Mehdi Salimi
We consider a pursuit-evasion differential game with a Hybrid system of dynamics in Hilbert space with integral constraints on the control functions of players. We show that the pursuer has a winning strategy.
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Analysis of First-Order Linear Pursuit and Evasion Differential Games with Gronwall-Type Constraints
该论文研究n维空间中受格朗沃尔型约束的一阶线性追逃微分对策，分析追击结果与参与者可达域的关系，并给出逃避可行的充分条件。
An infinite dimensional pursuit-evasion differential game with finite number of players
研究了希尔伯特空间中有限个追逐者和一个逃避者的追逐-逃避微分对策，其中局中人的控制函数受到几何约束.我们解决了这个游戏，提出明确的战略，保证他们的追求，以及一个战略，保证其逃避的追求者。
On extension for infinite horizon game of pursuit-evasion
构造了一个具有无限时域的冲突控制问题的推广。这个扩张就是限制对策的投射极限。研究了“目标集灵敏度”与最优控制存在性的关系。特别关注的是“联合控制/放松控制”的追逃对策。
Safe Control for Pursuit-Evasion with Density Functions
针对追逃问题，提出基于密度函数的安全控制框架，将追逃微分博弈转化为鲁棒安全控制问题，通过凸平方和规划求解，避免了Hamilton-Jacobi-Isaacs方程的高复杂度，仿真验证了方法有效性。
Qualitative Criterion for Interception in a Pursuit/Evasion Game
对微分追赶/规避对策进行了定性的描述。拦截解的存在性的一个标准是使用未来的圆锥，包含所有可达到的轨迹的目标或拦截器从一个初始位置。拦截机会总是存在的一个充分和必要条件是，经过一段初始时间后，目标的未来锥体被包含在拦截器的未来锥体内。该充分条件可以看作是一种纳什均衡。
Pursuit and evasion conflicts represent challenging problems with important applications in aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must consider the adversary's potential strategies. Differential game theory provides an adequate framework to analyze possible outcomes of the conflict without assuming particular behaviors by the opponent. This article presents an organized introduction of pursuit-evasion differential games with an overview of recent advances in the area. First, a summary of the seminal work is outlined, highlighting important contri…
Analytical Pursuit-Evasion Game Strategy in Arbitrary Keplerian Reference Orbits
本文提出了一种适用于任意开普勒参考轨道的分析性追捕-逃避博弈策略，通过解析解实现高效求解，显著提升计算效率并适用于复杂轨道场景。
A Numerical Analysis for Pursuit-Evasion Games under the Stackelberg Eqilibrium
本文提出了一种在Stackelberg均衡下求解追捕-躲避微分博弈的数值分析框架，引入Semi-DCNLP方法用于飞行路径优化，并验证了该方法的有效性。
New strategies for some pursuit-evasion differential games with Gronwall-type constraints
本文在序列空间$l_{2}$中研究受Gronwall型约束的非合作追逃微分博弈，构造追方新策略、逃方容许策略，建立对应充分条件，扩展了微分博弈相关现有结果。
A decomposition technique for pursuit evasion games with many pursuers
本文给出了一类微分对策的分解技巧。该技术包括在一个分解的目标集，产生的几何原因，分解的维度的问题。利用Hamilton-Jacobi方程理论的一些元素，我们找到了解的正则性和分解问题的可能性之间的关系。我们使用这种技术来解决一个追逃对策与多个代理。
Brachistochrone Pursuit - Evasion Games and Riemann-Finsler Geometry
一个几何方法微分对策理论的说明。平行追击被认为是一个两人零和微分对策。基于Riemann-Finsler几何设计了各局中人的最优策略。我们的方法采用了闭环最优控制和介绍是熟悉的Brachistochrone型问题。
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 region, however, it was unclear whether the evader could reach outside the initial AC without being captured. We construct a pursuit strategy that guarantees the capture of an evader within an arbitrarily close neighborhood of the initial AC. The pursuer strategy is derived by reformulating the game into a nonlinear control problem, and the guarantee holds agains…
A single player and a mass of agents: a pursuit evasion-like game
本研究探讨单个玩家与大量智能体间的有限时域追逃微分博弈，利用输运方程描述群体动态，推导无限维Isaacs方程，并证明值函数为希尔伯特空间不变子集上的唯一粘性解。
Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary
在一个追逃对策游戏中，一队追捕者试图抓住一个逃跑者。玩家交替轮流，以相同的速度移动，并拥有关于游戏状态的全部信息。我们考虑最难控制的捕获条件：追逐者必须与逃避者共处一处才能赢得游戏。证明了拓扑空间中关于追逃对策的两个一般性结果。首先，我们证明了在这个限制性捕获准则下，在任何CAT（0）空间中，一个追踪者都有一个获胜策略。这补充了Alexander、Bishop和Ghrist的结果，他们为具有正捕获半径的游戏提供了获胜策略。其次，我们考虑了欧氏空间中具有分段解析边界和任意欧拉示性数的紧区域上的对策。我们表明，三个追求者总是有一个获胜的战略，最近的工作Bhadauria，克莱因，Isler和苏里从多边形环境中，我们更一般的设置。
Solution and Optimal Strategies for a Differential Game of Pursuit-Evasion with Point-Wise Constraints
研究序列空间$l_2$中受逐点约束、含可数追逃者与单个逃避者的微分博弈，明确双方动力学规则与收益目标，给出博弈解、最优策略构造及博弈值估计。
Pursuit-Evasion on a Sphere and When It Can Be Considered Flat
本文研究球面上的追逃博弈，将平面阿波罗尼斯圆推广为球面阿波罗尼斯域，推导出拦截点属于该域的条件，并据此分析了两追捕者对抗一较慢逃逸者的策略且进行了数值模拟。
In this paper, we address a pursuit-evasion game involving multiple players by utilizing tools and techniques from reinforcement learning and matrix game theory. In particular, we consider the problem of steering an evader to a goal destination while avoiding capture by multiple pursuers, which is a high-dimensional and computationally intractable problem in general. In our proposed approach, we first formulate the multi-agent pursuit-evasion game as a sequence of discrete matrix games. Next, in order to simplify the solution process, we transform the high-dimensional state space into a low-di…
Interception in differential pursuit/evasion games
利用\emph{future cones}：包含目标或截击机从初始位置出发的所有可达轨迹的拓扑锥，给出了一类微分对策中截击机截击目标的定性判据.拦截解在某个初始时间后存在，当且仅当目标的未来圆锥位于拦截器的未来圆锥内。该解可以看作是一种纳什均衡。这个结果被应用到两个例子：1。两辆车的游戏：未来的锥条件被证明是等效的条件，由Cockayne获得的拦截。\cite{ref2} 2.卫星战：本文得到了航天器或直接上升式反卫星武器（ASAT）在中心引力场中机动的未来锥，并证明了它与仅通过锥顶处的单一速度变化机动的航天器的未来锥相等。后一种结果是通过对2007年1月拦截风云-1C号航天器的分析来说明的。
Cooperative Nonlinear Guidance Strategies for Guaranteed Pursuit-Evasion
本文研究三体追逃问题，为逃跑者-防御者团队提出基于几何的协同非线性制导策略，保证在任意初始交战几何下拦截追击者，且无需获知对方策略，误差变量可在预定有限时间内收敛至零。
Dominance Regions of Pursuit-evasion Games in Non-anticipative Information Patterns
本文研究非预期信息模式下追逃博弈中逃避者支配区域的性质，首次证明初始支配区域等于开环可达区域，并给出无障碍、有障碍及单角点障碍场景下追捕者非预期捕获策略存在的条件。
Elliptical Pursuit and Evasion -Extended Version-
本研究针对一对一椭圆追逃问题，验证了追方轨迹形状仅与双方速度比有关、不受逃方速度变化影响的假设，并补充分析了不同轨道下追逃动力系统的特性及相关微分方程。
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 state comes with two costs: the direct cost of observing and the implicit cost of exposing his state. We call games of this type a Pursuit-Evasion-Exposure-Concealment (PEEC) game. The PEEC game constitutes two types of strategies: The control strategies and the observation strategies. We fully characterize the Nash control strategies of the PEEC game using…
Value of Multi-pursuer Single-evader Pursuit-evasion Game with Terminal Cost of Evader's Position: Relaxation of Convexity Condition
本研究提出了一种无需凸性条件的追捕游戏价值函数计算方法，通过几何方法和粘性解理论，解决了终端成本局部Lipschitz连续的非凸情况。
In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to bring the system from a given initial state to the origin for a finite time and the evader's purpose is opposite. We obtain a guaranteed pursuit time and construct a strategy for pursuer.
Anytime computation algorithms for approach-evasion differential games
研究了一类接近-逃避微分对策，其中一个局中人的目标是在最短时间内将动态系统的状态引导到给定的目标集合，同时避免某些不允许的状态集合，而另一个局中人的目标则相反.提出了一类新的任意时刻计算算法，分析了它们的收敛性，并通过大量的数值模拟验证了它们的性能。我们的算法显着优于多重网格方法的接近-逃避微分对策在理论和数值。我们的技术方法利用机器人运动规划和可行性理论中的增量采样。
This paper considers a pursuit-evasion scenario among three agents -- an evader, a pursuer, and a defender. We design cooperative guidance laws for the evader and the defender team to safeguard the evader from an attacking pursuer. Unlike differential games, optimal control formulations, and other heuristic methods, we propose a novel perspective on designing effective nonlinear feedback control laws for the evader-defender team using a time-constrained guidance approach. The evader lures the pursuer on the collision course by offering itself as bait. At the same time, the defender protects th…
Dynamical Systems in Elliptical Pursuit and Evasion
本文研究一对一追击逃避问题中圆形与椭圆形的差异，通过假设追击者轨迹形状不受逃避者速度影响，推导出动力系统，并分析了捕获时间上界和周期解的存在性。
Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its target while minimizing the cumulative exposure to a moving enemy Observer. That Observer is simultaneously aiming to maximize the same exposure by choosing how often to use each of its predefined patrol trajectories. Following the framework introduced in Gilles and Vladimirsky (arXiv:1812.10620), we develop efficient algorithms for finding Nash Equilibrium policies for both players by blending techniques from semi-i…
We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes occluded. Optimal controls for game can be formulated as a Hamilton-Jacobi-Isaac equation. We use an upwind scheme to compute the feedback value function, corresponding to the end-game time of the differential game. Although the value function enables optimal controls, it is prohibitively expensive to compute, even for a single pursuer and single evader on a small grid. We consider a discrete variant of the surveilla…
Convex Pursuit-Evasion Games for Spacecraft Proximity Operations on Circular and Elliptical Orbits
针对航天器近距离操作的追击-逃逸博弈，提出基于支撑函数的逃逸证书与安全策略，提供精确单侧保证，并利用投影外梯度法快速求解，适用于圆轨道与椭圆轨道。
Two-player pursuit-evasion differential game and time optimal zero control problem in $\ell^2$ are considered. Optimal control for the corresponding zero control problem is found. A strategy for the pursuer that guarantees the solution for the pursuit problem is constructed.
On a fixed duration pursuit differential game with geometric and integral constraints
本文研究了一个微分对策，其中有可数个动态对象追求一个动态对象。所有的球员都做简单的动作。游戏的持续时间是固定的。一组追踪者的控制受到几何约束，而其他追踪者和规避者的控制受到积分约束。博弈的收益是博弈结束时逃避者和最近的追赶者之间的距离。我们为参与者构造最优策略，并找到博弈的价值。
Usable boundary for visibility-based surveillance-evasion games
该研究针对带障碍物环境下的监视-规避双人零和博弈，分析目标集边界附近博弈值函数的不连续性，揭示障碍物正则性对边界分布特性的影响并证明半渗透屏障的存在，完善了这类可见性博弈的边界理论。
Pursuit-evasion differential games using the Disturbance Attenuation approach are revisited. Under this approach, the pursuer actions are considered to be control actions, whereas all external actions, such as target maneuvers, measurement errors and initial position uncertainties, are considered to be disturbances. Two open issues have been addressed, namely the effect of noise on the control gains, and the effect of trajectory shaping on the solution. These issues are closely related to the question of the best choice for the disturbance attenuation ratio. Detailed analyses are performed for…
We study computability-theoretic aspects of differential games. Our focus is on pursuit and evasion games played in Euclidean spaces in the tradition of Rado's "Lion versus Man" game. In some ways, these games can be viewed as continuous versions of reachability games. We prove basic undecidability of differential games, and study natural classes of pursuit-evasion games in Euclidean spaces where the winners can win via computable strategies. The winning strategy for Man found by Besicovitch for the traditional "Lion versus Man" is not computable. We show how to modify it to yield a computable…
Interception Conditions in Multi-Agent Pursuit Games Governed by Linear Dynamics with Gronwall-type Constraints
本文针对受Gronwall型约束的线性动力学多智能体追逃问题，构建追捕者许可策略并推导拦截保证的充分条件，通过数值示例验证策略有效性与分析条件。
We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are linear-quadratic in the control. Also, we obtain necessary conditions for one type of pursuit-evasion Volterra games.
On the Optimal Policies for Visibility-Based Target Tracking
在本文中，我们研究了一个追逃对策，其中移动观察者试图跟踪一个目标在一个环境中包含障碍物。我们把这个博弈归结为一个简单环境下的具有状态不等式约束的最优控制问题。我们发现，对于某些初始条件，有两个不同的政权在最优策略的追求者取决于状态约束是否被激活。我们推导出表征两个政权之间的切换时间的方程。将简单环境下追踪者的最优跟踪策略推广到一般的多多边形障碍物环境。我们提出了基于最优解构建“追踪场”的技术，以引导观察者在一般环境中的运动。
The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with a positive capture radius). We assume that Lion wins if he manages the capture independently of the initial positions of the players and the evader's strategy. We prove that the discrete-time simple pursuit strategy is a Lion's winning strategy in a compact geodesic space satisfying the betweenness property. In particular, it means that Lion wins in compact …
Flyby Distance Pursuit for Guarding a Target with an Inferior Guard
针对较慢守卫保护目标免受快速攻击者威胁的问题，提出微分博弈模型，通过引入辅助状态变量记录最小分离距离，将终止条件与飞越距离结合，求解两点边值问题，揭示终端速度与飞越距离的权衡。
Differential game of many pursuers with integral constraints on a convex set in the plane
研究了一个平面上多个追赶者和一个逃避者的简单运动微分对策。我们在平面上给出一个非空闭凸集，追踪者和逃避者在这个凸集上运动。他们在比赛中不能离开这一组。参与者的控制功能受到坐标积分约束。如果逃避者$y$的状态与追踪者$x_i$的状态$i=\{1,...,m\}$在某个时间$t_i$（未指定），即$x_i(t_i)=y(t_i)$，重合，那么我们说追踪完成。我们得到了一些条件下，可以完成追求从任何位置的局中人在给定的集合。此外，我们为追求者构建策略。
This paper studies a planar multiplayer Homicidal Chauffeur reach-avoid differential game, where each pursuer is a Dubins car and each evader has simple motion. The pursuers aim to protect a goal region cooperatively from the evaders. Due to the high-dimensional strategy space among pursuers, we decompose the whole game into multiple one-pursuer-one-evader subgames, each of which is solved in an analytical approach instead of solving Hamilton-Jacobi-Isaacs equations. For each subgame, an evasion region (ER) is introduced, based on which a pursuit strategy guaranteeing the winning of a simple-m…
Decomposition of Differential Games
本文提出了一种分解技巧，以简化某些零和微分对策的解。当状态达到目标时，游戏被认为是终止的，这可以表示为目标子集的集合的并集;分解包括用每个目标子集替换原始目标。然后，原始博弈的值作为分解产生的博弈集合的值的下包络而获得，这比原始博弈容易得多。标准的分解的有效性。本文包括的例子，说明了应用技术的追求/规避对策，其中的分解产生于考虑个人追求者/逃避者对的相互作用。
This paper considers the blocking or football pursuit-evasion differential game. Two pursuers cooperate and try to capture the ball carrying evader as far as possible from the goal line. The evader wishes to be as close as possible to the goal line at the time of capture and, if possible, reach the line. In this paper the solution of the game of kind is provided: The Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is constructed. Under optimal play, the winning team is determined by evaluating the associated Barrier functi…
Information Relaxations and Dynamic Zero-Sum Games
动态零和博弈是一类重要的问题，其应用范围从逃避追击和单挑扑克到某些对抗版本的控制问题，如多臂强盗和多类排队问题。这些游戏通常很难解决，即使一个球员的策略是固定的，因此构建和评估良好的次优策略，为每个球员是一个重要的实际问题。在本文中，我们提出了使用信息松弛来构建对偶的最优值的游戏上下限。我们注意到，信息松弛的方法，这已被开发和成功地应用于许多大规模的动态规划问题，立即适用于零和博弈问题。我们提供了一些简单的数值例子，并确定有趣的问题和并发症的背景下出现的零和游戏。
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