The Research About The Barrier And Guidance Law Of Misslie Intercepting Aircraft Terminal Guidance

Along with the progress of science and technology, the maneuverability of target is increasing, so classic guidance can no longer meet the guidance precision requirement. Differential game guidance think not only missile has maneuverability but also target. This paper is based on differential game theory to study three-dimensional space missile intercepting aircraft terminal guidance. Through trajectory linearization, the original three-dimensional nonlinear free-final-time problem was transformed into two-dimensional linear fixed-final-time problem. the simplified problem is perpendicular to the line of sight. This paper has three tasks:Firstly, build differential game model of missile intercepting aircraft terminal guidance problem and simplify the model. The author established equations of motion, where the six state variables are relative displacement components, relative velocity components and missile acceleration components. Round control set was projected in the plane perpendicular to the line of sight becoming elliptical. It caused control quantity. This paper focuses on relative distance when game ends, so we choose the relative distance as cost function. This paper introduces the state transition matrix to simplify solving this problem. The simplification makes the original six dimensional state variables reduce two dimensions. New state variables are the miss distance.Secondly, use the Minimax Principle to solve the optimal control and optimal trajectory. Build Hamiltonian function for solving the optimal control. The answer consists of smooth solutions and singular solution. The optimal control was substituted in the equations to get the optimal trajectory. The barrier consists of all optimal trajectories. If cost value is smaller the minimum smooth isocost, the barrier is singular. On the contrary, it is smooth. The barrier is singular on the plane ofy20.Thirdly, construct the isocost surface based on matlab. This surface is the barrier which divided game space into capture zone and escape zone. In capture zone, the optimal trajectory can reach terminal surface and penetrate it. However, in escape zone, the optimal trajectory cannot reach the terminal surface. On the barrier, the optimal trajectory can reach terminal surface but cannot penetrate it. This paper also compare and analysis effect of time to go, acceleration amplitude ratio and missile response delay constant on capture zone and capture initial conditions.