A cooperative stochastic differential game of transboundary industrial pollution

Though cooperation in environmental control holds out the best promise of effective actions, limited success has been observed because existing multinational joint initiatives fail to satisfy the property of subgame consistency. A cooperative solution is subgame consistent if the solution optimality principle is maintained in any subgame which starts at a later time with any feasible state brought about by prior optimal behaviors. This paper presents a cooperative stochastic differential game of transboundary industrial pollution with two novel features. The first feature is that industrial production creates short-term local impacts and long-term global impacts on the environment. Secondly, a subgame consistent cooperative solution is derived in this stochastic differential game together with a payment distribution mechanism that supports the subgame consistent solution. This is the first time that pollution management is analyzed in a cooperative stochastic differential game framework under these novel features.     

A differential game of retailer promotions

The paper identifies equilibrium marketing strategies over time in a marketing channel of distribution. A number of retailers promote locally a manufacturer's brand in order to increase their sales. However, sustained and substantial retailer promotions will damage the image of the manufacturer's brand. The manufacturer advertises nationally to improve the brand image. Demand at the retail outlets increase both by the local promotions and by the strength of brand image. First, we identify a noncooperative equilibrium of a differential game played with Markovian strategies. Next, we study a cooperative game where the players make coordinated marketing decisions and address the question whether the manufacturer can design an incentive strategy such that the retailers will stick to their parts of the agreed solution.     

电力系统一二次调频的反馈微分博弈协同控制

风能等间歇式能源并网将是未来电网发展趋势,其输出功率的波动将加剧一二次调频之间的冲突反调问题.本文将反馈微分博弈应用于电力系统频率控制中,建立起一二次调频的协同控制模型,并考虑调速器死区、控制动作幅值限制、机组爬坡速率约束等工程实际因素,用协同进化算法求得该模型的反馈纳什均衡解.用仿真验证了该方法在满足各种工程因素下有效解决一二次调频的冲突反调问题,充分挖掘了系统蕴藏的调频能力.     

A differential game of joint implementation of environmental projects

This paper proposes a two-player, finite-horizon differential game model to analyze joint implementation in environmental projects, one of the flexible mechanisms considered in the Kyoto Protocol. Our results show that allowing for foreign investments could in some cases increase the welfares of both parties involved in the project. Further, imposing an environmental target constraint does not necessarily deteriorate the payoffs of both players.     

A differential pursuit/evasion game of capture between an omnidirectional agent and a differential drive robot,and their winning roles

This paper addresses a differential pursuit/evasion game. The players are an omnidirectional agent (OA) and a differential drive robot (DDR). They move in an obstacle-free environment; the DDR is faster than the OA but it can only change its motion direction up to a bounded rate. First, we analyse the scenario in which the OA has as objective to capture a DDR in minimum time and the DDR wants to retard the capture as long as possible. We present the time optimal motion primitives of the players to achieve their goals. Later, we allow the agents to change the roles, namely, the DDR is allowed to play as the pursuer and the OA is allowed to play as the evader. This later analysis allows one to establish which is the winner role for each agent, based only on the initial position of the players and their maximum speed.     

Slowing deforestation pace through subsidies: a differential game

This paper deals with the issue of deforestation, one of the main global environmental problems. We consider two players having different utilities for forest conservation. The first one (call it North) represents a set of countries having as an objective to maximize the size of tropical forest at a certain time horizon. The (South) second player's revenue function involves a trade-off between forest exploitation and agricultural activities. We study two scenarios. In the first one, the assumption is a laisser-faire policy, where the South solves an optimal control problem over a finite horizon. Revenue and optimal forest exploitation obtained represent a benchmark for the second scenario, where the North offers subsidies to the South to reduce the deforestation rate. The two scenarios are analyzed and compared in terms of strategies, outcomes and forest conservation.     

Deforestation and foreign transfers: a Stackelberg differential game approach

In this paper, our concern is with deforestation as a global environmental issue. Foreign transfers from developed or Northern countries to developing or Southern countries have been proposed to deal with that issue. We use a Stackelberg differential game approach where the two players are: a donor community (the leader) and a recipient country (the follower). We study the impact of different specifications for the transfer function, related to the different information structures the players can consider when playing the Stackelberg game. The different scenarios are compared both from the environmental and economic points of view.     

Linear quadratic differential games with cheap control

This paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero. It is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero.     

非零和微分博弈系统的事件触发最优跟踪控制（英文）

近年来,对于具有未知动态的非零和微分博弈系统的跟踪问题,已经得到了讨论,然而这些方法是时间触发的,在传输带宽和计算资源有限的环境下并不适用.针对具有未知动态的连续时间非线性非零和微分博弈系统,本文提出了一种基于积分强化学习的事件触发自适应动态规划方法.该策略受梯度下降法和经验重放技术的启发,利用历史和当前数据更新神经网络权值.该方法提高了神经网络权值的收敛速度,消除了一般文献设计中常用的初始容许控制假设.同时,该算法提出了一种易于在线检查的持续激励条件(通常称为PE),避免了传统的不容易检查的持续激励条件.基于李亚普诺夫理论,证明了跟踪误差和评价神经网络估计误差的一致最终有界性.最后,通过一个数值仿真实例验证了该方法的可行性.     

A differential control method for the proportional directional valve

For the proportional directional valve controlled by two proportional solenoids, the normal control method （NCM） energizes only one solenoid at a time. The performance of the valve is greatly influenced by the nonlinearity of the proportional solenoid, such as dead zone and low force gain with a small current, and this effect cannot be eliminated by a simple dead-zone current compensation. To avoid this disadvantage, we propose the differential control method （DCM）. By employing DCM, the controller outputs differential signals to simultaneously energize both solenoids of the proportional valve, and the operating point is found by analyzing the force output of the two solenoids to make a minimum variation of the current force gain. The comparisons of the valve response characteristics are made between NCM and DCM by nonlinear dynamic simulation and experiments. Simulation and experimental results show that by using DCM, the frequency response of the valve is greatly enhanced, especially when the input is small, which means that the dynamic characteristics of the proportional valve are improved.     

Analysis of a simple capacity game

We study a two‐player two‐fare‐class static single‐period capacity allocation game with complete information. Nonnested (partitioned) booking limit policies are investigated in both noncooperative and cooperative situations. We show the existence of unique Nash equilibrium in the noncooperative situation. In the cooperative game, we analyze the cost saving of the two players and investigate the concavity of the objective function. For both noncooperative and cooperative settings, we assume the demands to be a truncated normal distribution and provide a comprehensive sensitivity analysis to discover the effects of unit revenue, rejection cost, and transfer rate on the equilibrium solution. Our numerical experiments show that the nonnested model can be a good approximation to the nested booking limit model. For the cooperative setting, we identify conditions that give rise to improvements in the total system revenue. Finally, under each game‐theoretic setting, we present the managerial implications of our solutions along with numerical examples.     

The singular zero-sum differential game with stability usingH ∞ control theory

In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH _∞ problem with state feedback, i.e., theH _∞ problem where the direct feedthrough matrix from control input to output is not necessarily injective.     

A result on output feedback linear quadratic control

In this note we consider the static output feedback linear quadratic control problem. We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depends only on the output and control variables.This result is used to present both necessary and sufficient conditions under which the corresponding linear quadratic differential game has a Nash equilibrium in case the players use static output feedback control.Another consequence of this result is that the conditions also provide sufficient conditions for the static output stabilizability problem. Of course, in case these conditions are not met this does not mean that the system is not stabilizable via static output feedback.     

A linear differential game with a fixed termination time and restrictions on resources

A linear game with a fixed termination time and integral restrictions on player controls is considered. The pursuer constructs his control with knowledge of the control of the evader, and the evader uses information on all previous actions of his opponent at each instant of time. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 178–183, July–August, 2000.     

认知无线电中基于非合作博弈的功率控制算法

针对认知无线电中的功率控制问题,基于非合作博弈模型,提出了一种新的效用函数,证明了该博弈中纳什均衡的存在性和唯一性。设计了一种分布式功率控制算法并证明了其收敛性。讨论了几个参数对系统性能的影响。仿真表明,该算法可实现对认知用户发射功率的有效控制。与SINR平衡算法和Koskie-Gajic算法相比,本算法既保障了每个认知用户的QoS需求,又增加了系统吞吐量。     

Robust control and differential games on a finite time horizon

It is well known that theH control problem has a state space formulation in terms of differential games. For a finite time horizon control problem, the analogous differential game is considered. The disturbance is the control for the maximizing player. In order to allow forL ² disturbances, the controls for at least one player must be allowed to be unbounded. It is shown that the value of the game is the viscosity solution of the corresponding Isaacs equation under rather general conditions.     

Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.     

一种基于非合作博弈的无线传感器网络功率控制算法

提出了一种无线传感器网络中以容量最大化为目标的非合作博弈功率控制算法。通过效益函数来选择合适的发射功率,以保证网络连通性并缓解分组碰撞状况。而后给出了对该算法纳什均衡存在性和唯一性的证明。仿真结果表明:该算法可有效提高能量效率和网络容量。