Necessary Conditions for Optimal Strategies in a Class of Noncooperative <i>N</i>-Person Differential Games

Sarma, I. G.; Ragade, Rammohan K.; Prasad, U. R.

doi:10.1137/0307046

Cited by 12 publications

(4 citation statements)

References 3 publications

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“…The orbital pursuit-evasion-defense model given in the second section can be formulated as a non-cooperative N-person differential game. Necessary conditions for optimal strategies in this game are provided by Sarma [28] and applied to the system composed of (7) and (8) to obtain the form of optimal strategies.…”

Section: Necessary Conditions For Optimal Strategiesmentioning

confidence: 99%

Pursuer’s Control Strategy for Orbital Pursuit-Evasion-Defense Game with Continuous Low Thrust Propulsion

et al. 2019

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This paper studies the orbital pursuit-evasion-defense problem with the continuous low thrust propulsion. A control strategy for the pursuer is proposed based on the fuzzy comprehensive evaluation and the differential game. First, the system is described by the Lawden's equations, and simplified by introducing the relative state variables and the zero effort miss (ZEM) variables. Then, the objective function of the pursuer is designed based on the fuzzy comprehensive evaluation, and the analytical necessary conditions for the optimal control strategy are presented. Finally, a hybrid method combining the multi-objective genetic algorithm and the multiple shooting method is proposed to obtain the solution of the orbital pursuit-evasion-defense problem. The simulation results show that the proposed control strategy can handle the orbital pursuit-evasion-defense problem effectively. Appl. Sci. 2019, 9, 3190 2 of 16 information game and presented the adaptive strategies for the pursuer and the evader. Ghosh et al. [17] developed a near-optimal feedback controller for the two-player pursuit-evasion games by using a new extremal-field approach. The above works were studied in the two-player pursuit-evasion game framework. However, in this framework, the evader can only perform maneuvers by itself to avoid threats. It is called self-defense, which disturbs the original mission of the evader and requires a large additional amount of fuel.To overcome this disadvantage, a defender is introduced in [18]. The role of the defender is intercepting the pursuer. In this way, the evader can perform its original mission without being disturbed. A hybrid method combined particle swarm optimization with a Newton-Interpolation algorithm was proposed to solve the orbital defense problem. However, because of the introduction of the defender, the pursuer must avoid the interception by the defender while capturing the evader [19], which makes the design of the pursuer's control strategy more complicated. In order to develop control strategies for pursuers, Liu et al. [19] proposed a distributed online mission plan algorithm for pursuers to access targets. However, these works on the orbital pursuit-evasion-defense game adopted the impulsive thrust, which suffers the drawback that the interception will fail when the target can perform evasive maneuvers [4].Compared with the impulse thrust, the continuous low thrust allows players to perform multiple, continuous maneuvers, which meets the requirements of the frequently orbital transfers in the game. When applying the continuous low thrust, the hypothesis about players' maneuverable is removed. It is closer to the actual situation of the orbital pursuit-evasion-defense game. Therefore, in this paper, the orbital pursuit-evasion-defense game model is constructed based on the continuous low thrust. Different from the model based on impulse thrust, the model based on continuous low thrust cannot adopt the Keplerian dynamics [20]. Its dynamic equations are based on the non-Keplerian motion. T...

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Section: Necessary Conditions For Optimal Strategiesmentioning

confidence: 99%

Pursuer’s Control Strategy for Orbital Pursuit-Evasion-Defense Game with Continuous Low Thrust Propulsion

et al. 2019

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“…In addition to the M-subsystems, we assume that we have a coordinator subsystem modeled by M • • x°(k+l) = A°(k)x°(k) + ig 1A 03'(k)x1 (k) + 0 (k) (4) and the measurement of the coordinator subsystem is given by M • • n z°(k) = H°(k)x°(k)+ £ H°1 (k)x1 (k) + 5 (k) (5) u is an m -dimensional control vector chosen by the coordinator DM , z is the j^°-dimensional measured output vector of the coordinator subsystem.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Associated with each subsystem is a decision-maker or controller and a performance criterion function or cost function. A framework for studying strategies for the control of such systems is non-zero N-person differential games [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Decentralized Stackelberg Strategies for Interconnected Stochastic Dynamic Systems *

Glankwamdee

1978

IFAC Proceedings Volumes

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A two-level sequential decision formulation for the control of interconnected stochastic linear discrete-time systems is investigated.A n interconnection of several systems is considered, whereby each subsystem has a decision maker and an associated quadratic cost function. One of the decision makers is designated as leader or coordinator and his control strategies are to be chosen prior to those of the others. The information available to each decision maker may be different from those of the others.The second level decision makers are regarded as followers in the context of Stackelberg strategies. Their strategies are in accordance with the Nash equilibrium concept except that the coordinator's strategy is known to all of them. The coordinator chooses his strategy under the assumption that the followers will fully exploit the prior announcement of his strategy.Recursive equations for determining the control laws for each subsystem are derived for various types of information structures. Centralized information is considered first. Finally feedback Stackelberg strategies are derived for the more realistic but more complicated (from a design computation viewpoint) situation where the subsystem control laws are based only on local subsystem measurements.

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“…For this case, there a single performance criterion which one player tries to minimize and the other tries to maximize. On the other hand, many authors (see [16,8,9,11,19,22,23,25,27,26,30]discussed N-person non-zero sum differential games. For this case, there may be more than two players and each player tries to minimize his individual performance criterion, and the sum of all player's criteria is not zero or is it constant.…”

Section: Introductionmentioning

confidence: 99%

Non-zero Sum Stochastic Differential Games of Fully Coupled Forward-Backward Stochastic Systems

Tang¹,

Meng²,

Sun³

2010

Preprint

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In this paper, an open-loop two-person non-zero sum stochastic differential game is considered for forward-backward stochastic systems. More precisely, the controlled systems are described by a fully coupled nonlinear multi-dimensional forward-backward stochastic differential equation driven by a multi-dimensional Brownian motion. one sufficient (a verification theorem) and one necessary conditions for the existence of open-loop Nash equilibrium points for the corresponding two-person non-zero sum stochastic differential game are proved. The control domain need to be convex and the admissible controls for both players are allowed to appear in both the drift and diffusion of the state equations.

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Necessary Conditions for Optimal Strategies in a Class of Noncooperative N-Person Differential Games

Cited by 12 publications

References 3 publications

Pursuer’s Control Strategy for Orbital Pursuit-Evasion-Defense Game with Continuous Low Thrust Propulsion

Pursuer’s Control Strategy for Orbital Pursuit-Evasion-Defense Game with Continuous Low Thrust Propulsion

Decentralized Stackelberg Strategies for Interconnected Stochastic Dynamic Systems *

Non-zero Sum Stochastic Differential Games of Fully Coupled Forward-Backward Stochastic Systems

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