arity ranking problems. This settles the approximation status of the Betweenness problem in…
Reachability analysis plays a central role in system design and verification. The reachability problem, denoted $\Diamond^J\,\Phi$, asks whether the system will meet the property $\Phi$ after some time in a given time interval $J$.…
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…
We study an extensive class of movement minimization problems which arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
Knowledge of a manipulator's workspace is fundamental for a variety of tasks including robot design, grasp planning and robot base placement. Consequently, workspace representations are well studied in robotics. Two important…
Reachability types are a recent proposal that has shown promise in scaling to higher-order but monomorphic settings, tracking aliasing and separation on top of a substrate inspired by separation logic. The prior $\lambda^*$ reachability…
In the allocation of indivisible goods, a prominent fairness notion is envy-freeness up to one good (EF1). We initiate the study of reachability problems in fair division by investigating the problem of whether one EF1 allocation can be…
The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a discrete de Rham complex that preserves the structure of the…