A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strate...A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated.Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss(ZEM) distance between the attacker and the target is the smallest.After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.展开更多
In practical combat scenarios,Hypersonic Glide Vehicles(HGV)face the challenge of evading Successive Pursuers from the Same Direction while satisfying the Homing Constraint(SPSDHC).To address this problem,this paper p...In practical combat scenarios,Hypersonic Glide Vehicles(HGV)face the challenge of evading Successive Pursuers from the Same Direction while satisfying the Homing Constraint(SPSDHC).To address this problem,this paper proposes a parameterized evasion guidance algorithm based on reinforcement learning.The three-player optimal evasion strategy is firstly analyzed and approximated by parametrization.The switching acceleration command of HGV optimal evasion strategy considering the upper limit of missile acceleration command is analyzed based on the optimal control theory.The terminal miss of HGV in the case of evading two missiles is analyzed,which means that the three-player optimal evasion strategy is a linear combination of two one-toone strategies.Then,a velocity control algorithm is proposed to increase the terminal miss by actively controlling the flight speed of the HGV based on the parametrized evasion strategy.The reinforcement learning method is used to implement the strategy in real time and a reward function is designed by deducing homing strategy for the HGV to approach the target,which ensures that the HGV satisfies the homing constraint.Experimental results demonstrate the feasibility and robustness of the proposed parameterized evasion strategy,which enables the HGV to generate maximum terminal miss and satisfy homing constraint when facing single or double missiles.展开更多
This paper investigates a new approach for a scenario in which an Attacker attempts to intercept a defended aerial Target. The problem is formulated as a game among three players, an Attacker, a Defender, and a Target...This paper investigates a new approach for a scenario in which an Attacker attempts to intercept a defended aerial Target. The problem is formulated as a game among three players, an Attacker, a Defender, and a Target, with bounded controls. In the considered pursuit–evasion problem, the Target uses an optimal evasion strategy and the Defender uses an optimal pursuit strategy.The proposed approach focuses on the miss distance as the outcome of the conflict. The infeasible region for the initial Zero-Effort-Miss（ZEM） distance between the Attacker and the Defender, for a scenario in which the Attacker evades the Defender, is analyzed, assuming that the Attacker uses a control effort chosen from the permitted control region. The sufficient conditions are investigated under which, for ideal players, the Attacker can pursue the Target while evading the Defender launched by the Target. The guidance provided on how the Attacker can accomplish the task is divided into two parts. During the final time between the Attacker and the Defender, the Attacker chooses the control effort that guarantees the miss distance, and then uses the optimal pursuit strategy to accomplish the task. The derived guidance law is verified by nonlinear simulation.展开更多
This paper considers the autonomous racing of three cars,including a team of two cars and an opponent car.To handle it,the competition is modeled as a two-leader one-follower Stackelberg game to obtain the optimal str...This paper considers the autonomous racing of three cars,including a team of two cars and an opponent car.To handle it,the competition is modeled as a two-leader one-follower Stackelberg game to obtain the optimal strategies for each car.In the sequential game,all the cars maximise their progress while avoiding collisions.In the blocking game,blocking behaviours are taken into account by adding a reward to the payoff function.Through successful collaboration,actions are more aggressive in the second game.Given that the Stackelberg equilibrium is not unique in both games,the cost functions are designed for the players to cope with multiple strategies that have the same progress.The competitions are performed in a receding horizon fashion,and the aim of the research is to study the effects of cooperation and make the team have successful blocking behaviours under constraints as well as speed disadvantages.展开更多
基金supported by the National Natural Science Foundation of China(11672093)
文摘A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated.Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss(ZEM) distance between the attacker and the target is the smallest.After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.
基金supported by the National Natural Science Foundation of China(No.62103014)。
文摘In practical combat scenarios,Hypersonic Glide Vehicles(HGV)face the challenge of evading Successive Pursuers from the Same Direction while satisfying the Homing Constraint(SPSDHC).To address this problem,this paper proposes a parameterized evasion guidance algorithm based on reinforcement learning.The three-player optimal evasion strategy is firstly analyzed and approximated by parametrization.The switching acceleration command of HGV optimal evasion strategy considering the upper limit of missile acceleration command is analyzed based on the optimal control theory.The terminal miss of HGV in the case of evading two missiles is analyzed,which means that the three-player optimal evasion strategy is a linear combination of two one-toone strategies.Then,a velocity control algorithm is proposed to increase the terminal miss by actively controlling the flight speed of the HGV based on the parametrized evasion strategy.The reinforcement learning method is used to implement the strategy in real time and a reward function is designed by deducing homing strategy for the HGV to approach the target,which ensures that the HGV satisfies the homing constraint.Experimental results demonstrate the feasibility and robustness of the proposed parameterized evasion strategy,which enables the HGV to generate maximum terminal miss and satisfy homing constraint when facing single or double missiles.
基金supported by the National Natural Science Foundation of China (No. 11672093)Shanghai Aerospace Science and Technology Innovation Foundation of China (No. SAST2016039)
文摘This paper investigates a new approach for a scenario in which an Attacker attempts to intercept a defended aerial Target. The problem is formulated as a game among three players, an Attacker, a Defender, and a Target, with bounded controls. In the considered pursuit–evasion problem, the Target uses an optimal evasion strategy and the Defender uses an optimal pursuit strategy.The proposed approach focuses on the miss distance as the outcome of the conflict. The infeasible region for the initial Zero-Effort-Miss（ZEM） distance between the Attacker and the Defender, for a scenario in which the Attacker evades the Defender, is analyzed, assuming that the Attacker uses a control effort chosen from the permitted control region. The sufficient conditions are investigated under which, for ideal players, the Attacker can pursue the Target while evading the Defender launched by the Target. The guidance provided on how the Attacker can accomplish the task is divided into two parts. During the final time between the Attacker and the Defender, the Attacker chooses the control effort that guarantees the miss distance, and then uses the optimal pursuit strategy to accomplish the task. The derived guidance law is verified by nonlinear simulation.
基金supported by the National Science and Technology Major Project under grant 2022ZD0119702the National Natural Science Foundation of China under Grant 62103305,62088101,U23B2059the Shanghai Municipal Science and Technology Major Project,No.2021SHZDZX0100.
文摘This paper considers the autonomous racing of three cars,including a team of two cars and an opponent car.To handle it,the competition is modeled as a two-leader one-follower Stackelberg game to obtain the optimal strategies for each car.In the sequential game,all the cars maximise their progress while avoiding collisions.In the blocking game,blocking behaviours are taken into account by adding a reward to the payoff function.Through successful collaboration,actions are more aggressive in the second game.Given that the Stackelberg equilibrium is not unique in both games,the cost functions are designed for the players to cope with multiple strategies that have the same progress.The competitions are performed in a receding horizon fashion,and the aim of the research is to study the effects of cooperation and make the team have successful blocking behaviours under constraints as well as speed disadvantages.
