• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    A Predator-prey Particle Swarm Optimization Approach to Multiple UCAV Air Combat Modeled by Dynamic Game Theory

    2015-08-11 11:57:20HaibinDuanPeiLiandYaxiangYu
    IEEE/CAA Journal of Automatica Sinica 2015年1期

    Haibin Duan,Pei Li,and Yaxiang Yu

    A Predator-prey Particle Swarm Optimization Approach to Multiple UCAV Air Combat Modeled by Dynamic Game Theory

    Haibin Duan,Pei Li,and Yaxiang Yu

    —Dynamic game theory has

    Although finding the Nash equilibrium in a two-playergame may be easy since the zero-sum version can be solved in polynomialtime by linearprogramming,this problem has been proved to be indeed PPAD-complete[17?18].So the problem of computing Nash equilibria in games is computationally extremely difficult,if not impossible.Based on the analogy of the swarm of birds and the school of fi sh,Kennedy and Eberhart developed a powerful optimization method,particle swarm optimization(PSO)[19?20],addressing the social interaction,ratherthan purely individualcognitive abilities.As one of the most representative method aiming at producing computational intelligence by simulating the collective behavior in nature,PSO has been seen as an attractive optimization tool for the advantages of simple implementation procedure, good performance and fast convergence speed.However,it has been shown that this method is easily trapped into local optima when coping with complicated problems,and various tweaks and adjustments have been made to the basic algorithm over the past decade[20?22].To overcome the aforementioned problems,a hybrid predator-prey PSO(PP-PSO)was firstly proposed in[21]by introducing the predator-prey mechanism in the biological world to the optimization process.

    Recently,bio-inspired computation in UCAVs have attracted much attention[23?25].However,the game theory and solutions to the problem of task assignment have been studied independently.The main contribution of this paper is the developmentof a game theoretic approach to dynamic UCAV air combat in a military operation based on the PP-PSO algorithm.The dynamic task assignment problem is handled from a game theoretic perspective,where the assignmentscheme is obtained by solving the mixed Nash equilibrium using PP-PSO ateach decision step.

    The remainder of the paper is organized as follows:Section II describes the formulation of the problem,including the attrition model of a military air operation and its game theoretic representation.Subsequently,we propose a predator-prey PSO forthe mixed Nash equilibrium computing oftwo-player,noncooperative game in Section III.An example of an adversary scenario of UCAV combat involving two opposing sides is presented in Section IV to illustrate the effectiveness and adaption of the proposed methodology.Concluding remarks are offered in the last section.

    II.A DYNAMIC GAME THEORETIC FORMULATION FOR UCAV AIR COMBAT

    A.Dynamic Model of UCAV Air Combat

    There are two combatsides in the UCAV air combatmodel. Specifically,the attacking side is labeled as Red and the defending force as B lue.Each side consists of differentcombat units,which are made up of different numbers of combat platforms armed with weapons.Each unitis fully described by its location,number of platforms and the average number of weapons per platform.Thus,the state of each unit attime k isrepresents the unitlocation,corresponds to the number ofplatforms ofthe i th unitattime k,andto the number of weapons on each platform in the i th unitof X.The number of platforms for the moving units changes according to the following attrition equations

    The term in(1)represents the percentage of platforms in the i th unitof X force,which survive the transition from time k to k+1.For each unitin force X,this percentage is dependenton the identities ofthe attacking and the attacked units determined by the choice of target control,and is expressed as

    It is assumed in(2)that Ndunits of Y fire at the i th unit of X.The engagement factor QXYij(k)of the j th unit of Y attacking the i th unit of X at time k is computed from

    whereβXYijrepresents the probability that the j th unit of Y acquires the i th unit of X as a target,and is calculated by

    The attrition factor PXYij(k)in(2)representsthe probability of the platforms in the i th unit of X being destroyed by the salvo of sYj(k)fired from the j th unit of Y at time k,and is computed as follows

    where the term 0≤βw≤1 represents the weather impact which reduces the kill probability according to the weather condition,i.e.,1 corresponds to ideal weather condition while 0 corresponds to the worst weather condition.P KXYijis the probability of i th unitof X being completely destroyed by the j th unit of Y under ideal weather and terrain conditions.

    In the equation mentioned above sYiis the average effective kill factor when the j th unit of X attacks the i th unit of Y with salvo cYi(k),and is calculated from

    where cYiis the salvo size of j th combat unit of Y and c is a constant referred to as Wes coefficient.

    The controlvector for each unitfor both sides is chosen as

    where VxXi(k)and VyXi(k)are respectively the relocating control corresponding to the x-coordinate and y-coordinate,many weapons should fire.The numberofweapons is updated according to

    The state equations of each unit engaged in an air combat are defined as

    B.Game Theoretic Formulation for UCAV Air Combat

    The problem of dynamic task assignmentin the air combat is modeled from a game theoretic perspective in this paper. Suppose Red consists of N R units(UCAVs)and it fires C R missiles during each attack or defense.There are N B units in the B lue force,whose salvo size is also a constant C B.At each decision making step k,both sides decide on which units of its own side should be chosen to attack and which units of the opponent should be chosen as targets,with the purpose of maximizing its own objective function.Each combination of attacking and attacked units is seen as a pure strategy in the game.Foreach side,the numberofpure strategies is calculated as

    The payoff matrix for both sides is an NRS×NBSmatrix, expressed as

    Each entry JRi,j(k)in M R corresponds to the payoff of Red when it takes the i th pure strategy against the j th pure strategy of B lue.Forthe attacking force of Red,the objective function JRi,j(k)is calculated as

    whereεandτare weightcoefficients.The objection function for the defense of B lue is calculated,by the same token,as

    From a game theoretic pointofview,the cooperative UCAV task assignment problem is for the tagged side,Red,to maximize its own payoff ateach decision step,by calculating a mixed Nash equilibrium for the NRS×NBSmatrix game.

    III.PREDATOR-PREY PSO FOR THE MIXED NASH SOLUTION

    A.Predator-prey PSO

    In the gbest-model of PSO,each particle has information of its current position and velocity in the solution space[21]. And ithas the bestsolution found so far of itself as pbest and the bestsolution of a whole swarm as gbest.The gbest-model can be expressed as

    where vij(k)and xij(k)respectively denote the velocity and position of the i th particle in the j th dimension at step k,and c1and c2are weight coefficients,r1and r2are random numbers between 0 and 1 to reflect the stochastic algorithm nature.The personal best position picorresponds to the position in the search space where particle i has the minimum fitness value.The global best position denoted by girepresents the position yielding the bestfitness value among all the particles.

    Unfortunately,the basic PSO algorithm is easy to fall into local optima.In this condition,the concept of predator-prey behavior is introduced into the basic PSO to improve the optima finding performance[26?28].This adjustment takes a cue from the behavior of schools of sardines and pods of killer whales.In this model,particles are divided into two categories, predator and prey.Predators show the behavior of chasing the center of preys'swarm;they look like chasing preys.And preys escape from predators in the multidimensional solution space.After taking a tradeoff between predation risk and their energy,escaping particles would take different escaping behaviors.The velocities of the predator and the prey in the PP-PSO can be defined by

    where d and r denote the predator and prey,respectively,pdiis the best position of predators,priis the best position of preys,g is the best position which all the particles have ever found.Andωdandωrare defined as

    whereωdandωrare the inertia weights ofpredators and preys, which regulate the trade-offbetween the global(wide-ranging) and local(nearby)exploration abilities of the swarm and are considered critical for the convergence behavior of PSO. iterationmaxrepresents the maximum number of iterations andωmaxandωmindenote the maximum and minimum value ofωr,respectively.And the definition of I is given by the following expression

    Then I denotes the number ofthe i th prey’s nearestpredator. In(18),P is used to decide if the prey escapes or not(P=0 or P=1),and a and b are the parameters thatdetermines the difficulty of the preys escaping from the predators.The closer the prey and the predator,the harder the prey escapes from the predator.Moreover,a and b are shown as

    where xspanis the span of the variable.

    B.Nash Equilibrium

    As a competitive(non-cooperative)strategy of multiobjective multi-criterion system first proposed by Nash[29], Nash equilibrium is basically a local optimum:a strategy profile(s1,s2,···,sn)such that no player can benefit from switching to a different strategy if nobody else switches,?i,?s'i∈Sj

    where UPjdenotes the expected payment of person j,sjand Sjrespectively denote the i th strategy of player j and the set of strategies.Note that every dominant strategy equilibrium is a Nash equilibrium,but not vice versa.Every game has one Nash equilibrium at least.In this paper,the expected payment is substituted by the objective function which is used to calculate the payoff matrixes denoted by M Am×nand M Bm×n.We define the vector of mixed strategies form=NRSand n=NBS.So,for each mixed strategy Xi,the Nash equilibrium solution(X?,Y?)must satisfy the given conditions

    C.Proposed Approach for the Mixed Nash Equilibrium

    For utilizing the proposed algorithm to compute Nash equilibrium here,we give the fitness functions as

    In the last two expressions,Xdi,1:m(k)means the mixed strategies which are produced by the i th predator for the A force and the B force,respectively.Similarly,Xri,1:m(k) and Xri,m+1:m+n(k)denote the mixed strategies which are produced by the i th prey for the A and B forces.Note that the proposed variables must satisfy the following conditions:

    Importantly,the mixed Nash equilibrium corresponds to the minimum of the fi tness function and the optimal or the sub-optimal solution will be the closest to zero.The detailed procedure of PP-PSO for the mixed Nash equilibrium computing is demonstrated in Fig.1.

    Fig.1 Procedure of Nash equilibrium computing based on the PPPSO.

    To validate the effectiveness of the proposed method,here we illustrated the Nash equilibrium computing both for zerosum game and non-zero-sum game using two simple examples. For a fair comparison among these two method,they use the same maximum iteration number Nmax=100,the same population size m=30,and the same up and lower bounds for inertia weightsωmax=0.9,ωmin=0.2.Besides,in our proposed PP-PSO,the numbers of predators and preys are set md=10,mr=20,respectively.

    Example 1.Consider two-person,zero-sum game and nonzero-sum game illustrated by Tables I and II[30].

    ?

    TABLE II PAY-OFF MATRIX OF A AND B IN A TWO PLAYER, NON-ZERO-SUM GAME

    As we can see from the above two tables,the first column and the fi rst row represents the strategies of player A and B, respectively.For example,in the zero-sum game,each player has three strategies,which are specified by the number of rows and the number of columns.The payoffs are provided in the interior.The first number is the payoff received by the column player;the second is the payoff for the row player. To reduce statistical errors,each algorithm is tested 100 times independently for these two games.Evolution curves for the two-player,zero sum game are depicted in Figs.2~4.Besides, the simulation results are illustrated from the perspective of average fitness value,best fitness value ever found(Tables III and IV),the minimum error and times thatthe results satisfied that error≤0.01,where error is defined as the following expressions:

    Fig.2. Comparison results of average fitness values for the two player,zero-sum game.

    Fig.3. Comparison results ofaverage errors forthe two player,zerosum game.

    Fig.4. Comparison results of global best solutions for the two player,zero-sum game.

    where eh(k)and eb(k)denote the error of the basic PSO and our proposed PP-PSO,E S represents the mixed Nash equilibrium solution of the game that the players participate in.Note£ that for the zero-su?m game shown in Table I,

    TABLE III COMPARISON RESULTS FOR THE TWO PLAYER,ZERO-SUM GAME

    TABLE IV COMPARISON RESULTS FOR THE TWO PLAYER, NON-ZERO-SUM GAME

    It is reasonable to conclude from the simple example demonstrated above that the proposed PP-PSO outperforms the basic PSO in terms of solution accuracy,convergence speed,and reliability for Nash equilibrium computing.So itis appropriate to use this method to solve the problem of multiple UCAV air combat modeled by dynamic game theory in the following section.

    IV.GAME THEORETIC APPROACH TO UCAV AIR COMBAT BASED ON PP-PSO

    A.Experimental Settings

    To validate the effectiveness of the dynamic game theoretic formulation for UCAV air combat,a computational example is performed based on Matlab 2009b using our proposed PPPSO.Consider an adversary scenario involving two opposing forces here.The attacking force is labeled as Red team,while the defending force is labeled as B lue team.The missionof the B lue force is transporting military supplements from its base to the battlefront while the task of the Red force is attacking and destroying the aerotransports of the B lue force at least 80%and then returning to their air base.

    As shown in Fig.5,the B lue force consists of one transportation unit,which is represented by the solid square,and two combatunits.They are on the way back to the base after accomplishing a military mission.The Red force consists of three combatunits and aims to destroy the B lue transportation unit.The Red force is also programmed to return the base after the mission.For simplification of the problem,each unit ofboth sides is assumed to consistofthe same type of UCAVs, and each UCAV is equipped with a certain number of air-toair missiles.Assume that the speed of Red force is nearly 0.25 km/s while the speed of B lue force is nearly 0.2 km/s, and the state variables will be updated every 2 minutes.So the positions of the Red force and the B lue force willchange 30 km and 24 km,respectively at each step.The configuration parameters used in the simulation for the Red force and the B lue force are listed in Table V and Table VI,respectively.

    Fig.5.Scenario of cooperative UCAV task assignment.

    TABLE V INITIAL CONFIGURATION OF Red FORCE

    TABLE VI INITIAL CONFIGURATION OF B lue FORCE

    In the simulation,the objective functions of the two forces are chosen as

    B.Experimental Results and Analysis

    Fig.6 presents the flying trajectories for both sides in the air military operations,which result from the proposed game theoretic formulation of task assignmentin a dynamic combat environment and the PP-PSO based solution methodology. The Red force starts from near its base and launches attacks to eliminate the B lue transportation force,which is on the way returning to its base after a military mission.The task assignmentscheme for both sides are calculated based on the proposed approach described above.

    Fig.6.Resulting trajectories of both sides from the proposed approach.

    The detailed evolution and convergence behavior with time of platform numbers in combating units are shown in Fig.7. The combating units of both sides start to fight at the 9th time step.After 3 time steps of engagement,this air military operation ends up at the 11th time step,with Red defeating the B lue force and the surviving forces ofboth sides returning to their own bases.At the end of the combat,the Red force manages to inflict more than 90%of the platforms in B lue's transportation unit,78%of platforms in B2,and 70%of platforms in B3.Meanwhile,the Red team pays a price for the victory.The first unit R1 and the third one R3 suffer a slight damage and 30%platforms are destroyed in the attack. However,the second unit R2 of the Red force suffer a serious damage,with more than 60%of the platforms being destroyed in the engagement with the B lue force.The result can be explained from Fig.8,where snapshots of the dynamic task assignmentresults atSteps 9,10,and 11 are given.Itillustrates that the engagement of both sides has a different pattern at each time step and proves the task assignment process to be a dynamic process with time.Atthe 9th and 10th time steps,the second unit R2 of the Red force takes actions in accordance with the resulting mixed Nash equilibrium and chooses thefirst and second units of B lue force as targets,respectively. However,the B lue force insists on attacking R2 by the first unit B1,which is the most powerful unit of its 10 combat platforms.Consequently,R2 suffers the most serious damage in the three units of Red.

    Fig.7.Number of platforms.

    It is important to note that both the attacking side and the defense side take advantage of the proposed approach to acquire the assignment scheme over the engagement duration. Therefore,the engagement outcome mainly depends on the initial configuration of each force.The Red force has an advantage in performances and numbers of weapons,whichimplies the possible result of B lue's defeat.The experimental results are coincident with the theoretical analysis and verify the effectiveness and feasibility of the proposed approach.

    Fig.8.Snapshots of dynamic task assignment results.

    V.CONCLUSIONS

    This paper developed a game theoretic method for UCAV combat,which is based on the PP-PSO model.By considering both the adversary side and the attacking side as rational game participants,we represented the task allocation scheme as an optional policy set of both sides,and the cooperative task allocation results of both sides were achieved by solving the mixed Nash equilibrium using PP-PSO.An example of military operation involving an attacking side Red and a defense side B lue was presented to verify the effectiveness and adaptive ability ofthe proposed method.Simulation results show that the combination of game theoretic representation of the task assignment and the application of PP-PSO for the mixed Nash solutions can effectively solve the UCAV dynamic task assignment problem involving an adversary opponent.

    REFERENCES

    [1]Richards A,Bellingham J,Tillerson M,How J.Coordination and control of multiple UAVs.In:Proceedings of the 2002 AIAA Guidance,Navigation,and Control Conference.Monterey,CA:AIAA,2002.145?146

    [2]Alighanbari M,Kuwata Y,How JP.Coordination and controlofmultiple UAVs with timing constraints and loitering.In:Proceedings of the 2003 American Control Conference.Denver,Colorado:IEEE,2003. 5311?5316

    [3]Li C S,Wang Y Z.Protocol design for output consensus of portcontrolled Hamiltonian multi-agent systems.Acta Automatica Sinica, 2014,40(3):415?422

    [4]Duan H,Li P.Bio-inspired Computation in Unmanned Aerial Vehicles. Berlin:Springer-Verlag,2014.143?181

    [5]Duan H,Shao S,Su B,Zhang L.New developmentthoughts on the bioinspired intelligence based control for unmanned combat aerial vehicle. Science China Technological Sciences,2010,53(8):2025?2031

    [6]Chi P,Chen Z J,Zhou R.Autonomous decision-making of UAV based on extended situation assessment.In:Proceedings of the 2006 AIAA Guidance,Navigation,and Control Conference and Exhibit.Colorado, USA:AIAA,2006.

    [7]Ruz J J,Arelo O,Pajares G,de la Cruz J M.Decision making among alternative routes for uavs in dynamic environments.In:Proceedings of the 2007 IEEE Conference on Emerging Technologies and Factory Automation.Patras:IEEE,2007.997?1004

    [8]Jung S,Ariyur K B.Enabling operationalautonomy forunmanned aerial vehicles with scalability.Journal of Aerospace Information Systems, 2013,10(11):516?529

    [9]Berger J,Boukhtouta A,Benmoussa A,Kettani O.A new mixed-integer linear programming model for rescue path planning in uncertain adversarial environment.Computers&Operations Research,2012,39(12): 3420?3430

    [10]Duan H B,Liu S.Unmanned air/ground vehicles heterogeneous cooperative techniques:current status and prospects.ScienceChina Technological Sciences,2010,53(5):1349?1355

    [11]Cruz Jr J B,Simaan M A,Gacic A,Jiang H,Letelliier B,Li M,Liu Y.Game-theoretic modeling and control of a military air operation. IEEE Transactions on Aerospace and Electronic Systems,2001,37(4): 1393?1405

    [12]Dixon W.Optimaladaptive controland differential games by reinforcement learning principles.Journal of Guidance,Control,and Dynamics, 2014,37(3):1048?1049

    [13]Semsar-Kazerooni E,Khorasani K.Multi-agent team cooperation:a game theory approach.Automatica,2009,45(10):2205?2213

    [14]Gu D.A game theory approach to target tracking in sensor networks. IEEE Transactions onSystems,Man,and Cybernetics,Part B:Cybernetics,2011,41(1):2?13

    [15]Duan H,Wei X,Dong Z.Multiple UCAVs cooperative air combat simulation platform based on PSO,ACO,and game theory.IEEE Aerospace and Electronic Systems Magazine,2013,28(11):12?19

    [16]Turetsky V,Shinar J.Missile guidance laws based on pursuit-evasion game formulations.Automatica,2003,39(4):607?618

    [17]Porter R,Nudelman E,Shoham Y.Simple search methods for finding a Nash equilibrium.Games and Economic Behavior,2008,63(2): 642?662

    [18]Chen X,Deng X,Teng S-H.Settling the complexity of computing twoplayer Nash equilibria.Journal of the ACM,2009,56(3):Article No. 14

    [19]Kennedy J,Eberhart R.Particle swarm optimization.In:Proceedings of the 1st IEEE International Conference on Neural Networks.Perth, Australia:IEEE,1995.1942?1948

    [20]Eberhart R,Kennedy J.A new optimizer using particle swarm theory. In:Proceedings of the 6th International Symposium on Micro Machine and Human Science.Nagoya:IEEE,1995.39?43

    [21]Higashitani M,Ishigame A,Yasuda K.Particle swarm optimization considering the concept of predator-prey behavior.In:Proceedings of the 2006 IEEE Congress on Evolutionary Computation.Vancouver,BC, Canada:IEEE,2006.434?437

    [22]Liu F,Duan H B,Deng Y M.A chaotic quantum-behaved particle swarm optimization based on lateral inhibition for image matching. Optik-InternationalJournalforLightandElectronOptics,2012,123(21): 1955?1960

    [23]Edison E,Shima T.Genetic algorithm for cooperative UAV task assignment and path optimization.In:Proceedings of the 2008 AIAA Guidance,Navigation and Control Conference and Exhibit.Honolulu, Hawaii:AIAA,2008.340?356

    [24]Duan H,Luo Q,Shi Y,Ma G.Hybrid particle swarm optimization and genetic algorithm for multi-UAV formation reconfiguration.IEEE Computational IntelligenceMagazine,2013,8(3):16?27

    [25]Liu G,Lao S Y,Tan D F,Zhou Z C.Research status and progress on anti-ship missile path planning.Acta Automatica Sinica,2013,39(4): 347?359

    [26]Duan H B,Yu Y X,Zhao Z Y.Parameters identification of UCAV flightcontrolsystem based on predator-prey particle swarm optimization. Science China Information Sciences,2013,56(1):1?12

    [27]Duan H,Li S,Shi Y.Predator-prey based brain storm optimization for DC brushless motor.IEEE Transactions on Magnetics,2013,49(10): 5336?5340

    [28]Pan F,Li X T,Zhou Q,Li W X,Gao Q.Analysis of standard particle swarm optimization algorithm based on Markov chain.ActaAutomatica Sinica,2013,39(4):381?389

    [29]Nash J F.Equilibrium points in n-person games.Proceedings of the National Academy of Sciences of the United States of America,1950, 36(1):48?49

    [30]Yu Qian,Wang Xian-Jia.Evolutionary algorithm for solving Nash equilibrium based on particle swarm optimization.Journal of Wuhan University(Natural Science Edition),2006,52(1):25?29(in Chinese)

    Haibin Duan Professor atthe Schoolof Automation Science and Electrical Engineering,Beihang University,China.He received his Ph.D.degree from Nanjing University of Aeronautics and Astronautics in 2005.His is the Head of Bio-inspired Autonomous Flight Systems(BAFS)Research Group. His research interests include multiple UAVs cooperative control,biological computer vision and bioinspired computation.Corresponding author of this paper.

    Pei Li Ph.D.candidate atthe Schoolof Automation Science and Electrical Engineering,Beihang University,China.He received his bachelor degree from Harbin Engineering University in 2012.He is a member of BUAA Bio-inspired Autonomous Flight Systems(BAFS)Research Group.His research interests include multiple UAV cooperative controland game theory.

    Yaxiang Yu Master student at the School of Automation Science and ElectricalEngineering,Beihang University,China.She received her bachelor degree from Beihang University in 2007.She was once a technician at the Changhe Aircraft Industries Group Co.,Ltd.from 2007 to 2008.She is a member of BUAA Bio-inspired Autonomous Flight Systems (BAFS)Research Group.Her research interests include multiple UAV cooperative control and bioinspired computation.

    I.INTRODUCTION

    ame theory has received increasingly intensive attention as a promising technique for formulating action strategies for agents in such a complex situation,which involves competition againstan adversary.The priority of game theory in solving control and decision-making problems with an adversary opponenthas been shown in many studies[12?15]. A game theory approach was proposed for target tracking problems in sensor networks in[14],where the target is assumed to be an intelligent agent who is able to maximize filtering errors by escaping behavior.The pursuit-evasion game formulations were employed in[16]for the development of improved interceptor guidance laws.Cooperative game theory was used to ensure team cooperation by Semsar-Kazerooni et al.[13],where a team of agents aimed to accomplish consensus over a common value for their output.

    Manuscript received July 24,2013;accepted July 18,2014.This work was supported by National Natural Science Foundation of China(61425008, 61333004,61273054),Top-Notch Young Talents Program of China,and Aeronautical Foundation of China(2013585104).Recommended by Associate Editor Changyin Sun

    :Haibin Duan,Pei Li,Yaxiang Yu.A predator-prey particle swarm optimization approach to multiple UCAV air combat modeled by dynamic game theory.IEEE/CAA Journal of AutomaticaSinica,2015,2(1):11?18

    Haibin Duan,Pei Li,and Yaxiang Yu are with the Science and Technology on Aircraft Control Laboratory,School of Automation Science and Electrical Engineering,Beihang University(BUAA),Beijing 100191,China(e-mail:hbduan@buaa.edu.cn;peilibuaa@asee.buaa.edu.cn; yaxiangyu03@asee.buaa.edu.cn).

    considerable attention as a promising technique for formulating controlactions for agents in an extended complex enterprise that involves an adversary.At each decision making step,each side seeks the best scheme with the purpose of maximizing its own objective function.In this paper,a game theoretic approach based on predatorprey particle swarm optimization(PP-PSO)is presented,and the dynamic task assignmentproblem for multiple unmanned combat aerial vehicles(UCAVs)in military operation is decomposed and modeled as a two-player game ateach decision stage.The optimal assignment scheme of each stage is regarded as a mixed Nash equilibrium,which can be solved by using the PP-PSO.The effectiveness of our proposed methodology is verified by a typical example of an air military operation that involves two opposing forces:the attacking force RReeeddd and the defense force BB lluueee.

    Index Terms—Unmanned combat aerialvehicle(UCAV),game theory,air combat,predator-prey,particle swarm optimization (PSO),Nash equilibrium.

    C OMPARED to unmanned combat aerial vehicles (UCAVs)that perform solo missions,greater efficiency and operational capability can be realized from teams of UCAVs operating in a coordinated fashion[1?5].Designing UCAVs with intelligent and coordinated action capabilities to achieve an overallobjective is a major partof multiple UCAVs control in a complicated and uncertain environment[6?10]. Actually,a military air operation involving multiple UCAVs is a complex dynamic system with many interacting decisionmaking units which have even conflicting objectives.Modeling and controlof such a system is an extremely challenging task, whose purpose is to seek a feasible and optimal scheme to assign the limited combat resource to specifi c units of the adversary while taking into account the adversary's possible defense strategies[8,11].The difficulty lies notonly in thatitis often very difficult to mathematically describe the underlying processes and objectives of the decision makerbutalso in that the fitness of one decision maker depends on both its own control input and the opponent's strategies as well.

    亚洲黑人精品在线| 校园人妻丝袜中文字幕| 国产91精品成人一区二区三区| 日韩强制内射视频| 一个人观看的视频www高清免费观看| 听说在线观看完整版免费高清| 国产av不卡久久| 有码 亚洲区| 波多野结衣高清作品| 久久久久久国产a免费观看| 少妇猛男粗大的猛烈进出视频 | av黄色大香蕉| 国产精品电影一区二区三区| 伊人久久精品亚洲午夜| 九色国产91popny在线| 成人永久免费在线观看视频| av福利片在线观看| 色哟哟哟哟哟哟| 欧美日韩瑟瑟在线播放| 91狼人影院| 国产伦一二天堂av在线观看| 欧美一级a爱片免费观看看| 乱码一卡2卡4卡精品| 看免费成人av毛片| 美女免费视频网站| 欧美在线一区亚洲| 直男gayav资源| 国产精品乱码一区二三区的特点| 日韩欧美精品v在线| 国产精品自产拍在线观看55亚洲| 欧美色欧美亚洲另类二区| 波多野结衣巨乳人妻| ponron亚洲| 国产欧美日韩精品亚洲av| 国产精华一区二区三区| 免费观看精品视频网站| 欧美一区二区精品小视频在线| 亚洲自偷自拍三级| 乱系列少妇在线播放| 精品久久久噜噜| 国产熟女欧美一区二区| 国产91精品成人一区二区三区| 午夜老司机福利剧场| 国产精品久久电影中文字幕| 日本成人三级电影网站| 国产精品人妻久久久影院| 97热精品久久久久久| 免费黄网站久久成人精品| 欧美日韩瑟瑟在线播放| www.色视频.com| 夜夜爽天天搞| av在线老鸭窝| ponron亚洲| 国产一区二区亚洲精品在线观看| 日本撒尿小便嘘嘘汇集6| 成人精品一区二区免费| 国产一区二区三区av在线 | 国产av不卡久久| 亚洲国产色片| 亚洲av中文字字幕乱码综合| 又粗又爽又猛毛片免费看| 有码 亚洲区| 久99久视频精品免费| 黄色欧美视频在线观看| 中文字幕av成人在线电影| 国产一区二区在线av高清观看| av女优亚洲男人天堂| 午夜精品一区二区三区免费看| 亚洲第一区二区三区不卡| 五月玫瑰六月丁香| 三级毛片av免费| 国产在线男女| 美女大奶头视频| 校园人妻丝袜中文字幕| 精品久久久久久久久久久久久| 婷婷精品国产亚洲av| 搡女人真爽免费视频火全软件 | 精品一区二区三区视频在线| 波多野结衣巨乳人妻| 亚洲av中文av极速乱 | 国产黄片美女视频| 久久精品国产亚洲av香蕉五月| 一个人观看的视频www高清免费观看| 亚洲精品乱码久久久v下载方式| 色综合色国产| 美女高潮喷水抽搐中文字幕| 在线免费观看不下载黄p国产 | 毛片一级片免费看久久久久 | 亚洲美女黄片视频| 一个人免费在线观看电影| 久久精品国产99精品国产亚洲性色| 欧美激情国产日韩精品一区| 一区福利在线观看| 国产精品久久久久久av不卡| 精品久久久久久久久久免费视频| 色哟哟哟哟哟哟| 久久久久久国产a免费观看| 久久久久性生活片| 99久久九九国产精品国产免费| 丰满的人妻完整版| 成人av在线播放网站| 中文字幕高清在线视频| 亚洲成人中文字幕在线播放| 毛片女人毛片| 国产精品人妻久久久久久| 亚洲乱码一区二区免费版| 欧美日韩乱码在线| 午夜久久久久精精品| 欧美三级亚洲精品| 亚洲狠狠婷婷综合久久图片| 日韩欧美在线二视频| 变态另类成人亚洲欧美熟女| 色综合站精品国产| 精品99又大又爽又粗少妇毛片 | 国产人妻一区二区三区在| 小蜜桃在线观看免费完整版高清| 日韩中字成人| 男人的好看免费观看在线视频| 国产在线精品亚洲第一网站| 亚洲av中文av极速乱 | 久久精品91蜜桃| 国产亚洲91精品色在线| 91精品国产九色| 婷婷精品国产亚洲av| 久久久久久久久久黄片| 精品人妻一区二区三区麻豆 | 男女啪啪激烈高潮av片| 超碰av人人做人人爽久久| 如何舔出高潮| 国产精品98久久久久久宅男小说| 精品久久久久久久久av| 99热这里只有是精品在线观看| 老司机深夜福利视频在线观看| 日韩精品有码人妻一区| 国产欧美日韩一区二区精品| 欧美一级a爱片免费观看看| 又粗又爽又猛毛片免费看| 欧美日韩乱码在线| 亚洲在线观看片| 久久精品人妻少妇| 啪啪无遮挡十八禁网站| 日韩一区二区视频免费看| 亚洲真实伦在线观看| 精品免费久久久久久久清纯| 午夜精品一区二区三区免费看| 日韩欧美国产一区二区入口| 日本 欧美在线| 人妻丰满熟妇av一区二区三区| 嫩草影视91久久| 日韩欧美免费精品| 久久精品国产亚洲av天美| 精品一区二区三区人妻视频| 搡老妇女老女人老熟妇| 淫妇啪啪啪对白视频| 精品人妻偷拍中文字幕| 欧美在线一区亚洲| 人人妻人人看人人澡| 男人舔女人下体高潮全视频| 午夜爱爱视频在线播放| 少妇高潮的动态图| 天堂√8在线中文| 国产亚洲欧美98| 国产乱人伦免费视频| 久久人人爽人人爽人人片va| 成人二区视频| 国内精品美女久久久久久| a级毛片a级免费在线| 亚洲一区高清亚洲精品| 亚洲经典国产精华液单| 综合色av麻豆| 亚洲天堂国产精品一区在线| 免费看a级黄色片| 午夜福利在线观看吧| 国产探花在线观看一区二区| 国内揄拍国产精品人妻在线| 午夜激情福利司机影院| 欧美日韩综合久久久久久 | 观看免费一级毛片| 少妇人妻一区二区三区视频| 男人和女人高潮做爰伦理| 日韩在线高清观看一区二区三区 | 成年免费大片在线观看| 精品一区二区三区视频在线观看免费| 露出奶头的视频| 91麻豆av在线| 亚洲国产精品合色在线| 他把我摸到了高潮在线观看| 国产精品嫩草影院av在线观看 | 午夜影院日韩av| 亚洲va在线va天堂va国产| 精品久久久久久久人妻蜜臀av| 婷婷色综合大香蕉| 亚洲人成伊人成综合网2020| av天堂中文字幕网| 欧美日韩中文字幕国产精品一区二区三区| 精品日产1卡2卡| 麻豆久久精品国产亚洲av| av在线天堂中文字幕| 中文在线观看免费www的网站| 大型黄色视频在线免费观看| 亚洲欧美日韩卡通动漫| 天堂网av新在线| 久久人人精品亚洲av| 国模一区二区三区四区视频| 国产成人一区二区在线| 国产一区二区在线av高清观看| 色av中文字幕| 2021天堂中文幕一二区在线观| a在线观看视频网站| 在线播放无遮挡| 精品国产三级普通话版| 97超级碰碰碰精品色视频在线观看| 亚洲经典国产精华液单| 观看美女的网站| av在线老鸭窝| 精品人妻视频免费看| 美女cb高潮喷水在线观看| 国产伦在线观看视频一区| 一进一出好大好爽视频| 免费看日本二区| 欧美三级亚洲精品| 亚洲av熟女| 免费在线观看日本一区| 99热网站在线观看| 成年女人毛片免费观看观看9| 免费观看在线日韩| 国产伦人伦偷精品视频| 日韩大尺度精品在线看网址| 国产精品久久久久久精品电影| 热99re8久久精品国产| 黄色日韩在线| 一夜夜www| 可以在线观看毛片的网站| 日本 av在线| 可以在线观看的亚洲视频| 国产精品一区二区三区四区免费观看 | 欧美日韩精品成人综合77777| 亚洲四区av| 国内精品一区二区在线观看| 日韩强制内射视频| 可以在线观看毛片的网站| 草草在线视频免费看| 亚洲成人久久爱视频| 网址你懂的国产日韩在线| 成年女人永久免费观看视频| 国产色爽女视频免费观看| 亚洲成人中文字幕在线播放| 亚洲成a人片在线一区二区| 亚洲中文字幕日韩| 国产高清有码在线观看视频| 日日夜夜操网爽| 成人国产麻豆网| bbb黄色大片| .国产精品久久| 久久久精品欧美日韩精品| 国产精品一区二区免费欧美| 亚洲美女视频黄频| 成熟少妇高潮喷水视频| 精品久久久久久,| 在线免费十八禁| 精品福利观看| 一夜夜www| 看片在线看免费视频| 精品一区二区免费观看| 啦啦啦啦在线视频资源| 婷婷精品国产亚洲av在线| 久久国内精品自在自线图片| 女同久久另类99精品国产91| 啪啪无遮挡十八禁网站| 又黄又爽又免费观看的视频| 亚洲av一区综合| 午夜精品一区二区三区免费看| 日韩精品有码人妻一区| 国产v大片淫在线免费观看| 成人毛片a级毛片在线播放| 国模一区二区三区四区视频| 网址你懂的国产日韩在线| 美女xxoo啪啪120秒动态图| 久久久精品大字幕| 久久中文看片网| 十八禁国产超污无遮挡网站| 草草在线视频免费看| 女人被狂操c到高潮| 国产免费一级a男人的天堂| 久久亚洲真实| 婷婷亚洲欧美| 欧美激情在线99| 欧美高清成人免费视频www| 久久久久久久久久黄片| 国产综合懂色| 我的女老师完整版在线观看| 日本三级黄在线观看| 欧美日本亚洲视频在线播放| 在现免费观看毛片| 国产亚洲精品久久久久久毛片| 亚洲av第一区精品v没综合| 国产激情偷乱视频一区二区| 免费高清视频大片| 久久精品国产鲁丝片午夜精品 | 观看免费一级毛片| 免费电影在线观看免费观看| 亚洲第一电影网av| 草草在线视频免费看| 国产v大片淫在线免费观看| 国产精品久久久久久亚洲av鲁大| 禁无遮挡网站| 全区人妻精品视频| 一本久久中文字幕| 夜夜看夜夜爽夜夜摸| 最近最新免费中文字幕在线| 少妇高潮的动态图| 色播亚洲综合网| 亚洲欧美日韩东京热| 亚洲最大成人av| 九色国产91popny在线| 国产精品av视频在线免费观看| 成年女人毛片免费观看观看9| 99国产极品粉嫩在线观看| 国产真实乱freesex| 国产亚洲精品久久久久久毛片| 一个人观看的视频www高清免费观看| 国产精品99久久久久久久久| 偷拍熟女少妇极品色| 中文字幕av在线有码专区| 亚洲内射少妇av| 亚洲在线观看片| 国产精品一及| 国产色爽女视频免费观看| 国产免费av片在线观看野外av| 91麻豆av在线| 男人舔女人下体高潮全视频| 亚洲不卡免费看| 18禁黄网站禁片免费观看直播| 亚洲欧美激情综合另类| 亚洲精品在线观看二区| 欧美色欧美亚洲另类二区| 中文字幕av成人在线电影| 麻豆成人午夜福利视频| 久久久久久九九精品二区国产| 1024手机看黄色片| av在线蜜桃| 一本久久中文字幕| 日本黄大片高清| 99久久精品国产国产毛片| 熟女电影av网| 春色校园在线视频观看| 国产精品久久久久久久电影| www.www免费av| 亚洲经典国产精华液单| 一边摸一边抽搐一进一小说| 日韩中文字幕欧美一区二区| 一本一本综合久久| 日本免费一区二区三区高清不卡| 久99久视频精品免费| 身体一侧抽搐| 久9热在线精品视频| 成年女人看的毛片在线观看| 午夜精品在线福利| 国产高清视频在线播放一区| 乱系列少妇在线播放| 一区二区三区高清视频在线| 成人av在线播放网站| 国产高潮美女av| 久久久色成人| 日韩人妻高清精品专区| 99热6这里只有精品| 亚洲av中文av极速乱 | 婷婷六月久久综合丁香| 国产av一区在线观看免费| 99久久精品热视频| 老女人水多毛片| 久久久久久久久大av| 亚洲图色成人| 我的女老师完整版在线观看| 国产色婷婷99| 国产一区二区激情短视频| 亚洲av中文字字幕乱码综合| 乱人视频在线观看| 欧美+日韩+精品| 国产黄色小视频在线观看| 欧美日韩国产亚洲二区| 精品免费久久久久久久清纯| 国产黄片美女视频| 禁无遮挡网站| 精品人妻偷拍中文字幕| 麻豆精品久久久久久蜜桃| 欧美又色又爽又黄视频| 又爽又黄无遮挡网站| 深夜a级毛片| 特大巨黑吊av在线直播| 久久亚洲精品不卡| 级片在线观看| 哪里可以看免费的av片| 91在线观看av| 午夜亚洲福利在线播放| 国语自产精品视频在线第100页| 欧美成人a在线观看| 一级黄色大片毛片| 午夜福利视频1000在线观看| 我的老师免费观看完整版| 国产淫片久久久久久久久| 成人av一区二区三区在线看| 日本撒尿小便嘘嘘汇集6| 无遮挡黄片免费观看| 久久草成人影院| avwww免费| 亚洲国产精品久久男人天堂| 深夜精品福利| 亚洲中文日韩欧美视频| 国产黄色小视频在线观看| 国内精品一区二区在线观看| 在线观看午夜福利视频| 永久网站在线| 乱系列少妇在线播放| 神马国产精品三级电影在线观看| 最新在线观看一区二区三区| 精品国产三级普通话版| 国产在线精品亚洲第一网站| 丰满乱子伦码专区| 国产伦一二天堂av在线观看| 久久亚洲真实| 国内精品美女久久久久久| 国产成人aa在线观看| 男女啪啪激烈高潮av片| 久久久国产成人精品二区| 欧美日韩精品成人综合77777| 亚洲国产精品久久男人天堂| 天堂动漫精品| 中文字幕av在线有码专区| 日韩欧美免费精品| 亚洲专区国产一区二区| 亚洲四区av| 又粗又爽又猛毛片免费看| 成人鲁丝片一二三区免费| 国产一区二区在线观看日韩| 最近最新中文字幕大全电影3| 国产精品一区二区三区四区久久| 午夜日韩欧美国产| 丝袜美腿在线中文| 在线天堂最新版资源| 亚洲国产色片| 亚洲成人精品中文字幕电影| 久久精品国产亚洲av天美| 88av欧美| 国产精品不卡视频一区二区| 一区二区三区四区激情视频 | 日韩国内少妇激情av| 国产精品久久久久久av不卡| 三级国产精品欧美在线观看| 97超级碰碰碰精品色视频在线观看| www日本黄色视频网| av黄色大香蕉| 琪琪午夜伦伦电影理论片6080| 91狼人影院| 99久久无色码亚洲精品果冻| 精品一区二区三区人妻视频| 麻豆av噜噜一区二区三区| avwww免费| 亚洲人成网站高清观看| 成人特级av手机在线观看| 一个人看视频在线观看www免费| 99久久精品一区二区三区| 亚洲最大成人av| 国产精品国产高清国产av| 俺也久久电影网| 91久久精品电影网| 蜜桃亚洲精品一区二区三区| 国产精品免费一区二区三区在线| 午夜免费男女啪啪视频观看 | 亚洲欧美精品综合久久99| 草草在线视频免费看| 黄色欧美视频在线观看| 免费大片18禁| 日本成人三级电影网站| 国产一级毛片七仙女欲春2| 能在线免费观看的黄片| 精华霜和精华液先用哪个| 乱码一卡2卡4卡精品| 久久精品综合一区二区三区| 国产午夜精品论理片| 最近最新免费中文字幕在线| 欧美一区二区精品小视频在线| 干丝袜人妻中文字幕| 99久久精品热视频| 天堂av国产一区二区熟女人妻| 免费看美女性在线毛片视频| 国产黄片美女视频| 可以在线观看的亚洲视频| 一级a爱片免费观看的视频| 精品久久久久久久久久久久久| 国产精品三级大全| 日韩精品中文字幕看吧| 麻豆国产av国片精品| 精品人妻偷拍中文字幕| 午夜福利成人在线免费观看| 十八禁网站免费在线| 亚洲精华国产精华液的使用体验 | 黄色视频,在线免费观看| 亚洲经典国产精华液单| 国产精品美女特级片免费视频播放器| 久久精品国产自在天天线| 国产精品一区二区免费欧美| 欧美一区二区亚洲| 成人特级黄色片久久久久久久| 18禁黄网站禁片午夜丰满| 日韩中字成人| 国产大屁股一区二区在线视频| 久久久久久大精品| 伦理电影大哥的女人| 日本欧美国产在线视频| 亚洲国产精品sss在线观看| 最近最新中文字幕大全电影3| 亚洲最大成人av| 国语自产精品视频在线第100页| 99精品久久久久人妻精品| www日本黄色视频网| 天堂网av新在线| 午夜亚洲福利在线播放| 国产一级毛片七仙女欲春2| 欧美丝袜亚洲另类 | 欧美最黄视频在线播放免费| 免费观看人在逋| 欧美三级亚洲精品| 久久久国产成人精品二区| 日韩欧美三级三区| 国产免费男女视频| 日韩亚洲欧美综合| 美女大奶头视频| 久久久精品大字幕| а√天堂www在线а√下载| 一区二区三区激情视频| 两人在一起打扑克的视频| 91麻豆精品激情在线观看国产| 91在线观看av| 亚洲欧美清纯卡通| 2021天堂中文幕一二区在线观| 国产aⅴ精品一区二区三区波| 极品教师在线免费播放| 亚洲中文字幕日韩| 又爽又黄无遮挡网站| 天堂动漫精品| 欧美激情久久久久久爽电影| 久久久国产成人免费| 午夜福利欧美成人| 99久久精品一区二区三区| 毛片一级片免费看久久久久 | 亚洲四区av| 国产 一区精品| 啦啦啦观看免费观看视频高清| 一区二区三区四区激情视频 | 亚洲中文字幕日韩| 又爽又黄无遮挡网站| 亚洲国产欧洲综合997久久,| 欧美日韩瑟瑟在线播放| 可以在线观看的亚洲视频| 草草在线视频免费看| 色综合婷婷激情| 最近最新免费中文字幕在线| av天堂在线播放| 国产高清三级在线| 狠狠狠狠99中文字幕| 国内精品美女久久久久久| 亚洲av不卡在线观看| 男女边吃奶边做爰视频| 在线观看66精品国产| 国产视频内射| 99热网站在线观看| 啦啦啦观看免费观看视频高清| 成年女人永久免费观看视频| av在线亚洲专区| 麻豆久久精品国产亚洲av| 国产亚洲精品久久久com| 国产aⅴ精品一区二区三区波| 欧美性猛交黑人性爽| 国内精品一区二区在线观看| 亚洲欧美清纯卡通| 国产av在哪里看| 亚洲第一电影网av| 女生性感内裤真人,穿戴方法视频| 搡老熟女国产l中国老女人| 一区二区三区免费毛片| 日本黄大片高清| 麻豆av噜噜一区二区三区| 男女下面进入的视频免费午夜| 老女人水多毛片| 长腿黑丝高跟| 亚洲中文日韩欧美视频| 欧美性感艳星| 黄色一级大片看看| 在线观看午夜福利视频| 三级国产精品欧美在线观看| 国内精品久久久久久久电影| 亚洲国产精品sss在线观看| 色尼玛亚洲综合影院| 亚州av有码| 在线国产一区二区在线| 男女之事视频高清在线观看| 在线a可以看的网站| 在线免费十八禁| 亚洲成人精品中文字幕电影| 亚洲第一电影网av| 亚洲精品粉嫩美女一区| 一个人看视频在线观看www免费| 欧美成人a在线观看| 99久久久亚洲精品蜜臀av| 亚洲一区高清亚洲精品| 国产精品久久久久久精品电影| 免费在线观看日本一区| 久久久久久大精品| av福利片在线观看| 久久草成人影院| 淫秽高清视频在线观看| 不卡一级毛片| 久久久国产成人精品二区| 国产精品久久久久久精品电影|