scholarly journals Some questions of differential game theory with phase constraints

2020 ◽  
Vol 56 ◽  
pp. 138-184
Author(s):  
A.G. Chentsov
Keyword(s):  
Differential Game ◽  
Position Space ◽  
Natural Topology ◽  
Differential Game Theory ◽  
Phase Constraints ◽  
Target Set ◽  
Program Iteration ◽  
Guidance Problem ◽  
Relaxed Problem

Differential game (DG) of guidance-evasion is considered; moreover, its relaxations constructed with due account for priority considerations in the implementation of target set (TS) guidance and phase constraints (PC) validity are considered. We suppose that TS is closed in a natural topology of position space. With respect to the set that defines PC, it is postulated that the sections corresponding to time fixing are closed. For this setting, with the use of program iteration method (PIM), a variant of alternative for some natural (asymmetric) classes of strategies is established. A scheme of relaxation for the game guidance problem with nonclosed (in general case) set defining PC is considered. Under relaxation construction, reasons connected with priority in the implementation of guidance to TS and PC validity are taken into account (the case of asymmetric weakening of conditions of game ending is investigated). A position function is introduced, values of which (with priority correction) play the role of an analogue of least size for neighborhoods of TS and set defining PC under which it is possible to get a guaranteed solution of a relaxed problem of a player interested in approaching with TS while observing PC. It is demonstrated that the value of given function (when fixing the position of the game) is a price of DG for minimax-maximin quality functional which characterizes both the “degree” of approaching with TS and the “degree” of observance of initial PC.

Relaxation of the game problem of guidance connected with alternative in guidance-evasion differential game

2020 ◽  
pp. 196-244
Author(s):  
Aleksandr G. Chentsov
Keyword(s):  
Fixed Point ◽  
Differential Game ◽  
Game Problem ◽  
Time Interval ◽  
Finite Time Interval ◽  
Alternative Theorem ◽  
Phase Constraints ◽  
Target Set ◽  
Program Iteration ◽  
Solvability Set

Differential game (DG) of guidance-evasion for a finite time interval is considered;as parameters, the target set (TS) and the set defining phase constraints (PC) are used.Player I interested in realization of guidance with TS under validity PC uses set-valuedquasistrategies (nonanticipating strategies) and Player II having opposite target uses strategieswith nonanticipating choice of correction instants and finite numbers of such instants.On informative level, the setting corresponds to alternative theorem of N. N. Krasovskii andA. I. Subbotin. For position not belonging to solvability set of Player I, determination ofthe least size of neighborhoods for set-parameters under that Player I guarantees guidance(under weakened conditions) is interested. In article, this scheme is supplemented by priorityelements in questions of TS attainment and PC validity; this is realized by special parameterdefining relation for sizes of corresponding neighborhoods. Under these conditions, a functionof the least size of TS neighborhood is defined by procedure used program iteration methodfor two variants. The above-mentioned function is fixed point for one of two used “program”operators. Special type of the quality functional for which values of the above-mentionedfunction coincide with values of the minimax-maximin games is established.

scholarly journals Coordinating Pricing and Advertising Decisions for Supply Chain under Consignment Contract in the Dynamic Setting

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Zhihui Wu ◽  
Lichao Feng ◽  
Dongyan Chen
Keyword(s):  
Supply Chain ◽  
Differential Game ◽  
Optimal Strategies ◽  
Feasible Region ◽  
Comparison Analysis ◽  
On Demand ◽  
Dynamic Setting ◽  
State Dependent ◽  
Differential Game Theory ◽  
Advertising Effort

In this paper, via the differential game method, the problems of the pricing and advertising decision are investigated by considering the effect of number of the platform users on demand. In addition, a novel contract is developed to coordinate the supply chain. Firstly, the optimal strategies of the pricing and advertising are given in the decentralized and centralized scenarios by applying the differential game theory. Also, the comparison analysis concerning on the optimal strategies is proposed in two decision scenarios. It is shown that the centralized scenario could lead to the higher advertising effort of each member and a lower retail price. Next, we construct the state-dependent contract with hope to coordinate the supply chain and then improve the performance of the supply chain. Finally, a numerical example is provided to illustrate the impacts of the price-elasticity index of demand and the effectiveness of the number of retailer’s platform users onto the feasible region of the corresponding contract.

Hybrid Method Based on Artificial Potential Field and Differential Game Theory for the UAV Path Planing

2014 ◽  
Vol 687-691 ◽  
pp. 260-264
Author(s):  
Feng Tian ◽  
Ji Feng Zou ◽  
Tong Zhang
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Potential Field ◽  
Artificial Potential Field ◽  
Complex Environment ◽  
Pursuit Evasion ◽  
Differential Game Theory ◽  
Evasion Game ◽  
Simulation Results ◽  
Dynamic Path

In this paper, a method of the UAV path planing in the complex environment by using artificial potential field and differential game theory is introduced. This article studies the pursuit evasion game of the dynamic path planing for the UAV. The fly zone of either the pursuer or the evader is divided into two categories, namely the obstacle areas and the obstacle-free areas. So we can use the artificial potential field in the obstacle areas,and we use differential game theory in the obstacle-free areas for the UAV. This method can apply to pursuit-evasion game in the complex environment for the UAV path planing.Not only the UAV can avoid obstacles but also they can find the best capture path.Finally,the simulation results verify its correctness and validity .

scholarly journals Evasion-Pursuit Strategy against Defended Aircraft Based on Differential Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qilong Sun ◽  
Minghui Shen ◽  
Xiaolong Gu ◽  
Kang Hou ◽  
Naiming Qi
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Optimal Strategies ◽  
Open Loop ◽  
Active Defense ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
One To One ◽  
The One

The active defense scenario in which the attacker evades from the defender and pursues the target is investigated. In this scenario, the target evades from the attacker, and the defender intercepts the attacker by using the optimal strategies. The evasion and the pursuit boundaries are investigated for the attacker when the three players use the one-to-one optimal guidance laws, which are derived based on differential game theory. It is difficult for the attacker to accomplish the task by using the one-to-one optimal guidance law; thus, a new guidance law is derived. Unlike other papers, in this paper, the accelerations of the target and the defender are unknown to the attacker. The new strategy is derived by linearizing the model along the initial line of sight, and it is obtained based on the open-loop solution form as the closed-loop problem is hard to solve. The results of the guidance performance for the derived guidance law are presented by numerical simulations, and it shows that the attacker can evade the defender and intercept the target successfully by using the proposed strategy.

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