The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainl...The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.展开更多
This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential ra...This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.展开更多
In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set o...In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set of the mixed strategy.Using dual theory and robust optimization technique,we obtain a result that the counterpart of the primitive uncertainty with ellipsoidal norm for each player can be formulated as a second-order cone programming(SOCP)and solving the corresponding equilibrium can be converted to solving a second-order cone complementarity problem(SOCCP).Then we present a numerical experiment to illustrate the behavior of robust cooperative dual equilibrium.展开更多
Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardseq...Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.展开更多
基金supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences(XDA27030100)National Natural Science Foundation of China(72293575, 11832001)。
文摘The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.
基金Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093)。
文摘This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.
基金supported by Ministry of Education Planning Fund granted 15YJA790043Guangdong Province Education Department Foundation granted 2016WTSCX079
文摘In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set of the mixed strategy.Using dual theory and robust optimization technique,we obtain a result that the counterpart of the primitive uncertainty with ellipsoidal norm for each player can be formulated as a second-order cone programming(SOCP)and solving the corresponding equilibrium can be converted to solving a second-order cone complementarity problem(SOCCP).Then we present a numerical experiment to illustrate the behavior of robust cooperative dual equilibrium.
基金National Natural Science Foundation of China Under Grants No. 50508003 and No.50478042, and A Municipal New Star Plan Program Approved by Beijing Municipal Science & Technology Commission
文摘Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.
