相关论文: Positive Alexander Duality for Pursuit and Evasion

The classical setting of optimal control theory assumes full knowledge of the process dynamics and the costs associated with every control strategy. The problem becomes much harder if the controller only knows a finite set of possible…

We study a pursuit-evasion game between a double integrator-driven pursuer with bounded velocity and bounded acceleration and a single integrator-driven evader with bounded velocity in a two-dimensional plane. The pursuer's goal is to…

The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We use the Bousfield-Kan spectral sequence for homotopy inverse…

This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance…

This paper introduces a new family of pursuit strategies for multi-pursuer single-evader games in a planar environment. They leverage conditions under which the minimum-time solution of the game becomes equivalent to that of a suitable…

We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the…

We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for…

Pursuit-evasion games are ubiquitous in nature and in an artificial world. In nature, pursuer(s) and evader(s) are intelligent agents that can learn from experience, and dynamics (i.e., Newtonian or Lagrangian) is vital for the pursuer and…

We prove excision in entire and periodic cyclic cohomology and construct a Chern-Connes character for Fredholm modules over a C*-algebra without summability restrictions, taking values in a variant of Connes's entire cyclic cohomology.…

Given a compact manifold $X$ with boundary and a submersion $f : X \rightarrow Y$ whose restriction to the boundary of $X$ has isolated critical points with distinct critical values and where $Y$ is $[0,1]$ or $S^1$, the connected…

Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…

Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any…

The cohomology jump loci of a space $X$ are of two basic types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems, and the resonance varieties, constructed from information encoded in…

Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching…

This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while…

We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the the monitored area, visit a target region, and then leave the area, while minimizing…

This paper studies a two-person linear-quadratic-Gaussian pursuit-evasion differential game with costly but controlled information. One player can decide when to observe the other player's state. However, one observation of another player's…

Linear complementarity programming is a generalization of linear programming which encompasses the computation of Nash equilibria for bimatrix games. While the latter problem is PPAD-complete, we show that the tropical analogue of the…

In the incentivized exploration model, a principal aims to explore and learn over time by interacting with a sequence of self-interested agents. It has been recently understood that the main challenge in designing incentive-compatible…