A study of differential models for hierarchical control systems via their discretization

Угольницкий, Геннадий Анатольевич; Усов, А. Б.

doi:10.1134/s0005117913020070

Cited by 19 publications

(6 citation statements)

References 4 publications

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“…In real world control systems (for example, in fisheries) the strategies of agents remain constant during some periods of time due to natural inertia of the control processes [37].…”

Section: A Discrete Version Of the Modelmentioning

confidence: 99%

“…Compulsion means the supervisor's impact to the sets of feasible actions of the agents, while impulsion means her impact on their payoff functionals.The numerical investigation of the model uses two authors' ideas. First, we suppose that even in the continuous processes the values of control variables are changed only in some discrete moments of time that allow for a discretization of the initial continuous model [37,38]. Second, in most real applications it is possible to choose a very small number of representative scenarios (values of control variables and model parameters) that give a qualitatively good description of the model trajectories of the controlled dynamical system including the optimal one [39].For a comparative evaluation of the efficiency of the methods of hierarchical control we use an index of the system compatibility [36].…”

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confidence: 99%

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Spatially Distributed Differential Game Theoretic Model of Fisheries

Ougolnitsky¹,

Усов²

2019

Mathematics

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We consider a differential game of fisheries in a fan-like control structure of the type "supervisor-several agents". The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two spatial coordinates is conducted. Different information structures of the game are generated by the control methods of compulsion (supervisor restricts the feasible strategies of agents) and impulsion (she exerts an impact to their payoff functionals). Both Stackerlberg and inverse Stackelberg games are considered. For the numerical investigation we use a discretization of the initial model and the method of qualitatively representative scenarios in simulation modeling.Mathematics 2019, 7, 732 2 of 13 the Stackelberg games to fisheries can be found in [16,[18][19][20]. Game theoretic models of biological resource management with asymmetric players and different planning horizons are studied in [21,22]. Game problems of harvesting in a biological community are considered also in [23].The papers [24][25][26][27] present non-linear differential equation models of the shallow bodies of water (on the example of Azov Sea). The works [28,29] develop these models by the consideration of fish capture as a control impact: in [28] an optimal control problem is solved, and [29] treats a conflict control model which is formalized as a hierarchical differential game (a Stackelberg game).The differential Stackelberg games are described in the monograph [30], and the inverse Stackelberg games (with a feedback by control) are reviewed in [31]. An original approach to the analysis of differential Stackelberg games with consideration of different information structures which determine the order of moves of all players, their knowledge about the strategies of other players, and the state of the controlled dynamical system is presented in [32]. In that paper, the structure of optimal strategies is described and a method of solution of Stackelberg games and inverse Stackelberg games is proposed. The method is based on building of a mutually advantageous program of actions and punishment of the defectors [32].This paper develops the results presented in [28,29]. Unlike them, we consider here a fan-like control system (a differential game of a supervisor and several agents) and closed-loop strategies of the players. In the case of several agents, the set of their best responses to the supervisor's strategy is the set of Nash equilibria in the normal-form game of the agents. Besides, we consider a spatial coordinate [33].The authors' approach to the modeling of fisheries is based on the concept of sustainable management [34][35][36]. In this frame, the hierarchical control mechanisms (compulsion and impulsion methods) are presented as solutions of the Stackelberg games with phase constraints which reflect the requirements to the state of a controlled system (the conditions of sustainable development). Compulsion means the supervisor's impact to the sets of feasible ac...

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“…In real world control systems (for example, in fisheries) the strategies of agents remain constant during some periods of time due to natural inertia of the control processes [37].…”

Section: A Discrete Version Of the Modelmentioning

confidence: 99%

mentioning

confidence: 99%

Spatially Distributed Differential Game Theoretic Model of Fisheries

Ougolnitsky¹,

Усов²

2019

Mathematics

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“…The authors' approach to the problem is presented in [9][10][11][12][13][14][15]. In [9] the authors' theory of modeling of the dynamical hierarchical control systems is described according to which the basic modeling pattern is the hierarchical system "principal -supervisor(s) -agent(s) -object" in different modifications.…”

Section: Introductionmentioning

confidence: 99%

“…In [10,11,14] the algorithms of building of the solutions in hierarchical differential games for different methods of hierarchical control and information structures are proposed. A method of investigation of the hierarchical differential games based on the hypothesis of constancy of the control actions for some periods of time is proposed in [13]. In [15] a problem of the sustainable management in the biological rehabilitation of the Azov Sea in the case of compulsion is studied.…”

Section: Introductionmentioning

confidence: 99%

Sustainable Management in Regional Fisheries: Mechanisms of Motivation of Myopic Agents

Ougolnitsky¹,

Усов²

2018

Proceedings of the International Scientific Conference "Competitive, Sustainable and Secure Development of the Regional Economy

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This paper is dedicated to the game theoretic investigation of a dynamical model of optimal fishing with consideration of the interests of regional control agents on two levels of hierarchy and building of an original incentive mechanism. The main distinctive property of the paper consists in the consideration of a "myopic" agent who maximizes his payoff only in the one time period (one fishing season). Besides, the impulsion instead of compulsion is used as a method of control. The problem is solved by the simulation modeling, and for the investigation of the respective non-antagonistic differential two-players game a method of qualitatively representative scenarios is used. Its principal idea is that from a very big and even infinite set of the potentially existing control scenarios it is possible to choose a very small number of scenarios that reflect qualitatively different development paths of the controlled system. These scenarios are distinguished principally, while the others do not give anything essential new. The numerical verification of the formal requirements of the method using real data on the Azov Sea is made.

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“…An original approach to the solution of dynamic Stackelberg games is proposed in [9]. We describe our modification of this approach for several followers in [16], [17]. In this case a best response of the followers to the leader's strategy is defined as a Nash equilibrium in the followers' game in normal form.…”

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confidence: 99%

Optimal resource allocation in the difference and differential Stackelberg games on marketing networks

Korolev

Ougolnitsky²

2020

Journal of Dynamics &Amp; Games

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We consider difference and differential Stackelberg game theoretic models with several followers of opinion control in marketing networks. It is assumed that in the stage of analysis of the network its opinion leaders have already been found and are the only objects of control. The leading player determines the marketing budgets of the followers by resource allocation. In the basic version of the models both the leader and the followers maximize the summary opinions of the network agents. In the second version the leader has a target value of the summary opinion. In all four models we have found the Stackelberg equilibrium and the respective payoffs of the players analytically. It is shown that the hierarchical control system is ideally compatible in all cases.

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A study of differential models for hierarchical control systems via their discretization

Cited by 19 publications

References 4 publications

Spatially Distributed Differential Game Theoretic Model of Fisheries

Spatially Distributed Differential Game Theoretic Model of Fisheries

Sustainable Management in Regional Fisheries: Mechanisms of Motivation of Myopic Agents

Optimal resource allocation in the difference and differential Stackelberg games on marketing networks

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