Border Defense Pursuit Differential Game Model And Its Inverse Metho

In recent years,with the complex changes in the world situation,boundary security issues have become a hot spot of concern for all countries.Traditional human protection systems can no longer meet the demands of complex tasks.Intelligent,unmanned,and clustered boundary defense systems have become a new research direction for scholars.This paper examines the boundary defense problem from both forward and inverse perspectives by establishing a multi-player boundary defense pursuit-evasion differential game model,using geometric methods,Hamilton function method,inverse differential game theory,and inverse reinforcement learning methods.For small moving targets with flexible steering and strong maneuverability,this paper has established the first type of boundary defense pursuit-evasion differential game model.The simple motion is used to describe the motion of the local people,the general equation form of the quadratic curve is used to describe the shape of the boundary,and the payment function is defined as the distance from the capture point to the boundary.By studying the problem through geometric methods,a more concise form of the value function is obtained in the case of the circular boundary,and the optimal strategy of the player is constructed.On the basis of the circular boundary,a general algorithm for the case of the conic boundary is further obtained.Finally,the model is perfected from two-dimensional to three-dimensional,from multiple people chasing one person to multiple people chasing multiple people,and the conclusions and algorithms are verified by numerical simulation.For large moving targets with limited steering and weak maneuverability,this paper has established a second type of boundary defense pursuit-evasion differential game model.Using the linear constant system state equation to depict the player’s movement,using the general equation form of the quadratic curve to depict the boundary shape,respectively define the pursuer and evader payment function,the payment function consists of the distance of the evader from the boundary,the distance between the pursuer and evader,and the control energy term.This paper uses the Hamilton function method to construct the Hamilton function.According to Hamilton’s first-order optimality condition,the two-point boundary value problem(TPBVP)of the boundary defense differential game model is given in combination with the determination conditions,and numerical solutions are used to verify the correctness of the built model and the solution method.On the basis of solving the forward differential game problem,this paper examines the inverse model.For players with a payment function structure,the inverse algorithm is proposed in this paper.The algorithm converts the problem of solving the parameters of the payment function into the problem of solving the linear quadratic optimization,and obtains the information of the player payment function by solving the optimization problem.For players without a payment function structure,this paper trains the neural network to obtain the player’s payment function information by establishing an inverse deep reinforcement learning model and using the observed player motion trajectory and control trajectory as input.On the basis of obtaining payment function information,this paper establishes an inverse intervention algorithm to achieve the goal of faster capture of evader by inverse intervention of evader’s payment function.Finally,the feasibility and accuracy of the algorithm are verified by numerical simulation examples.This paper hopes to solve intelligent boundary defense problems such as aerial drone clusters and ground robot clusters from theory and algorithms through the investigation of the above-mentioned problems,and provide new ideas for solving boundary crossing,drug trafficking,smuggling and other problems.