Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

An optimal guidance method for free-time orbital pursuit-evasion game

With the development of space rendezvous and proximity operations(RPO)in recent years,the scenarios with noncooperative spacecraft are attracting the attention of more and more researchers.A method based on the costate normalization technique and deep neural networks is presented to generate the optimal guidance law for free-time orbital pursuit-evasion game.Firstly,the 24-dimensional problem given by differential game theory is transformed into a three-parameter optimization problem through the dimension-reduction method which guarantees the uniqueness of solution for the specific scenario.Secondly,a close-loop interactive mechanism involving feedback is introduced to deep neural networks for generating precise initial solution.Thus the optimal guidance law is obtained efficiently and stably with the application of optimization algorithm initialed by the deep neural networks.Finally,the results of the comparison with another two methods and Monte Carlo simulation demonstrate the efficiency and robustness of the proposed optimal guidance method.

Guidance strategy of motion camouflage for spacecraft pursuit-evasion game

This work is inspired by a stealth pursuit behavior called motion camouflage whereby a pursuer approaches an evader while the pursuer camouflages itself against a predetermined background.We formulate the spacecraft pursuit-evasion problem as a stealth pursuit strategy of motion camouflage,in which the pursuer tries to minimize a motion camouflage index defined in this paper.The Euler-Hill reference frame whose origin is set on the circular reference orbit is used to describe the dynamics.Based on the rule of motion camouflage,a guidance strategy in open-loop form to achieve motion camouflage index is derived in which the pursuer lies on the camouflage constraint line connecting the central spacecraft and evader.In order to dispose of the dependence on the evader acceleration in the open-loop guidance strategy,we further consider the motion camouflage pursuit problem within an infinite-horizon nonlinear quadratic differential game.The saddle point solution to the game is derived by using the state-dependent Riccati equation method,and the resulting closed-loop guidance strategy is effective in achieving motion camouflage.Simulations are performed to demonstrate the capabilities of the proposed guidance strategies for the pursuit–evasion game scenario.

Optimal Strategy for Aircraft Pursuit-evasion Games via Self-play Iteration

In this paper,the pursuit-evasion game with state and control constraints is solved to achieve the Nash equilibrium of both the pursuer and the evader with an iterative self-play technique.Under the condition where the Hamiltonian formed by means of Pontryagin’s maximum principle has the unique solution,it can be proven that the iterative control law converges to the Nash equilibrium solution.However,the strong nonlinearity of the ordinary differential equations formulated by Pontryagin’s maximum principle makes the control policy difficult to figured out.Moreover the system dynamics employed in this manuscript contains a high dimensional state vector with constraints.In practical applications,such as the control of aircraft,the provided overload is limited.Therefore,in this paper,we consider the optimal strategy of pursuit-evasion games with constant constraint on the control,while some state vectors are restricted by the function of the input.To address the challenges,the optimal control problems are transformed into nonlinear programming problems through the direct collocation method.Finally,two numerical cases of the aircraft pursuit-evasion scenario are given to demonstrate the effectiveness of the presented method to obtain the optimal control of both the pursuer and the evader.

A physics-informed deep learning framework for spacecraft pursuit-evasion task assessment

Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics,intractable terminal constraints and heavy computational cost.In this paper,A physics-informed framework is proposed for the problem,providing an intuitive method for spacecraft threat relationship determination,situation assessment,mission feasibility analysis and orbital game rules summarization.For the first time,situation adjustment suggestions can be provided for the weak player in orbital game.First,a dimension-reduction dynamics is derived in the line-of-sight rotation coordinate system and the qualitative model is determined,reducing complexity and avoiding the difficulty of target set presentation caused by individual modeling.Second,the Backwards Reachable Set(BRS)of the target set is used for state space partition and capture zone presentation.Reverse-time analysis can eliminate the influence of changeable initial state and enable the proposed framework to analyze plural situations simultaneously.Third,a time-dependent Hamilton-Jacobi-Isaacs(HJI)Partial Differential Equation(PDE)is established to describe BRS evolution driven by dimension-reduction dynamics,based on level set method.Then,Physics-Informed Neural Networks(PINNs)are extended to HJI PDE final value problem,supporting orbital game rules summarization through capture zone evolution analysis.Finally,numerical results demonstrate the feasibility and efficiency of the proposed framework.

基于定性微分博弈的通信网络攻击预警方法

通信网络攻击预警方法覆盖面不足,无法预警位于通信网络隐藏区内的攻击情况,导致通信网络攻击预警结果准确率较低。文章提出基于定性微分博弈的通信网络攻击预警方法。首先,建立通信网络安全状态演化分析模型,获取网络运行的实时工况以及存在攻击威胁的路径。其次,基于定性微分博弈原理,划分通信网络攻击多维状态空间,全面设计网络攻击预警算法。最后,在此基础上,建立网络攻击预警指标体系,设计预警等级。实验结果表明,应用新的预警方法后,预警精度优势显著,准确率达到95%以上。

Evasion guidance algorithms for air-breathing hypersonic vehicles in three-player pursuit-evasion games

In practical combat scenario,the cooperative intercept strategies are often carefully designed,and it is challenging for the hypersonic vehicles to achieve successful evasion.Based on the analysis,it can be found that if several Successive Pursuers come from the Same Direction(SPSD)and flight with a proper spacing,the evasion difficulty may increase greatly.To address this problem,we focus on the evasion guidance strategy design for the Air-breathing Hypersonic Vehicles(AHVs)under the SPSD combat scenario.In order to avoid the induced influence on the scramjet,altitude and speed of the vehicle,the lateral maneuver and evasion are employed.To guarantee the remnant maneuver ability,the concept of specified miss distance is introduced and utilized to generate the guidance command for the AHV.In the framework of constrained optimal control,the analytical expression of the evasion command is derived,and the constraints of the overload can be ensured to be never violated.In fact,by analyzing the spacing of the pursers,it can be classified whether the cooperative pursuit is formed.For the coordination-unformed multiple pursers,the evasion can be achieved lightly by the proposed strategy.If the coordination is formed,the proposed method will generate a large reverse direction maneuver,and the successful evasion can be maintained as a result.The performance of the proposed algorithms is tested in numerical simulations.

追逃定性微分对策中界栅的确定

应用定性微分对策理论对无人机、无人车追逃问题进行分析,给出在对局环境中存在障碍物的情况下,躲避区与捕获区分界界栅的确定过程。设置对局场景,建立对局双方的运动学方程,针对双方的运动特性分析结局并得出对局策略。然后考虑讨论环境中障碍物的影响,分析对局终止条件,最终解算出界栅,并给出实例说明。

三维空间中追逃对抗定性微分对策模型研究

为有效解决一类双方各有优势和劣势的追逃对抗问题,基于定性微分对策理论,在原有的三维空间中追逃对抗定量微分对策模型的基础上,针对三维空间中的一类追逃对抗问题,建立定性微分对策模型,具体构造模型的界栅,并通过冲突分析得到对作战指挥决策有实际意义的结论。

协同微分对策制导参数及性能分析

为有效提高复杂水声对抗环境下拦截器的作战效能,寻求最佳制导参量范围,文中对协同微分制导参数约束条件和过程误差敏感性进行了分析.在建立三方对抗协同微分对策制导线性化伴随模型的基础上,根据追逃微分界栅原理分析对策空间,推导拦截器与舰船的加速度对抗系数及时间常数比的解析形式,并利用伴随理论定性分析导引探测误差、舰船机动和机动过载比等因素对微分制导拦截性能的敏感性,得出制导系统参数与制导性能的关系,预估舰船最佳机动时机.仿真结果表明,通过制导参数约束转换,舰船以最佳时机规避,可有效增强拦截器的作战效能.

面向机动威胁单目标定性微分对策的航路重规划

航迹规划是飞行器规划系统的一个重要子任务。针对具有主动性而非纯粹动态的敌方威胁类型,以单目标定性微分对策解决航路的动态重规划问题。在假设对静态威胁的参考航迹和安全走廊已预规划确定基础上,构建了基于单目标定性微分对策面向主动威胁安全走廊内飞行器航路对策的数学模型,并对航路的单目标定性微分对策系统进行了求解。

无人战车追逃定性微分对策中界栅的确定

研究无人战车在无障碍、有障碍两种对局环境中的追逃问题,主要讨论了追逃定性微分对策中界栅的确定。在无障碍条件下,建立对局双方的运动模型,由于两者到达捕获点的时间是相同的,因此可以通过消除时间参数构建界栅。该方法与Isaac提出的构造界栅的经典方法结果一致,并在此基础上分析了躲避区的最大面积。在无人车的实际行驶过程中肯定会受到障碍物的影响,探讨了在有障碍条件下的追逃微分对策界栅的构建。考虑线性障碍物的影响,分析在障碍物存在的条件下双方的等时线分布情况,并提出用等时线的交集确定界栅的方法。

基于定性微分博弈的网络安全威胁预警方法

目前,基于博弈理论的网络安全研究大多采用静态博弈或多阶段动态博弈模型,不符合实际网络攻防连续对抗、实时变化的特点,为了更加贴近攻防实际进行安全威胁预警,借鉴传染病动力学模型分析安全威胁传播过程,基于定性微分博弈理论构建网络攻防博弈模型,推演安全威胁动态变化趋势。在此基础上,提出攻防定性微分博弈求解方法,构造攻防界栅以及捕获区和躲避区;引入多维欧氏距离,度量不同安全状态的威胁严重程度;进而设计预警算法,实现对网络安全威胁的动态预警,且具有更好的准确性和时效性。仿真实验结果表明,所提模型和算法有效且可行。

机动能力受限的目标-攻击-防御定性微分对策

针对导弹攻击具有防御导弹保护和机动躲避能力的目标的三体博弈问题,构建了攻击弹、防御弹和机动能力受限目标的三人微分对策模型,提出了显示策略法求解了三人定性微分对策,给出了导弹突防成功的必要条件和最优突防策略.研究结果表明,目标机动能力受限时攻击弹具有更宽的突防成功条件,与实际情况相符,证明了方法的有效性.

Open-loop solution of a defender–attacker–target game:penalty function approach

A defender–attacker–target problem with non-moving target is considered.This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional.In this game,the pursuer is the defender,while the evader is the attacker.The objective of the pursuer is to minimise the cost functional,while the evader has two objectives:to maximise the cost functional and to keep a given terminal state inequality constraint.The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders.