Noncooperative Model Predictive Game With Markov Jump Graph

In this paper,the distributed stochastic model predictive control(MPC)is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs)with the undirected Markov jump graph.To reflect the reality,the state and input constraints have been considered along with the external disturbances.An iterative algorithm is designed such that model predictive noncooperative game could converge to the socalledε-Nash equilibrium in a distributed manner.Sufficient conditions are established to guarantee the convergence of the proposed algorithm.In addition,a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs.Finally,a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.

Multiplicity of Solutions for a Class of Noncooperative Elliptic Systems

In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in RN with smooth boundary ∂Ω, λ,δ,γ are real parameters, and . We assume that F is subquadratic at zero with respect to the variables u,v. By using a variant Clark’s theorem, we obtain infinitely many nontrivial solutions (uk,vk) with as k → ∞. Compared with the existing literature, we do not need to assume the behavior of the nonlinearity ∇F at infinity.

Theoretical and Experimental Investigation of Driver Noncooperative-Game Steering Control Behavior

This paper investigates two noncooperative-game strategies which may be used to represent a human driver's steering control behavior in response to vehicle automated steering intervention.The first strategy,namely the Nash strategy is derived based on the assumption that a Nash equilibrium is reached in a noncooperative game of vehicle path-following control involving a driver and a vehicle automated steering controller.The second one,namely the Stackelberg strategy is derived based on the assumption that a Stackelberg equilibrium is reached in a similar context.A simulation study is performed to study the differences between the two proposed noncooperativegame strategies.An experiment using a fixed-base driving simulator is carried out to measure six test drivers'steering behavior in response to vehicle automated steering intervention.The Nash strategy is then fitted to measured driver steering wheel angles following a model identification procedure.Control weight parameters involved in the Nash strategy are identified.It is found that the proposed Nash strategy with the identified control weights is capable of representing the trend of measured driver steering behavior and vehicle lateral responses.It is also found that the proposed Nash strategy is superior to the classic driver steering control strategy which has widely been used for modeling driver steering control over the past.A discussion on improving automated steering control using the gained knowledge of driver noncooperative-game steering control behavior was made.

Exploration on the stability conditions in bubble columns by noncooperative game theory

The energy-minimization multiscale(EMMS)model,originally proposed for gas-solid fluidization,features a stability condition to close the simplified conservation equations.It was put forward to physically reflect the compromise of two dominant mechanisms,i.e.,the particle-dominated with minimal potential energy of particles,and the gas-dominated with the least resistance for gas to penetrate through the particle bed.The stability condition was then formulated as the minimization of the ratio of these two physical quantities.Analogously,the EMMS approach was later extended to the gas-liquid flow in bubble columns,termed dual-bubble-size model.It considers the compromise of two dominant mechanisms,i.e.,the liquid-dominated regime with small bubbles,and the gas-dominated regime with large bubbles.The stability condition was then formulated as the minimization of the sum of these two physical quantities.Obviously,the two stability conditions were expressed in different manner,though gas-solid and gas-liquid systems bear some analogy.In addition,both the conditions transform the original multiobjective variational problem into a single-objective problem.The mathematical formulation of stability condition remains therefore an open question.This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem,aiming to explo re the different pathways of compromise of dominant mechanisms.The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup,which is associated with flow regime transition.Hybrid of dominant mechanisms,noninferior solutions and noncooperative game theory can predict the flow regime transition.However,the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure.The game of the three mechanisms restores the two-bubble structure.The exploration on the formulation of stability conditions may help to understa nd the roles and interactions of different domina nt mechanisms in the origin of complexity in multiphase flow systems.

Dynamic aggregation evolution of competitive societies of cooperative and noncooperative agents

We propose an evolution model of cooperative agent and noncooperative agent aggregates to investigate the dynamic evolution behaviors of the system and the effects of the competing microscopic reactions on the dynamic evolution. In this model, each cooperative agent and noncooperative agent are endowed with integer values of cooperative spirits and nonco- operative spirits, respectively. The cooperative spirits of a cooperative agent aggregate and the noncooperative spirits of a noncooperative agent aggregate change via four competing microscopic reaction schemes： the win-win reaction between two cooperative agents, the lose-lose reaction between two noncooperative agents, the win-lose reaction between a coop- erative agent and a noncooperative agent （equivalent to the migration of spirits from cooperative agents to noncooperative agents）, and the cooperative agent catalyzed decline of noncooperative spirits. Based on the generalized Smoluchowski＇s rate equation approach, we investigate the dynamic evolution behaviors such as the total cooperative spirits of all coop- erative agents and the total noncooperative spirits of all noncooperative agents. The effects of the three main groups of competition on the dynamic evolution are revealed. These include： （i） the competition between the lose-lose reaction and the win-lose reaction, which gives rise to respectively the decrease and increase in the noncooperative agent spirits; （ii） the competition between the win-win reaction and the win-lose reaction, which gives rise to respectively the increase and decrease in the cooperative agent spirits; （iii） the competition between the win-lose reaction and the catalyzed-decline reaction, which gives rise to respectively the increase and decrease in the noncooperative agent spirits.

Radio frequency based distributed system for noncooperative UAV classification and positioning

With the increasing popularity of civilian unmanned aerial vehicles(UAVs),safety issues arising from unsafe operations and terrorist activities have received growing attention.To address this problem,an accurate classification and positioning system is needed.Considering that UAVs usually use radio frequency(RF)signals for video transmission,in this paper,we design a passive distributed monitoring system that can classify and locate UAVs according to their RF signals.Specifically,three passive receivers are arranged in different locations to receive RF signals.Due to the noncooperation between a UAV and receivers,it is necessary to detect whether there is a UAV signal from the received signals.Hence,convolutional neural network(CNN)is proposed to not only detect the presence of the UAV,but also classify its type.After the UAV signal is detected,the time difference of arrival(TDOA)of the UAV signal arriving at the receiver is estimated by the cross-correlation method to obtain the corresponding distance difference.Finally,the Chan algorithm is used to calculate the location of the UAV.We deploy a distributed system constructed by three software defined radio(SDR)receivers on the campus playground,and conduct extensive experiments in a real wireless environment.The experimental results have successfully validated the proposed system.

Feasibility analysis of angles-only navigation algorithm with multisensor data fusion for spacecraft noncooperative rendezvous

Relative navigation is crucial for spacecraft noncooperative rendezvous,and angles-only navigation using visible and infrared cameras provides a feasible solution.Herein,an angles-only navigation algorithm with multisensor data fusion is proposed to derive the relative motion states between two noncooperative spacecraft.First,the design model of the proposed algorithm is introduced,including the derivation of the state propagation and measurement equations.Subsequently,models for the sensor and actuator are introduced,and the effects of various factors on the sensors and actuators are considered.The square-root unscented Kalman filter is used to design the angles-only navigation filtering scherne.Additionally,the Clohessy-Wiltshire terminal guidance algorithm is introducedto obtain the theoretical relative motion trajectories during the rendezvous operations of two noncooperative spacecraft.Finally,the effectiveness of the proposed angles-only navigation algorithm is verified using a semi-physical simulation platform.The results prove that an optical navigation camera combined with average accelerometers and occasional orbital maneuvers is feasible for spacecraft noncooperative rendezvous using angles-only navigation.

INTERRELATIONSHIPS AMONG NONCOOPERATIVE AND COALITION STABILITY CONCEPTS

Insightful theorems are established on interrelationships among coalition and noncooperative stability concepts defined within the paradigm of the Graph Model for Conflict Resolution. More specifically, the newly defined coalition stability def＇mitions that are considered are coalition Nash stability （CNash）, coalition general metarationality （CGMR）, coalition symmetric metarationality （CSMR） and coalition sequential stability （CSEQ）, along with their earlier-defined noncooperative versions. A range of interesting new theorems are derived to establish connections among these coalition stability concepts as well as between noncooperative and coalition stability definitions. Applications with respect to the games of Prisoner＇s Dilemma and Chicken, as well as a groundwater contamination dispute, demonstrate how the various stability definitions can be applied in practice and confirm the validity of some of the theorems as well as point out, by example, certain types of relationships which cannot hold.

A Survey on Noncooperative Games and Distributed Nash Equilibrium Seeking over Multi-Agent Networks

The work gives a review on the distributed Nash equilibrium seeking of noncooperative games in multi-agent networks,which emerges as one of the frontier research topics in the area of systems and control community.Firstly,we give the basic formulation and analysis of noncooperative games with continuous action spaces,and provide the motivation and basic setting for distributed Nash equilibrium seeking.Then we introduce both the gradient-based algorithms and best-response based algorithms for various type of games,including zero-sum games,aggregative games,potential games,monotone games,and multi-cluster games.In addition,we provide some applications of noncooperative games.

A Game Theoretic Approach for Energy-Efficient In-Network Caching in Content-Centric Networks

Recently, content-centric networking （CCN） has become a hot research topic for the diffusion of contents over the Internet. Most existing works on CCN focus on the improvement of network resource utilization. Consequently, the energy consumption aspect of CCN is largely ignored. In this paper, we propose a distributed energyefficient in-network caching scheme for CCN, where each content router only needs locally available information to make caching decisions considering both caching energy consumption and transport energy consumption. We formulate the in-network caching problem as a non-cooperative game. Through rigorous mathematical analysis, we prove that pure strategy Nash equilibria exist in the proposed scheme, and it always has a strategy profile that implements the socially optimal configuration, even if the touters are self-interested in nature. Simulation results are presented to show that the distributed solution is competitive to the centralized scheme, and has superior performance compared to other popular caching schemes in CCN. Besides, it exhibits a fast convergence speed when the capacity of content routers varies.

Nash-Q learning-based collaborative dispatch strategy for interconnected power systems

The large-scale utilization and sharing of renewable energy in interconnected systems is crucial for realizing"instrumented,interconnected,and intelligent"power grids.The traditional optimal dispatch method can not coordinate the economic benefits of all the stakeholders from multiple regions of the transmission network,comprehensively.Hence,this study proposes a large-scale wind-power coordinated consumption strategy based on the Nash-Q method and establishes an economic dispatch model for interconnected systems considering the uncertainty of wind power,with optimal windpower consumption as the objective for redistributing the shared benefits between regions.Initially,based on the equivalent cost of the interests of stakeholders from different regions,the state decision models are respectively constructed,and the noncooperative game Nash equilibrium model is established.The Q-learning algorithm is then introduced for high-dimension decision variables in the game model,and the dispatch solution methods for interconnected systems are presented,integrating the noncooperative game Nash equilibrium and Q-learning algorithm.Finally,the proposed method is verified through the modified IEEE 39-bus interconnection system,and it is established that this method achieves reasonable distribution of interests between regions and promotes large-scale consumption of wind power.

A Novel Two-Stage Dynamic Spectrum Sharing Scheme in Cognitive Radio Networks

In order to enhance the efficiency of spectrum utilization and reduce communication overhead in spectrum sharing process, we propose a two-stage dynamic spectrum sharing scheme in which cooperative and noncooperative modes are analyzed in both stages. In particular, the existence and the uniqueness of Nash Equilibrium(NE) strategies for noncooperative mode are proved. In addition, a distributed iterative algorithm is proposed to obtain the optimal solutions of the scheme. Simulation studies are carried out to show the performance comparison between two modes as well as the system revenue improvement of the proposed scheme compared with a conventional scheme without a virtual price control factor.

Angles-only relative navigation in highly elliptical orbits

For angles-only relative navigation system only measures line-of-sight information,there are inherent problems in the ability to determine the range between Chaser and Target. Angles-only relative navigation is an attractive alternative for inspecting or rendezvous with noncooperative target,if adequate accuracy can be achieved. Angles-only relative navigation model considering J2 perturbation is presented for tracking and rendezvous with noncooperative target in highly elliptical orbit. Impulsive out-of-plane maneuvers of the Chaser are used to improve the navigation accuracy. The first impulse burns in cross-track directions to change the orbit inclination of the Chaser. The second impulse burns after one orbit period to change the orbit of the Chaser back. The simulation results show that the relative navigation system without maneuvers can't correct the initial state errors,while impulsive out-ofplane maneuvers of the Chaser improves the navigation accuracy. Angles-only relative navigation with chaser vehicle maneuvers to improve observability is effective when the spacecrafts are in highly elliptical orbits.

New Maintenance Strategies for Generating Companies in Power Market

A new approach to maintenance scheduling of generating units(MSU)in competitive electricity markets was presented,which was formulated as a noncooperative game with complete information.The payoff of each generating company(Genco)was defined as the profit from the energy auction market minus maintenance cost and risk loss.The compensation fee of interruptible load was a part of the maintenance cost when the permitted maintenance capacity in the system was insufficient.Hourly energy auction was incorporated in the computation of both revenues from energy market and risk loss of maintenance strategy as a nested game.A new heuristic search algorithm for the calculation of the game equilibrium of MSU was presented,which coordinates the solutions of non-equilibrium,unique equilibrium and multiple equilibria.Numerical results for a two-Genco system and a realistic system were used to demonstrate the basic ideas and the applicability of the proposed method,as well as its computational efficiency.

Multiple Criteria Games-Theory and Applications

After a reivew of basic concepts in multiple criteria optimization, the paper presents a characterization of noncooperative equilibria in multiple criteria games in normal form either by weighted sums or by. order-consistent achievement scalarizing functions, for convex and nonconvex cases. Possible applications of multiple criteria games and such characterizations of their equilibria are indicated. The analysis of multiple criteria games might be especially useful when studying reasons of possible conflict escalation processes and ways of preventing them.

Studying on equilibriums between price and QoS in multi-provider overlay access networks

From the viewpoint of game theory, this paper proposes a model that combines QoS index with price factor in overlay access networks, and uses the multinomial logit （MNL） to model the choice behaviour of users. Each service class is considered an independent and competitive entity offered by each provider, which aims at maximizing its own utility. Based on noncooperative game, we prove the existence and uniqueness of equilibriums between QoS levels and prices among various service classes, and demonstrate the properties of equilibriums. Finally, these results are verified via ntunerieal analysis.

A survey of static and dynamic potential games

Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.