Journal articles: 'Game theory and optimal control'

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Xu, Juanjuan, Wei Wang, and Huanshui Zhang. "Game theory approach to optimal control problem with multi-channel control." International Journal of Control, Automation and Systems 13, no. 1 (December 18, 2014): 58–64. http://dx.doi.org/10.1007/s12555-013-0023-y.

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Makhmudova, Sh D., A. D. Makhmudov, and A. N. Urazgalieva. "Sufficient conditions for the existence of equilibrium in the form of Hamilton-Jacobi equations." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 84, no. 2 (June 15, 2022): 183–94. http://dx.doi.org/10.47533/2020.1606-146x.167.

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The article discusses the application of the theory of optimal control for solving Hamilton-Jacob equations with phase constraints. A method for constructing generalized solutions using optimal control problems is proposed. The results and analysis of numerical experiments, conditions for the existence of equilibrium situations in noncooperative differential games of several persons, namely the conditions for the existence of equilibrium situations in noncooperative differential games of several persons, defining the action according to Hamilton, are stated. Necessary conditions in the form of Hamilton-Jacobi equations are obtained. Game theory as an applied mathematical theory is used to understand and explain the mechanisms that are used when people make decisions. The theory contributes to the functioning of the logic of strategic planning and the relationship between individuals. Game theory as a method of applied mathematics is used for behavioral studies in various conditions, and helps understand the behavior of economic agents. The theory has many applications and can be used in different areas such as: strategy games, administration, economics and artificial intelligence research. The article describes a mathematical method for studying optimal situations in game theory.

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Kim, Sungwook. "Sensor Communication Rate Control Scheme Based on Inference Game Approach." International Journal of Distributed Sensor Networks 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/127349.

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In real-life situations, decisions must be made even when limited or uncertain information is available. Therefore, the payoff of an action is not clearly known when the decision is made. Recently, game theory has become a powerful tool for analyzing the interactions between decision makers in many domains. However, the traditional game theory approach assumes that a player belief about the payoff of a strategy taken is accurate. To address this problem, we introduce a new kind of game, called an inference game, and study how degrees of uncertainty of belief about payoffs impact the outcomes of real-world games. To approximate an optimal decision, our proposed inference game model can clarify how to better manage ambiguous information. In this study, we apply our inference game model to the sensor communication paradigm and confirm that our approach achieves better performance than other existing sensor communication schemes in widely diverse Internet of Things (IoT) environments.

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Jadlovská, Anna, and Kamil Hrubina. "Algorithms of optimal control methods for solving game theory problems." Kybernetes 40, no. 1/2 (March 15, 2011): 290–99. http://dx.doi.org/10.1108/03684921111118059.

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Orlando, Paul A., Robert A. Gatenby, and Joel S. Brown. "Cancer treatment as a game: integrating evolutionary game theory into the optimal control of chemotherapy." Physical Biology 9, no. 6 (November 29, 2012): 065007. http://dx.doi.org/10.1088/1478-3975/9/6/065007.

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Chen, Miao Sheng, and Yung Tse Tsai. "Strategy on Energy Capacity Control." Advanced Materials Research 512-515 (May 2012): 1227–30. http://dx.doi.org/10.4028/www.scientific.net/amr.512-515.1227.

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In the past, energy authorities attempted to prevent potential entrants from participating in the energy market. This study posits that this two-stage game theory is insufficient to describe the modern-day situation. Ware (1984) modified the Dixit (1980) model to develop a three-stage game structure. We use this mathematical model to analyze the optimal cost of an energy authority and the strategy of excess capacity.

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Wang, Si Liang. "Dynamic Flow Scheduling in Air Traffic Network Based on Game Theory." Key Engineering Materials 439-440 (June 2010): 977–82. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.977.

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Recently, many works have employed deterministic strategies in dealt with flow scheduling problem in Air traffic flow management (ATFM). In practice, however, they are proved unreasonable for omitting airline’s preference in ATFM. In this paper, we develop a novel air traffic flow control model based on game theory to solve this problem in air traffic network. In the flow model, a resource (link/time pair in air traffic network) allocation strategy that uses sequential game method to predict traffic allocation is proposed in resource sharing environment. The problem of multiple airlines competes for an optimal route is formulated as a multi-player dynamic game. Through finding the Nash equilibrium solution of the multi-player dynamic game, the optimal flow scheduling is also formed at the same time. The flow model also incorporates many key characteristics of ATFM, such as competitive airlines, allowing multiply flow control strategies and so on. Numerical simulation results show the feasibility of solving the air traffic flow control problem using game theory on the air traffic network.

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Tian, Jin, Liang Yuan, Wendong Xiao, Teng Ran, Jianbo Zhang, and Li He. "Optimal robust control with cooperative game theory for lower limb exoskeleton robot." Nonlinear Dynamics 108, no. 2 (February 10, 2022): 1283–303. http://dx.doi.org/10.1007/s11071-022-07219-7.

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Li, Bowen, Hua Li, Qiubai Sun, and Rongjian Lv. "Optimal Control of False Information Clarification System under Major Emergencies Based on Differential Game Theory." Computational Intelligence and Neuroscience 2022 (September 23, 2022): 1–19. http://dx.doi.org/10.1155/2022/7291735.

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To further study the issue of false information classification on social platforms after major emergencies, this study regards opinion leaders and Internet users as a false-information classification system and constructs three differential game models of decentralized, centralized, and subsidized decision-making based on optimal control and differential game theory. Comparison analyses and numerical simulations of optimal equilibrium strategies and the optimal benefit between opinion leaders and Internet users, the optimal trajectory and the steady-state value of the total volume of real information, and the optimal benefit of the false information clarification system are carried out. It is found that under centralized decision-making, equilibrium strategy and total benefit of opinion leaders and Internet users, system total benefit, and total volume of real information can achieve Pareto optimality. Although subsidized decision-making fails to achieve Pareto optimality, with opinion leaders providing cost subsidies for Internet users, it is possible to reach relative Pareto improvement compared with decentralized decision-making.

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FALCONE, M. "NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS." International Game Theory Review 08, no. 02 (June 2006): 231–72. http://dx.doi.org/10.1142/s0219198906000886.

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In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

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Ananyev, Boris. "About control of guaranteed estimation." Cybernetics and Physics, Volume 7, 2018, Number 1 (June 18, 2018): 18–25. http://dx.doi.org/10.35470/2226-4116-2018-7-1-18-25.

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The control problem by parameters in the course of the guaranteed state estimation of linear non-stationary systems is considered. It is supposed that unknown disturbances in the system and the observation channel are limited by norm in the space of square integrable functions and the initial state of the system is also unknown. The process of guaranteed state estimation includes the solution of a matrix Riccati equation that contains some parameters, which may be chosen at any instant of time by the first player (an observer) and the second player (an opponent of the observer). The purposes of players are diametrically opposite: the observer aims to minimize diameter of information set at the end of observation process, and the second player on the contrary aims to maximize it. This problem is interpreted as a differential game with two players for the Riccati equation. All the choosing parameters are limited to compact sets in appropriate spaces of matrices. The payoff of the game is interpreted through the Euclidean norm of the inverse Riccati matrix at the end of the process. A specific case of the problem with constant matrices is considered. Methods of minimax optimization, the theory of optimal control, and the theory of differential games are used. Examples are also given.

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Turetsky, Vladimir, and Valery Y. Glizer. "Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis." Axioms 11, no. 5 (May 5, 2022): 214. http://dx.doi.org/10.3390/axioms11050214.

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In this work, a finite-horizon zero-sum linear-quadratic differential game, modeling a pursuit-evasion problem, was considered. In the game’s cost function, the cost of the control of the minimizing player (the minimizer/the pursuer) was much smaller than the cost of the control of the maximizing player (the maximizer/the evader) and the cost of the state variable. This smallness was expressed by a positive small multiplier (a small parameter) of the square of the L2-norm of the minimizer’s control in the cost function. Parameter-free sufficient conditions for the existence of the game’s solution (the players’ optimal state-feedback controls and the game value), valid for all sufficiently small values of the parameter, were presented. The boundedness (with respect to the small parameter) of the time realizations of the optimal state-feedback controls along the corresponding game’s trajectory was established. The best achievable game value from the minimizer’s viewpoint was derived. A relation between solutions of the original cheap control game and the game that was obtained from the original one by replacing the small minimizer’s control cost with zero, was established. An illustrative real-life example is presented.

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Lisowski, Józef. "Game control methods in avoidance of ships collisions." Polish Maritime Research 19, Special (October 1, 2012): 3–10. http://dx.doi.org/10.2478/v10012-012-0016-4.

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ABSTRACT The paper introduces application of selected methods of a game theory for automation of the processes of moving marine objects, the game control processes in marine navigation and the base mathematical model of game ship control. State equations, control and state constraints have been defined first and then control goal function in the form of payments - the integral payment and the final one. Multi-stage positional and multi-step matrix, non-cooperative and cooperative, game and optimal control algorithms in a collision situation has been presented. The considerations have been illustrated as an examples of a computer simulations mspg.12 and msmg.12 algorithms to determine a safe own ship’s trajectory in the process of passing ships encountered in Kattegat Strait.

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Tamaddoni, Seyed Hossein, Saied Taheri, and Mehdi Ahmadian. "Linear Quadratic Game Theory Approach to Optimal Preview Control of Vehicle Lateral Motion." SAE International Journal of Passenger Cars - Mechanical Systems 4, no. 1 (April 12, 2011): 740–48. http://dx.doi.org/10.4271/2011-01-0963.

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Hoogendoorn, S. P., W. Daamen, Y. Shu, and H. Ligteringen. "Modeling Human Behavior in Vessel Maneuver Simulation by Optimal Control and Game Theory." Transportation Research Record: Journal of the Transportation Research Board 2326, no. 1 (January 2013): 45–53. http://dx.doi.org/10.3141/2326-07.

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Wu, Yunhua, Mohong Zheng, Mengjie He, Dawei Zhang, Wei He, Bing Hua, Zhiming Chen, and Feng Wang. "Cooperative Game Theory-Based Optimal Angular Momentum Management of Hybrid Attitude Control Actuator." IEEE Access 7 (2019): 6853–65. http://dx.doi.org/10.1109/access.2018.2890086.

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Zou, Rui, Yubin Liu, Jie Zhao, and Hegao Cai. "A Framework for Human-Robot-Human Physical Interaction Based on N-Player Game Theory." Sensors 20, no. 17 (September 3, 2020): 5005. http://dx.doi.org/10.3390/s20175005.

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In order to analyze the complex interactive behaviors between the robot and two humans, this paper presents an adaptive optimal control framework for human-robot-human physical interaction. N-player linear quadratic differential game theory is used to describe the system under study. N-player differential game theory can not be used directly in actual scenerie, since the robot cannot know humans’ control objectives in advance. In order to let the robot know humans’ control objectives, the paper presents an online estimation method to identify unknown humans’ control objectives based on the recursive least squares algorithm. The Nash equilibrium solution of human-robot-human interaction is obtained by solving the coupled Riccati equation. Adaptive optimal control can be achieved during the human-robot-human physical interaction. The effectiveness of the proposed method is demonstrated by rigorous theoretical analysis and simulations. The simulation results show that the proposed controller can achieve adaptive optimal control during the interaction between the robot and two humans. Compared with the LQR controller, the proposed controller has more superior performance.

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Chen, Zhigang, Rongwei Xu, and Yongxi Yi. "Dynamic Optimal Control of Transboundary Pollution Abatement under Learning-by-Doing Depreciation." Complexity 2020 (June 9, 2020): 1–17. http://dx.doi.org/10.1155/2020/3763684.

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This paper analyzes a dynamic Stackelberg differential game model of watershed transboundary water pollution abatement and discusses the optimal decision-making problem under non-cooperative and cooperative differential game, in which the accumulation effect and depreciation effect of learning-by-doing pollution abatement investment are taken into account. We use dynamic optimization theory to solve the equilibrium solution of models. Through numerical simulation analysis, the path simulation and analysis of the optimal trajectory curves of each variable under finite-planning horizon and long-term steady state were carried out. Under the finite-planning horizon, the longer the planning period is, the lower the optimal emission rate is in equilibrium. The long-term steady-state game under cooperative decision can effectively reduce the amount of pollution emission. The investment intensity of pollution abatement in the implementation of non-cooperative game is higher than that of cooperative game. Under the long-term steady state, the pollution abatement investment trajectory of the cooperative game is relatively stable and there is no obvious crowding out effect. Investment continues to rise, and the optimal equilibrium level at steady state is higher than that under non-cooperative decision making. The level of decline in pollution stock under finite-planning horizon is not significant. Under the condition of long-term steady state, the trajectories of upstream and downstream pollution in the non-cooperative model and cooperative model are similar, but cooperative decision-making model is superior to the non-cooperative model in terms of the period of stabilization and steady state.

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Lisowski, Józef. "Optimization-Supported Decision-Making in the Marine Game Environment." Solid State Phenomena 210 (October 2013): 215–22. http://dx.doi.org/10.4028/www.scientific.net/ssp.210.215.

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This paper analyses optimization methods and game theory to support decision making by a navigator when controlling a vessel in various real navigational situations at sea. We have demonstrated the structure of a computer system for supporting manoeuvring decisions by a navigator. Navigational situations of an optimal and game ship control have been classified. We have also described game algorithms for supporting decision-making in a form of non-cooperative and cooperative positional and matrix games, respectively. The considerations have been illustrated with a computer simulation, using the Matlab/Simulink software, of algorithms for determining safe trajectories of a vessel in a real navigational situation at sea.

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Lee, Sang Hoon, Hyeokman Kim, and Lynn Choi. "Sleep Control Game for Wireless Sensor Networks." Mobile Information Systems 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/3085408.

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In wireless sensor networks (WSNs), each node controls its sleep to reduce energy consumption without sacrificing message latency. In this paper we apply the game theory, which is a powerful tool that explains how each individual acts for his or her own economic benefit, to analyze the optimal sleep schedule for sensor nodes. We redefine this sleep control game as a modified version of the Prisoner’s Dilemma. In the sleep control game, each node decides whether or not it wakes up for the cycle. Payoff functions of the sleep control game consider the expected traffic volume, network conditions, and the expected packet delay. According to the payoff function, each node selects the best wake-up strategy that may minimize the energy consumption and maintain the latency performance. To investigate the performance of our algorithm, we apply the sleep control game to X-MAC, which is one of the recent WSN MAC protocols. Our detailed packet level simulations confirm that the proposed algorithm can effectively reduce the energy consumption by removing unnecessary wake-up operations without loss of the latency performance.

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Brock, W. A., and W. D. Dechert. "The polluted ecosystem game." Indian Growth and Development Review 1, no. 1 (April 18, 2008): 7–31. http://dx.doi.org/10.1108/17538250810868116.

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PurposeThe purpose of this paper is to address the issue of optimal management of ecosystems by developing a dynamic model of strategic behavior by users/communities of an ecosystem such as a lake, which is subject to pollution resulting from the users. More specifically, it builds a model of two ecosystems that are spatially connected.Design/methodology/approachThe paper uses the techniques of optimal control theory and game theory.FindingsThe paper uncovers sufficient conditions under which the analysis of the dynamic game can be converted to an optimal problem for a pseudo authority. It is shown that if the discount rate on the future is high enough relative to ecological self‐restoration parameters then multiple stable states appear. In this case, if the pollution level is high enough it is too costly in terms of what must be given up today to restore the damaged system. By using computational methods, the paper evaluates the relative strengths of lack of coordination, strength of ecosystem self‐cleaning forces, size of discount rates, etc.Originality/valueThe methodology as well as findings can help to devise an optimal management strategy over time for ecosystems.

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GOMOYUNOV, MIKHAIL, DMITRI KORNEV, and NIKOLAI LUKOYANOV. "GAME THEORY APPLICATIONS TO GUARANTEE OPTIMIZATION IN DYNAMICAL SYSTEMS WITH CONTROL DELAYS." International Game Theory Review 16, no. 02 (April 3, 2014): 1440010. http://dx.doi.org/10.1142/s0219198914400106.

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In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem of calculating the value of the optimal guaranteed result and constructing a positional (closed-loop) control law that ensures this result is posed. For this problem, a solution procedure based on the recurrent construction of upper convex hulls of auxiliary program functions is elaborated. Results of numerical simulations are given.

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Jin, Zengwang, Shuting Zhang, Yanyan Hu, Yanning Zhang, and Changyin Sun. "Security State Estimation for Cyber-Physical Systems against DoS Attacks via Reinforcement Learning and Game Theory." Actuators 11, no. 7 (July 16, 2022): 192. http://dx.doi.org/10.3390/act11070192.

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This paper addressed the optimal policy selection problem of attacker and sensor in cyber-physical systems (CPSs) under denial of service (DoS) attacks. Since the sensor and the attacker have opposite goals, a two-player zero-sum game is introduced to describe the game between the sensor and the attacker, and the Nash equilibrium strategies are studied to obtain the optimal actions. In order to effectively evaluate and quantify the gains, a reinforcement learning algorithm is proposed to dynamically adjust the corresponding strategies. Furthermore, security state estimation is introduced to evaluate the impact of offensive and defensive strategies on CPSs. In the algorithm, the ε-greedy policy is improved to make optimal choices based on sufficient learning, achieving a balance of exploration and exploitation. It is worth noting that the channel reliability factor is considered in order to study CPSs with multiple reasons for packet loss. The reinforcement learning algorithm is designed in two scenarios: reliable channel (that is, the reason for packet loss is only DoS attacks) and unreliable channel (the reason for packet loss is not entirely from DoS attacks). The simulation results of the two scenarios show that the proposed reinforcement learning algorithm can quickly converge to the Nash equilibrium policies of both sides, proving the availability and effectiveness of the algorithm.

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Mouada, Takieddine, Milos V. Pavic, Bojan M. Pavkovic, Sasa Z. Zivkovic, and Mirko S. Misljen. "Application of optimal control law to laser guided bomb." Aeronautical Journal 122, no. 1251 (March 13, 2018): 785–97. http://dx.doi.org/10.1017/aer.2018.10.

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ABSTRACTThe paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.

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Li, Cui Ming, Ping Yang, Jun Gong, and Wan Cai Niu. "Swarm Robotics Cooperation Collision Strategies Based on Game Theory." Applied Mechanics and Materials 328 (June 2013): 182–86. http://dx.doi.org/10.4028/www.scientific.net/amm.328.182.

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In order to solve the problems in swarm robotics cooperation collision avoiding, this study tries to design some new cooperation collision avoiding strategies based on game theory so as to establish internal cooperation mechanism for swarm robotics. Specifically it aims at addressing the control issues in the swarm robotics cooperation collision avoiding system, which are caused by environmental restraints such as obstacles, special physical limit, etc. Cournot competition model is adopted here to build the game model of swarm robotics cooperation behavior and the game model is solved to find out the optimal cooperation solution. The numerical simulation verified the effectiveness and feasibility of the cooperation strategies put up by this study.

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Tang, Xu, Dong Ye, Sha Luo, Kay-Soon Low, and Zhaowei Sun. "A Hybrid Game Strategy for the Pursuit of Out-of-Control Spacecraft under Incomplete-Information." Aerospace 9, no. 8 (August 18, 2022): 455. http://dx.doi.org/10.3390/aerospace9080455.

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This paper investigates the pursuit problem of out-of-control spacecraft under incomplete-information, and provides new ideas for the disposal of dangerous spacecraft with obstacle avoidance capability. Throughout the pursuit process, the maneuver strategy of the out-of-control spacecraft is unknown, and its possibly unconventional and irregular maneuvers may endanger the safe operation of any other spacecraft on orbit. Based on the differential game theory, complete information game strategy pairs are derived. Then, considering that the control information of the target is unavailable to the pursuer, the target’s maneuver is regarded as the disturbance item. The incomplete information game strategy is derived from the unilateral optimal cost function. Furthermore, the disturbance estimator is designed to identify the missing information of the target. The optimal hybrid game strategy is proposed as an approach to compensate the target maneuver strategy. Simulation study has been conducted and the results have validated that the missing information can be effectively estimated using the estimator. The designed hybrid game strategy can achieve rapid approach, while saving fuel consumption for on-orbit service.

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Gluzman, Mark, Jacob G. Scott, and Alexander Vladimirsky. "Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory." Proceedings of the Royal Society B: Biological Sciences 287, no. 1925 (April 22, 2020): 20192454. http://dx.doi.org/10.1098/rspb.2019.2454.

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Recent clinical trials have shown that adaptive drug therapies can be more efficient than a standard cancer treatment based on a continuous use of maximum tolerated doses (MTD). The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are administered based on the current state of tumour. But the adaptive treatment policies examined so far have been largely ad hoc. We propose a method for systematically optimizing adaptive policies based on an evolutionary game theory model of cancer dynamics. Given a set of treatment objectives, we use the framework of dynamic programming to find the optimal treatment strategies. In particular, we optimize the total drug usage and time to recovery by solving a Hamilton–Jacobi–Bellman equation. We compare MTD-based treatment strategy with optimal adaptive treatment policies and show that the latter can significantly decrease the total amount of drugs prescribed while also increasing the fraction of initial tumour states from which the recovery is possible. We conclude that the use of optimal control theory to improve adaptive policies is a promising concept in cancer treatment and should be integrated into clinical trial design.

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Zhao, Jingang. "Adaptive Dynamic Programming and Optimal Control of Unknown Multiplayer Systems Based on Game Theory." IEEE Access 10 (2022): 77695–706. http://dx.doi.org/10.1109/access.2022.3193505.

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Parlar, Mahmut, Moosa Sharafali, and Mark Goh. "Optimal control and cooperative game theory based analysis of a by-product synergy system." Journal of Cleaner Production 233 (October 2019): 731–42. http://dx.doi.org/10.1016/j.jclepro.2019.05.243.

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Hati, Saroj K., and Robert G. Lamb. "An application of game theory in the design of optimal air pollution control measures." Atmospheric Environment (1967) 21, no. 8 (January 1987): 1833–41. http://dx.doi.org/10.1016/0004-6981(87)90124-7.

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Zameer, Hashim, Ying Wang, Humaira Yasmeen, Amirhossein Akhavan Mofrad, and Rashid Saeed. "A game-theoretic strategic mechanism to control brand counterfeiting." Marketing Intelligence & Planning 36, no. 5 (August 6, 2018): 585–600. http://dx.doi.org/10.1108/mip-02-2018-0053.

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Purpose The purpose of this paper is to design a game theory based model that not only provide theoretical basis to control brand counterfeiting, but it also provide a mechanism to enhance brand revenue. Design/methodology/approach This study used the dynamic game theory of incomplete information to understand and encounter the brand counterfeiting issues. The study analyzed the economic relationship of legitimate brand, counterfeiter and consumers using mixed strategy of the dynamic game theory of incomplete information. Findings The results have indicated that brands those take countermeasures to reduce counterfeiting earn maximum revenue, even when the legitimate brands and consumers are unaware from the actions of counterfeiting firms, the legitimate brands should take countermeasures to reduce counterfeiting to earn maximum revenue, and there exists optimal anti-counterfeiting cost for the legitimate brand. Further, this study provides theoretical basis where brand managers can decide to adopt or not to adopt anti-counterfeiting strategy, and also indicate the consequences of each decision. Practical implications Based upon the findings, the study put forward valuable managerial implications. The study revealed that the legitimate brand must emphasize on the significance of taking countermeasures against counterfeiter and also, brand managers should focus on making product traceable, empowering the consumer and ensuring coordination with government officials to control the counterfeiting issues. Originality/value This paper incorporates the role of legitimate brand, counterfeiter and a consumer to establish the dynamic game theory model using mixed strategy to understand and address the counterfeiting issues in the global market.

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Lisowski, Józef. "Computational Intelligence in Marine Control Engineering Education." Polish Maritime Research 28, no. 1 (March 1, 2021): 163–72. http://dx.doi.org/10.2478/pomr-2021-0015.

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Abstract This paper presents a new approach to the existing training of marine control engineering professionals using artificial intelligence. We use optimisation strategies, neural networks and game theory to support optimal, safe ship control by applying the latest scientific achievements to the current process of educating students as future marine officers. Recent advancements in shipbuilding, equipment for robotised ships, the high quality of shipboard game plans, the cost of overhauling, dependability, the fixing of the shipboard equipment and the requesting of the safe shipping and environmental protection, requires constant information on recent equipment and programming for computational intelligence by marine officers. We carry out an analysis to determine which methods of artificial intelligence can allow us to eliminate human subjectivity and uncertainty from real navigational situations involving manoeuvring decisions made by marine officers. Trainees learn by using computer simulation methods to calculate the optimal safe traverse of the ship in the event of a possible collision with other ships, which are mapped using neural networks that take into consideration the subjectivity of the navigator. The game-optimal safe trajectory for the ship also considers the uncertainty in the navigational situation, which is measured in terms of the risk of collision. The use of artificial intelligence methods in the final stage of training on ship automation can improve the practical education of marine officers and allow for safer and more effective ship operation.

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Glizer, Valery Y. "Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game." Axioms 10, no. 3 (June 25, 2021): 132. http://dx.doi.org/10.3390/axioms10030132.

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A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

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Liu, Yang, Changfu Zong, Xiaojian Han, Dong Zhang, Hongyu Zheng, and Chunmei Shi. "Spacing Allocation Method for Vehicular Platoon: A Cooperative Game Theory Approach." Applied Sciences 10, no. 16 (August 12, 2020): 5589. http://dx.doi.org/10.3390/app10165589.

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Recently, spacing policies of the vehicular platoon have been widely developed to enhance safety, traffic efficiency, and fuel consumption. However, the integrated spacing policies aim to maximum overall benefit, and the distributed spacing policies intense to get optimal monomer benefit. Ignoring the fairness of the benefit allocation of each vehicle will reduce the motivation to constitute the platoon. To fill this critical gap, this study proposes a spacing allocation method by treating spacing decisions as cooperative games. A flock’s model which is used to be the payoff function is introduced based on bionic motion principles. We present a characteristic function of the platoon for the cooperative game model considering the specific structure of the platoon. The τ value, Shapley value, and average lexicographic value are introduced and applied to allocate the spacing fairly. Proposed methods are compared with constant distance policy in some typical situations. The simulation results demonstrate that the spacing policy based on cooperative game theory improved the stable time for consistency control and the convergence of longitudinal following error.

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Cui, Rongxin, Ji Guo, and Bo Gao. "Game theory-based negotiation for multiple robots task allocation." Robotica 31, no. 6 (March 7, 2013): 923–34. http://dx.doi.org/10.1017/s0263574713000192.

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SUMMARYThis paper investigates task allocation for multiple robots by applying the game theory-based negotiation approach. Based on the initial task allocation using a contract net-based approach, a new method to select the negotiation robots and construct the negotiation set is proposed by employing the utility functions. A negotiation mechanism suitable for the decentralized task allocation is also presented. Then, a game theory-based negotiation strategy is proposed to achieve the Pareto-optimal solution for the task reallocation. Extensive simulation results are provided to show that the task allocation solutions after the negotiation are better than the initial contract net-based allocation. In addition, experimental results are further presented to show the effectiveness of the approach presented.

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Al-Mutairi, Mubarak S. "Fuzzy Optimal Approaches to 2-P Cooperative Games." International Journal of Applied Industrial Engineering 3, no. 2 (July 2016): 22–35. http://dx.doi.org/10.4018/ijaie.2016070102.

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In game theory, two or more parties need to make decisions with fully or partially conflicting objectives. In situations where reaching a more favourable outcome depends upon cooperation between the two conflicting parties, some of the mental and subjective attitudes of the decision makers must be considered. While the decision to cooperate with others bears some risks due to uncertainty and loss of control, not cooperating means giving up potential benefits. In practice, decisions must be made under risk, uncertainty, and incomplete or fuzzy information. Because it is able to work well with vague, ambiguous, imprecise, noisy or missing information, the fuzzy approach is effective for modeling such multicriteria conflicting situations. The well-known game of Prisoner's Dilemma, which reflects a basic situation in which one must decide whether to cooperate or not with a competitor, is systematically solved using a fuzzy approach. The fuzzy procedure is used to incorporate some of the subjective attitudes of the decision makers that are difficult to model using classical game theory. Furthermore, it permits researchers to consider the subjective attitudes of the decision makers and make better decisions in subjective, uncertain, and risky situations.

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Hamadène, S., R. Martyr, and J. Moriarty. "A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time." Advances in Applied Probability 51, no. 2 (June 2019): 425–42. http://dx.doi.org/10.1017/apr.2019.19.

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AbstractIn this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

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Kasarapu, Sreenitha, Rakibul Hassan, Houman Homayoun, and Sai Manoj Pudukotai Dinakarrao. "Scalable and Demography-Agnostic Confinement Strategies for COVID-19 Pandemic with Game Theory and Graph Algorithms." COVID 2, no. 6 (June 17, 2022): 767–92. http://dx.doi.org/10.3390/covid2060058.

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In the past, epidemics such as AIDS, measles, SARS, H1N1 influenza, and tuberculosis caused the death of millions of people around the world. In response, intensive research is evolving to design efficient drugs and vaccines. However, studies warn that new pandemics such as Coronavirus (COVID-19), variants, and even deadly pandemics can emerge in the future. The existing epidemic confinement approaches rely on a large amount of available data to determine policies. Such dependencies could cause an irreversible effect before proper strategies are developed. Furthermore, the existing approaches follow a one-size-fits-all control technique, which might not be effective. To overcome this, in this work, we develop a game-theory-inspired approach that considers societal and economic impacts and formulates epidemic control as a non-zero-sum game. Further, the proposed approach considers the demographic information that provides a tailored solution to each demography. We explore different strategies, including masking, social distancing, contact tracing, quarantining, partial-, and full-lockdowns and their combinations, and present demography-aware optimal solutions to confine a pandemic with minimal history information and optimal impact on the economy. To facilitate scalability, we propose a novel graph learning approach, which learns from the previously obtained COVID-19 game outputs and mobility rates of one state (region) depending on the other to produce an optimal solution. Our optimal solution is strategized to restrict the mobility between states based on the impact they are causing on COVID-19 spread. We aim to control the COVID-19 spread by more than 50% and model a dynamic solution that can be applied to different strains of COVID-19. Real-world demographic conditions specific to each state are created, and an optimal strategic solution is obtained to reduce the infection rate in each state by more than 50%.

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Wang, Hongbo. "Enhancing vehicle suspension system control performance based on the improved extension control." Advances in Mechanical Engineering 10, no. 7 (July 2018): 168781401877386. http://dx.doi.org/10.1177/1687814018773863.

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Vehicle suspension system is the key part in vehicle chassis, which has influence on the vehicle ride comfort, handling stability, and security. The extension control, which is not constrained by common control method, could further improve the suspension system performance. The 7 degree-of-freedom suspension model is built. The extension controller is designed according to the function differences. In different extension set domains according to the correlation function, the corresponding control strategy is designed to ensure the suspension system obtains optimal performance in the classical domain and expands the controllable range outside the classical domain as large as possible. By adopting game theory, the domain is optimally divided, and the domain boundary control jump is smoothed by introducing Takagi–Sugeno–Kang fuzzy control into the extension control. Through the simulation and results comparison, it is demonstrated that the extension control could further improve the vehicle ride comfort than the optimal control and the extension control ability can be further promoted through domain game and Takagi–Sugeno–Kang fuzzy control. The analysis of the influence of the extension controller parameter varieties on suspension system performance shows that the error-weighted coefficient and control coefficient have significant effect to the suspension system performance.

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Zhang, Jianliang, Yujun Li, Zhao Xu, Donglian Qi, and Chaoyong Li. "Game theory-based optimal deloading control of wind turbines under scalable structures of wind farm." IET Cyber-Physical Systems: Theory & Applications 3, no. 4 (December 1, 2018): 224–31. http://dx.doi.org/10.1049/iet-cps.2018.0027.

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Wang, Ziwen, Baichun Gong, Yanhua Yuan, and Xin Ding. "Incomplete Information Pursuit-Evasion Game Control for a Space Non-Cooperative Target." Aerospace 8, no. 8 (August 3, 2021): 211. http://dx.doi.org/10.3390/aerospace8080211.

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Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes.

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Shen, Jiajun, and Dongqin Feng. "Vulnerability Analysis of CSP Based on Stochastic Game Theory." Journal of Control Science and Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/4147251.

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With the development of industrial informatization, the industrial control network has gradually become much accessible for attackers. A series of vulnerabilities will therefore be exposed, especially the vulnerability of exclusive industrial communication protocols (ICPs), which has not yet been attached with enough emphasis. In this paper, stochastic game theory is applied on the vulnerability analysis of clock synchronization protocol (CSP), one of the pivotal ICPs. The stochastic game model is built strictly according to the protocol with both Man-in-the-Middle (MIM) attack and dependability failures being taken into account. The situation of multiple attack routes is considered for depicting the practical attack scenarios, and the introduction of time aspect characterizes the success probabilities of attackers actions. The vulnerability analysis is then realized through determining the optimal strategies of attacker under different states of system, respectively.

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Bukhalev, V. A., A. A. Skrynnikov, and V. A. Boldinov. "GAME CONTROL OF A FILTER WITH A RANDOM JUMP STRUCTURE." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 214 (April 2022): 12–19. http://dx.doi.org/10.14489/vkit.2022.04.pp.012-019.

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The game problem of synthesis of information-control algorithms of filtering of two opposing sides is considered. The opponents’ control objects are described by multidimensional linear stochastic recurrent equations. Each side controls the covariance of the output signals of its object and the covariance of additive signals in the channels of the enemy object meters. Covariances of noise signals of an object characterize the power of disturbances, and covariances of noise signals of meters characterize the power of interference.The goal of each player’s management is to reduce the filtering error of their system and at the same time increase the filtering error of the opponent’s system. The criterion of optimal control of one player is the minimax, and the other is the maximin of the average value of the quality indicator for a finite period of time. Quality indicators consist of a linear combination of three particular indicators, the first of which is the probability of one of the two states of the Markov jump structure, and the other two are restrictions on the probabilities of transitions of the Markov chain. Observation systems consist of structure indicators and meters of one-time coordinates. Each information-control algorithm is a set of five interconnected blocks: a structure classifier, a structure indicator, a regulator, a dispersiometer and a filter. The obtained information-control algorithms are described by a closed system of recurrent equations. The algorithms are based on the methods of the theory of multistep antagonistic games, the theory of systems with a random jump structure, stochastic dynamic programming and Bayesian filtering. An example of the construction of game information-control algorithms of two unmanned aerial vehicles of the opposing sides, aimed at the objects of the opponents, is considered.

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Yan, Xiang, Hongbo Li, Lide Wang, and Ping Shen. "Optimal Bandwidth Scheduling of Networked Learning Control System Based on Nash Theory and Auction Mechanism." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/540687.

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This paper addresses the optimal bandwidth scheduling problem for a double-layer networked learning control system (NLCS). To deal with this issue, auction mechanism is employed, and a dynamic bandwidth scheduling methodology is proposed to allocate the bandwidth for each subsystem. A noncooperative game fairness model is formulated, and the utility function of subsystems is designed. Under this framework, estimation of distribution algorithm (EDA) is used to obtain Nash equilibrium for NLCS. Finally, simulation and experimental results are given to demonstrate the effectiveness of the proposed approach.

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Guo, Chao, Cheng Gong, Juan Guo, Haitao Xu, and Long Zhang. "TCQG—Software-Defined Transmission Control Scheme in 5G Networks from Queuing Game Perspective." Sensors 19, no. 19 (September 26, 2019): 4170. http://dx.doi.org/10.3390/s19194170.

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The efficient processing and forwarding of big data is one of the key problems and challenges facing the next generation wireless communication network. Using a software definition method to virtualize the network can improve the efficiency of network operation and reduce the cost of network operation and maintenance. A software-defined transmission control scheme was presented to solve the excessive controller flow problem for 5G networks. Based on the queuing game theory, a system model was built due to the competition among the requests of the switch. The transmission control platform was in charge of resource allocation. It got maximum social welfare under a profit-maximizing fee. In this model, the optimal queue length was calculated and discussed in a first-come-first-served and last-come-first-served with preemption discipline. The optimal queue length was obtained and the optimal admission fee was calculated. Then, the single switch single controller transmission control model was extended to the multi-switches single controller model. As a result, the social welfare of the system containing the controller’s profit and switch surplus reaches the maximum.

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Guo, Zhenyang, Xuan Wang, Shuhan Qi, Tao Qian, and Jiajia Zhang. "Heuristic Sensing: An Uncertainty Exploration Method in Imperfect Information Games." Complexity 2020 (October 24, 2020): 1–9. http://dx.doi.org/10.1155/2020/8815770.

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Imperfect information games have served as benchmarks and milestones in fields of artificial intelligence (AI) and game theory for decades. Sensing and exploiting information to effectively describe the game environment is of critical importance for game solving, besides computing or approximating an optimal strategy. Reconnaissance blind chess (RBC), a new variant of chess, is a quintessential game of imperfect information where the player’s actions are definitely unobserved by the opponent. This characteristic of RBC exponentially expands the scale of the information set and extremely invokes uncertainty of the game environment. In this paper, we introduce a novel sense method, Heuristic Search of Uncertainty Control (HSUC), to significantly reduce the uncertainty of real-time information set. The key idea of HSUC is to consider the whole uncertainty of the environment rather than predicting the opponents’ strategy. Furthermore, we realize a practical framework for RBC game that incorporates our HSUC method with Monte Carlo Tree Search (MCTS). In the experiments, HSUC has shown better effectiveness and robustness than comparison opponents in information sensing. It is worth mentioning that our RBC game agent has won the first place in terms of uncertainty management in NeurIPS 2019 RBC tournament.

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Qing-min, Yuan, and Tan Xin. "Analysis of coordinated control of Beijing-Tianjin-Hebei smog based on evolutionary game theory." E3S Web of Conferences 248 (2021): 02030. http://dx.doi.org/10.1051/e3sconf/202124802030.

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Based on the perspective of ecological compensation and ecological claims, this paper analyzes the stability of Beijing Tianjin Hebei haze governance alliance by using asymmetric evolutionary game model, and obtains the optimal strategy combination. The results show that: a reasonable ecological compensation standard is very important for enterprises to adopt energy-saving and emission reduction strategies. Only when the total value of ecological claims in the two places is higher than the cost of energy-saving and emission reduction, enterprises will adopt energy-saving and emission reduction strategies, and the implementation of energy-saving and emission reduction strategies will not be shaken by the amount of ecological compensation.

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Nisio, Makiko. "Stochastic differential games and viscosity solutions of Isaacs equations." Nagoya Mathematical Journal 110 (June 1988): 163–84. http://dx.doi.org/10.1017/s0027763000002932.

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Recently P. L. Lions has demonstrated the connection between the value function of stochastic optimal control and a viscosity solution of Hamilton-Jacobi-Bellman equation [cf. 10, 11, 12]. The purpose of this paper is to extend partially his results to stochastic differential games, where two players conflict each other. If the value function of stochatic differential game is smooth enough, then it satisfies a second order partial differential equation with max-min or min-max type nonlinearity, called Isaacs equation [cf. 5]. Since we can write a nonlinear function as min-max of appropriate affine functions, under some mild conditions, the stochastic differential game theory provides some convenient representation formulas for solutions of nonlinear partial differential equations [cf. 1, 2, 3].

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Dey, Shawon, and Hao Xu. "Intelligent Distributed Swarm Control for Large-Scale Multi-UAV Systems: A Hierarchical Learning Approach." Electronics 12, no. 1 (December 26, 2022): 89. http://dx.doi.org/10.3390/electronics12010089.

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In this paper, a distributed swarm control problem is studied for large-scale multi-agent systems (LS-MASs). Different than classical multi-agent systems, an LS-MAS brings new challenges to control design due to its large number of agents. It might be more difficult for developing the appropriate control to achieve complicated missions such as collective swarming. To address these challenges, a novel mixed game theory is developed with a hierarchical learning algorithm. In the mixed game, the LS-MAS is represented as a multi-group, large-scale leader–follower system. Then, a cooperative game is used to formulate the distributed swarm control for multi-group leaders, and a Stackelberg game is utilized to couple the leaders and their large-scale followers effectively. Using the interaction between leaders and followers, the mean field game is used to continue the collective swarm behavior from leaders to followers smoothly without raising the computational complexity or communication traffic. Moreover, a hierarchical learning algorithm is designed to learn the intelligent optimal distributed swarm control for multi-group leader–follower systems. Specifically, a multi-agent actor–critic algorithm is developed for obtaining the distributed optimal swarm control for multi-group leaders first. Furthermore, an actor–critic–mass method is designed to find the decentralized swarm control for large-scale followers. Eventually, a series of numerical simulations and a Lyapunov stability proof of the closed-loop system are conducted to demonstrate the performance of the developed scheme.

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Knopoff, Damián A., and Germán A. Torres. "On an optimal control strategy in a kinetic social dynamics model." Communications in Applied and Industrial Mathematics 9, no. 2 (December 1, 2018): 22–33. http://dx.doi.org/10.2478/caim-2018-0014.

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Abstract Kinetic models have so far been used to model wealth distribution in a society. In particular, within the framework of the kinetic theory for active particles, some important models have been developed and proposed. They involve nonlinear interactions among individuals that are modeled according to game theoretical tools by introducing parameters governing the temporal dynamics of the system. In this present paper we propose an approach based on optimal control tools that aims to optimize this evolving dynamics from a social point of view. Namely, we look for time dependent control variables concerning the distribution of wealth that can be managed, for instance, by the government, in order to obtain a given social profile.

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Journal articles on the topic 'Game theory and optimal control'

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