In this work, a finite-horizon zero-sum linear-quadratic differential game, modeling pursuit-evasion problem, was considered. the game’s cost function, of control minimizing player (the minimizer/the pursuer) much smaller than maximizing maximizer/the evader) and state variable. This smallness expressed by positive small multiplier (a parameter) square L2-norm minimizer’s in function. Parameter...

We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than √ 5n and hence that bn/ √ 5c+ 1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869 · · ·n2 +O(n) cops can capture a robber in a n× n× n cube and that a robber can forev...

Real world tasks involving moving targets, such as driving a vehicle, are performed based on continuous decisions thought to depend upon the temporal derivative of the expected utility (∂V/∂t), where the expected utility (V) is the effective value of a future reward. However, the neural mechanisms that underlie dynamic decision-making are not well understood. This study investigates human neura...

B Abstract. In Part 1 of this paper (Ref. 1) necessary conditions for optimal open-loop strategies in diierential games of pursuit-evasion type have been developed for problems which involve state variable inequality constraints and nonsmooth data. These necessary conditions lead to multipoint boundary-value problems with jump conditions. These problems can be solved very eeciently and accurate...

The classical involute of a plane base curve intersects every tangent line at a right angle. This paper introduces a tanvolute, which intersects every tangent line at any given fixed angle. This minor change in the definition of a classical concept leads to a wealth of new examples and phenomena that go far beyond the original situation. Our treatment is based on two differential equations rela...

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber...

In this thesis we examine systems of pursuit and evasion with multiple evaders from several perspectives. Through the analysis of mathematical models and the study of field experiments we seek to understand how constraints on individual motion and sensing abilities affect outcomes on the level of the group and the individual. We present a nonlinear model of pursuit and evasion on the plane for ...

This paper presents an unusual perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. Information itself is modeled using information space concepts, which originated from dynamic game theory (rather than information theory, which was developed mainly for communication). The guiding principle in this...

Air-to-air combat between two aggressive aircraft , both equipped with medium-range guided missiles, is .a key element of future air warfare. This dynamic coni lict can be viewed as an interaction of a twotarget diiferential game (between the air-craft) and two independent missileaircraft pursuit-evasion games. The information structure is, however, rather intricate: though perfect information ...