A Novel Distributed Optimal Adaptive Control Algorithm for Nonlinear Multi-Agent Differential Graphical Games

In this paper, an online optimal distributed learning algorithm is proposed to solve leader-synchronization problem of nonlinear multi-agent differential graphical games. Each player approximates its optimal control policy using a single-network approximate dynamic programming(ADP) where only one critic neural network(NN) is employed instead of typical actorcritic structure composed of two NNs. The proposed distributed weight tuning laws for critic NNs guarantee stability in the sense of uniform ultimate boundedness(UUB) and convergence of control policies to the Nash equilibrium. In this paper, by introducing novel distributed local operators in weight tuning laws, there is no more requirement for initial stabilizing control policies. Furthermore, the overall closed-loop system stability is guaranteed by Lyapunov stability analysis. Finally, Simulation results show the effectiveness of the proposed algorithm.

Distributed power control algorithm based on game theory for wireless sensor networks

Energy saving is the most important issue in research and development for wireless sensor networks. A power control mechanism can reduce the power consumption of the whole network. Because the character of wireless sensor networks is restrictive energy, this paper proposes a distributed power control algorithm based on game theory for wireless sensor networks which objects of which are reducing power consumption and decreasing overhead and increasing network lifetime. The game theory and OPNET simulation shows that the power control algorithm converges to a Nash Equilibrium when decisions are updated according to a better response dynamic.

Game Modeling Research for Urbanization and Epidemic Control

To aid in the sustainable development of cities this paper examines methods for urbanization and epidemic control. Using, as a foundation, game theory from modern control theory, a set of strategies for modeling urbanization and epidemic control are examined by analyzing and studying the current condition of China including its population, economy, resources and city management methods. Urbanization and epidemic control solving strategies are probed and the solution to a simulated example is provided. The conclusion from this research is that the speed of Chinese urbanization should be slowed to match the condition of resources and level of city management available.

Size Distributions of Aerosol Sulfates and Nitrates in Beijing during the 2008 Olympic Games： Impacts of Pollution Control Measures and Regional Transport

For the 2008 Olympic Games, drastic control measures were implemented on industrial and urban emissions of sulfur dioxide （SO2）, nitrogen oxides （NOx） and other pollutants to address the issues of poor air quality in Beijing. To investigate the effects of SO2 and NOx reductions on the particulate sulfate and nitrate concentrations as well as their size distributions, size-segregated aerosol samples were collected using micro-orifice uniform deposit impactors （MOUDIs） at urban and downwind rural sites in Beijing before and after full-scale controls. During the sampling period, the mass concentrations of fine particles （PMI.s） at the urban and rural sites were 94.0 and 85.9 p.g m-3, respectively. More than 90% of the sulfates and 60% of nitrates formed as fine particles. Benefiting from the advantageous meteorological conditions and the source controls, sulfates were observed in rather low concentrations and primarily in condensation mode during the Olympics. The effects of the control measures were separately analyzed for the northerly and the southerly air-mass-dominated days to account for any bias. After the control measures were implemented, PM, sulfates, and nitrates were significantly reduced when the northerly air masses prevailed, with a higher percentage of reduction in larger particles. The droplet mode particles, which dominated the sulfates and nitrates before the controls were implemented, were remarkably reduced in mass concentration after the control measures were implemented. Nevertheless, when the polluted southerly air masses prevailed, the local source control measures in Beijing did not effectively reduce the ambient sulfate concentration due to the enormous regional contribution from the North China Plain.

CRSG:A congestion control routing algorithm for security defense based on social psychology and game theory in DTN

The inherent selfishness of each node for the enhancement of message successful delivery ratio and the network overall performance improvement are reflected in the contradiction relationship of competition and cooperation in delay/disruption tolerant networks (DTN). In particular, the existence of malicious node aggravates this contradiction. To resolve this contradiction, social relationship theory and group theory of social psychology were adopted to do an in-depth analysis. The concrete balancing approach which leveraged Nash equilibrium theory of game theory was proposed to resolve this contradiction in reality. Thus, a new congestion control routing algorithm for security defense based on social psychology and game theory (CRSG) was put forward. Through the experiment, this algorithm proves that it can enhance the message successful delivery ratio by more than 15% and reduce the congestion ratio over 15% as well. This algorithm balances the contradiction relationship between the two key performance targets and made all nodes exhibit strong cooperation relationship in DTN.

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

NOVEL POWER CONTROL GAME VIA PRICING ALGORITHM FOR COGNITIVE RADIOS

To compensate the service providers who have paid billions of dollars to use spectrum and to satisfy secondary users' requirements in cognitive radios, a Non-cooperative Power Control Game and Pricing algorithm (NPGP) is proposed. Simulation results show that the proposed algorithm can regulate the secondary users' transmitter powers, optimally allocate radio resource and increase the total throughput effectively.

A Trading Execution Model Based on Mean Field Games and Optimal Control

We present a trading execution model that describes the behaviour of a big trader and of a multitude of retail traders operating on the shares of a risky asset. The retail traders are modeled as a population of “conservative” investors that: 1) behave in a similar way, 2) try to avoid abrupt changes in their trading strategies, 3) want to limit the risk due to the fact of having open positions on the asset shares, 4) in the long run want to have a given position on the asset shares. The big trader wants to maximize the revenue resulting from the action of buying or selling a (large) block of asset shares in a given time interval. The behaviour of the retail traders and of the big trader is modeled using respectively a mean field game model and an optimal control problem. These models are coupled by the asset share price dynamic equation. The trading execution strategy adopted by the retail traders is obtained solving the mean field game model. This strategy is used to formulate the optimal control problem that determines the behaviour of the big trader. The previous mathematical models are solved using the dynamic programming principle. In some special cases explicit solutions of the previous models are found. An extensive numerical study of the trading execution model proposed is presented. The interested reader is referred to the website: http://www.econ.univpm.it/recchioni/finance/w19 to find material including animations, an interactive application and an app that helps the understanding of the paper. A general reference to the work of the authors and of their coauthors in mathematical finance is the website:?http://www.econ.univpm.it/recchioni/finance.

The Relationship between College Students’ Online Game Addiction, Family Function and Self-Control

Objective: To study the status of online game addiction, self-control ability and family function, analyze the influence factors and the relationship between them. Methods: The questionnaire of online game addiction, family function and self-control ability was used to investigate some college students. Results: 1) The detection rate of college students’ online game addiction is 40%. There are significant differences in sex, grade and only child in online game addiction. 2) There are significant differences in self-control ability and family function between online game addicts and non-addicts. 3) Self-control ability and family function have a significant predictive effect on online game addiction. Conclusion: College students’ online game addiction is affected by their self-control ability and family function, and it can be alleviated by improving their self-control ability and family function.

Game-theoretic approach to power and admission control in hierarchical wireless sensor networks

Power efficiency and link reliability are of great impor- tance in hierarchical wireless sensor networks （HWSNs）, espe- cially at the key level, which consists of sensor nodes located only one hop away from the sink node called OHS. The power and admission control problem in HWSNs is comsidered to improve its power efficiency and link reliability. This problem is modeled as a non-cooperative game in which the active OHSs are con- sidered as players. By applying a double-pricing scheme in the definition of OHSs＇ utility function, a Nash Equilibrium solution with network properties is derived. Besides, a distributed algorithm is also proposed to show the dynamic processes to achieve Nash Equilibrium. Finally, the simulation results demonstrate the effec- tiveness of the proposed algorithm.

Optimal Control of a Vaccinating Game toward Increasing Overall Coverage

In this paper, we study an asymmetric game that characterizes the intentions of players to adopt a vaccine. The game describes a decision-making process of two players differentiated by income level and perceived treatment cost, who consider a vaccination against an infectious disease. The process is a noncooperative game since their vaccination decision has a direct impact on vaccine coverage in the population. We introduce a replicator dynamics (RD) to investigate the players’ optimal strategy selections over time. The dynamics reveal the long-term stability of the unique Nash-Pareto equilibrium strategy of this game, which is an extension of the notion of an evolutionarily stable strategy pair for asymmetric games. This Nash-Pareto pair is dependent on perceived costs to each player type, on perceived loss upon getting infected, and on the probability of getting infected from an infected person. Last but not least, we introduce a payoff parameter that plays the role of cost-incentive towards vaccination. We use an optimal control problem associated with the RD system to show that the Nash-Pareto pair can be controlled to evolve towards vaccination strategies that lead to a higher overall expected vaccine coverage.

Optimal Adaptive Control of a Class of Stochastic Systems Using Game Theory

This paper attempts to study a optimal adaptive con tr ol problem using game theory, and proposes an important practical result that an adaptive processes is a set of sufficient conditions under which pure strategy is essentially complete, and thus the fact that yield a very useful desirable pu re optimal control rule.

Game theory approach to optimal capital cost allocation in pollution control

This paper tries to integrate game theory, a very useful tool to resolve conflict phenomena, with optimal capital cost allocation issue in total emission control. First the necessity of allocating optimal capital costs fairly and reasonably among polluters in total emission control was analyzed. Then the possibility of applying game theory to the issue of the optimal capital cost allocation was expounded. Next the cooperative N person game model of the optimal capital cost allocation and its solution ways including method based on Shapley value, least core method, weak least core methods, proportional least core method, CGA method, MCRS method and so on were delineated. Finally through application of these methods it was concluded that to apply game theory in the optimal capital cost allocation issue is helpful to implement the total emission control planning schemes successfully, to control pollution effectively, and to ensure sustainable development.

THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA

Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed： compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can＇t prevent defection from being evolutionary stable strategy （ESS）. On the other hand, compensation for the coopera- tor can＇t prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.

A CONNECTION ADMISSION CONTROL SCHEME BASED ON GAME THEORETICAL MODEL IN ATM NETWORKS

In this paper, the main schemes of connection admission control (CAC) in ATM networks are briefly discussed especially the principle of dynamic bandwidth allocation. Then the fair share of the bandwidth among different traffic sources is analyzed based on cooperative game model. A CAC scheme is proposed using the genetic algorithm (GA) to optimize the bandwidth-delay-product formed utilization function that ensures the fair share and accuracy of accepting/rejecting the incoming calls. Simulation results show that the proposed scheme ensures fairness of the shared bandwidth to different traffic sources.

Stochastic Differential Game Model for Decentralized Power Control with Wisdom Regulation Factor in Wearable Audio-Oriented BodyNets

In this study,aiming at the characteristics of randomness and dynamics in Wearable Audio-oriented BodyNets(WA-BodyNets),stochastic differential game theory is applied to the investigation of the problem of transmitted power control inconsumer electronic devices.First,astochastic differential game model is proposed for non-cooperative decentralized uplink power control with a wisdom regulation factor over WA-BodyNets with a one-hop star topology.This model aims to minimize the cost associated with the novel payoff function of a player,for which two cost functions are defined:functions of inherent power radiation and accumulated power radiation damage.Second,the feedback Nash equilibrium solution of the proposed model and the constraint of the Quality of Service(QoS) requirement of the player based on the SIR threshold are derived by solving the Fleming-Bellman-Isaacs partial differential equations.Furthermore,the Markov property of the optimal feedback strategies in this model is verified.The simulation results show that the proposed game model is effective and feasible for controlling the transmitted power of WA-BodyNets.

QoS awared power and admission controls based on non-cooperative game theory in wireless networks

In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative game where the users adjust their transmit powers to maximize the utility, thus restraining the interferences. By using adaptive utility functions and tunable pricing parameters according to QoS levels, this algorithm can well meet different QoS requirements and improve system capacity compared with those that ignore the QoS differences.

A Video Game Based on Optimal Control and Elementary Statistics

The video game presented in this paper is a prey-predator game where two preys (human players) must avoid three predators (automated players) and must reach a location in the game field (the computer screen) called preys’ home. The game is a sequence of matches and the human players (preys) must cooperate in order to achieve the best perform- ance against their opponents (predators). The goal of the predators is to capture the preys, which are the predators try to have a “rendez vous” with the preys, using a small amount of the “resources” available to them. The score of the game is assigned following a set of rules to the prey team, not to the individual prey. In some situations the rules imply that to achieve the best score it is convenient for the prey team to sacrifice one of his components. The video game pursues two main purposes. The first one is to show how the closed loop solution of an optimal control problem and elementary sta- tistics can be used to generate (game) actors whose movements satisfy the laws of classical mechanics and whose be- haviour simulates a simple form of intelligence. The second one is “educational”, in fact the human players in order to be successful in the game must understand the restrictions to their movements posed by the laws of classical mechanics and must cooperate between themselves. The video game has been developed having in mind as players for children aged between five and thirteen years. These children playing the video game acquire an intuitive understanding of the basic laws of classical mechanics (Newton’s dynamical principle) and enjoy cooperating with their teammate. The video game has been experimented on a sample of a few dozen children. The children aged between five and eight years find the game amusing and after playing a few matches develop an intuitive understanding of the laws of classical me- chanics. They are able to cooperate in making fruitful decisions based on the positions of the preys (themselves), of the predators (their opponents) and on the physical limitations to the movements of the game actors. The interest in the game decreases when the age of the players increases. The game is too simple to interest a teenager. The game engine consists in the solution of an assignment problem, in the closed loop solution of an optimal control problem and in the adaptive choice of some parameters. At the beginning of each match, and when necessary during a match, an assign- ment problem is solved, that is the game engine chooses how to assign to the predators the preys to chase. The resulting assignment implies some cooperation among the predators and defines the optimal control problem used to compute the strategies of the predators during the match that follows. These strategies are determined as the closed loop solution of the optimal control problem considered and can be thought as a (first) form of artificial intelligence (AI) of the preda- tors. In the optimal control problem the preys and the predators are represented as point masses moving according to Newton’s dynamical principle under the action of friction forces and of active forces. The equations of motion of these point masses are the constraints of the control problem and are expressed through differential equations. The formula- tion of the decision process through optimal control and Newton’s dynamical principle allows us to develop a game where the effectiveness and the goals of the automated players can be changed during the game in an intuitive way sim- ply modifying the values of some parameters (i.e. mass, friction coefficient, ...). In a sequence of game matches the predators (automated players) have “personalities” that try to simulate human behaviour. The predator personalities are determined making an elementary statistical analysis of the points scored by the preys in the game matches played and consist in the adaptive choice of the value of a parameter (the mass) that appears in the differential equations that define the movements of the predators. The values taken by this parameter determine the behaviour of the predators and their effectiveness in chasing the preys. The predators personalities are a (second) form of AI based on elementary statistics that goes beyond the intelligence used to chase the preys in a match. In a sequence of matches the predators using this second form of AI adapt their behaviour to the preys’ behaviour. The video game can be downloaded from the website: http://www.ceri.uniroma1.it/ceri/zirilli/w10/.