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.

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.

Ready,set,go:Medical preparations for the Paris 2024 Paralympic Games

1.Introduction In August 2024,over 4400 Paralympic athletes will gather in Paris for the Paralympic Summer Games—the pinnacle of every Paralympian’s(Para athletes competing at the Paralympic Games)career to showcase their ability and skills.Their training,preparation,and effort in the years leading up to the Games are unparalleled.To achieve success,Paralympians specifically rely on a medical support team to achieve their goals.So,what is required of the medical support team to prepare Paralympians to get ready,set,and go to Paris 2024?

Enhanced UAV Pursuit-Evasion Using Boids Modelling:A Synergistic Integration of Bird Swarm Intelligence and DRL

TheUAV pursuit-evasion problem focuses on the efficient tracking and capture of evading targets using unmanned aerial vehicles(UAVs),which is pivotal in public safety applications,particularly in scenarios involving intrusion monitoring and interception.To address the challenges of data acquisition,real-world deployment,and the limited intelligence of existing algorithms in UAV pursuit-evasion tasks,we propose an innovative swarm intelligencebased UAV pursuit-evasion control framework,namely“Boids Model-based DRL Approach for Pursuit and Escape”(Boids-PE),which synergizes the strengths of swarm intelligence from bio-inspired algorithms and deep reinforcement learning(DRL).The Boids model,which simulates collective behavior through three fundamental rules,separation,alignment,and cohesion,is adopted in our work.By integrating Boids model with the Apollonian Circles algorithm,significant improvements are achieved in capturing UAVs against simple evasion strategies.To further enhance decision-making precision,we incorporate a DRL algorithm to facilitate more accurate strategic planning.We also leverage self-play training to continuously optimize the performance of pursuit UAVs.During experimental evaluation,we meticulously designed both one-on-one and multi-to-one pursuit-evasion scenarios,customizing the state space,action space,and reward function models for each scenario.Extensive simulations,supported by the PyBullet physics engine,validate the effectiveness of our proposed method.The overall results demonstrate that Boids-PE significantly enhance the efficiency and reliability of UAV pursuit-evasion tasks,providing a practical and robust solution for the real-world application of UAV pursuit-evasion missions.

Problematic Use of Video Games in Schools in Northern Benin (2023)

Objective: To study the problematic use of video games among secondary school students in the city of Parakou in 2023. Methods: Descriptive cross-sectional study conducted in the commune of Parakou from December 2022 to July 2023. The study population consisted of students regularly enrolled in public and private secondary schools in the city of Parakou for the 2022-2023 academic year. A two-stage non-proportional stratified sampling technique combined with simple random sampling was adopted. The Problem Video Game Playing (PVP) scale was used to assess problem gambling in the study population, while anxiety and depression were assessed using the Hospital Anxiety and Depression Scale (HADS). Results: A total of 1030 students were included. The mean age of the pupils surveyed was 15.06 ± 2.68 years, with extremes of 10 and 28 years. The [13 - 18] age group was the most represented, with a proportion of 59.6% (614) in the general population. Females predominated, at 52.8% (544), with a sex ratio of 0.89. The prevalence of problematic video game use was 24.9%, measured using the Video Game Playing scale. Associated factors were male gender (p = 0.005), pocket money under 10,000 cfa (p = 0.001) and between 20,000 - 90,000 cfa (p = 0.030), addictive family behavior (p < 0.001), monogamous family (p = 0.023), good relationship with father (p = 0.020), organization of video game competitions (p = 0.001) and definite anxiety (p Conclusion: Substance-free addiction is struggling to attract the attention it deserves, as it did in its infancy everywhere else. This study complements existing data and serves as a reminder of the need to focus on this group of addictions, whose problematic use of video games remains the most frequent due to its accessibility and social tolerance. Preventive action combined with curative measures remains the most effective means of combating the problem at national level.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

The "Black Myth" Marks a New Milestone for China-Made Games in Overseas Market

Since its first launch on August 20th,the game"Black Myth:Wukong"has broken many previous records for domestic single-player games,and also provides a chance for global game players to see Chinese games as among the world's best games.The number of online users on the entire platform exceeded3 million at its most,and more than10 million copies of the games were sold within the first four days after the launch.It has received more than 270thousand reviews in total and 96%positive reviews on the Steam platform,providing a chance for global game players to enjoy the best of Chinese games。

Distributed Optimal Variational GNE Seeking in Merely Monotone Games

In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.

Zero-determinant strategies in iterated multi-strategy games

Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.

Video Games and School Performances of Dakar High School Students

The triptych (Smartphones, Video games, adolescents) has imposed itself on the collective consciousness in the form of questioning to the point of becoming a social phenomenon. It thus raises concerns about the uses that adolescents make of it and the effects on their academic performance, which we proposed to study among middle school students from the Dakar academy inspection. Where appropriate, we used mixed methods with the collection techniques of questionnaire survey, semi-structured interviews respectively with middle school students, adults (parents, supervisors, teachers, etc.), participant observation and literature review. Concretely, before accessibility to video games, the middle school students were more idle and well-behaved, watched a lot of TV, played with their brothers and sisters or did household chores. The majority of young people had good, very good or excellent conduct and their averages were fair, fairly good or good. With access to a diverse digital environment, middle school students have passionately turned to video games. As a result, their learning time, concentration and submission to parental injunctions have declined significantly. This situation negatively affected their academic performance and encouraged bad behavior.

Mongolian Traditional Game-“Shagai”Features of Mongolian Traditional Games

In today’s interconnected global society,a crucial aspect that defines the identity of an independent country is its distinctive national heritage and values.Every country has many different cultures,and children’s games exist in every culture.Every culture has unique characteristics and norms that have been agreed upon by the members of the culture(Usman&Yusuf,2022).Mongolians believe that the future of their nation can be discerned through the toys that children play with.These toys reflect Mongolia’s nomadic culture,rich heritage,customs,precious belongings,and unique playthings.Mongolian culture and mentality are nurtured in children through play,and an essential aspect of Mongolian games is their close association with people’s work and way of life.The Mongolian toys stand as a significant intellectual contribution of the Mongolian people to human history.

An AutoML based trajectory optimization method for long-distance spacecraft pursuit-evasion game

Current successes in artificial intelligence domain have revitalized interest in spacecraft pursuit-evasion game,which is an interception problem with a non-cooperative maneuvering target.The paper presents an automated machine learning(AutoML)based method to generate optimal trajectories in long-distance scenarios.Compared with conventional deep neural network(DNN)methods,the proposed method dramatically reduces the reliance on manual intervention and machine learning expertise.Firstly,based on differential game theory and costate normalization technique,the trajectory optimization problem is formulated under the assumption of continuous thrust.Secondly,the AutoML technique based on sequential model-based optimization(SMBO)framework is introduced to automate DNN design in deep learning process.If recommended DNN architecture exists,the tree-structured Parzen estimator(TPE)is used,otherwise the efficient neural architecture search(NAS)with network morphism is used.Thus,a novel trajectory optimization method with high computational efficiency is achieved.Finally,numerical results demonstrate the feasibility and efficiency of the proposed method.

THE 6^(th) SPORTS GAMES OF THE BUDDHIST ACADEMY OF XIZANG HELD IN LHASA

On May 8th,the 6th sportsgames of the Buddhist Academy of Xizang was held in Lhasa.The sports games featured field events,track events,and fun sports events,including 100 metres,standing long jump,shot put,400m relay,two-person running with legs tied up,and sandbag carrying-a traditional Tibetan sport.The teachers and students of the academy actively participated in and enjoyed the sports.Let's share their passion forsports together!

The Impact of Sports Games on the Psychological Health of Middle School Students

This study conducted a 16-week comparative experiment with 160 students from Jinan No.5 Middle School in Shandong Province as the experimental subjects.During the implementation of the experiment,the subjects were divided into two groups:an experimental group and a control group.The experimental group was subjected to physical exercise interventions using sports game teaching methods during physical education class,while the control group followed traditional physical education teaching methods.The results showed that the psychological health status of the students in the experimental group was significantly better than that of the control group after the experiment.The application of sports games helps to improve the psychological health of middle school students in the course of physical education,promoting a positive and forward direction in student psychology and is an effective means to enhance the psychological health level of middle school students.

An escape strategy in orbital pursuit-evasion games with incomplete information

The orbital pursuit-evasion game is typically formulated as a complete-information game,which assumes the payoff functions of the two players are common knowledge.However,realistic pursuit-evasion games typically have incomplete information,in which the lack of payoff information limits the player’s ability to play optimally.To address this problem,this paper proposes a currently optimal escape strategy based on estimation for the evader.In this strategy,the currently optimal evasive controls are first derived based on the evader’s guess of the pursuer’s payoff weightings.Then an online parameter estimation method based on a modified strong tracking unscented Kalman filter is employed to modify the guess and update the strategy during the game.As the estimation becomes accurate,the currently optimal strategy gets closer to the actually optimal strategy.Simulation results show the proposed strategy can achieve optimal evasive controls progressively and the evader’s payoff of the strategy is lower than that of the zero-sum escape strategy.Meanwhile,the proposed strategy is also effective in the case where the pursuer changes its payoff function halfway during the game.

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.

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

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.

Cooperative Anti-Jamming and Interference Mitigation for UAV Networks: A Local Altruistic Game Approach

To improve the anti-jamming and interference mitigation ability of the UAV-aided communication systems, this paper investigates the channel selection optimization problem in face of both internal mutual interference and external malicious jamming. A cooperative anti-jamming and interference mitigation method based on local altruistic is proposed to optimize UAVs’ channel selection. Specifically, a Stackelberg game is modeled to formulate the confrontation relationship between UAVs and the jammer. A local altruistic game is modeled with each UAV considering the utilities of both itself and other UAVs. A distributed cooperative anti-jamming and interference mitigation algorithm is proposed to obtain the Stackelberg equilibrium. Finally, the convergence of the proposed algorithm and the impact of the transmission power on the system loss value are analyzed, and the anti-jamming performance of the proposed algorithm can be improved by around 64% compared with the existing algorithms.