Nonlinear Impact Time Control Guidance Laws using Lyapunov Theory

Abstract

The primary objective of missile guidance is to intercept a target. However, modern warships equipped with state-of-the-art defense systems deteriorate the survivability of the anti-ship missiles. The possibility of mission achievement of anti-ship missiles can be improved by taking advantage of the vulnerability of a target or attacking a target simultaneously. In this dissertation, nonlinear guidance laws are proposed considering impact time constraints.

Two impact time control guidance (ITCG) laws are first proposed in the two-dimensional environment. Two well-known time-to-go estimation techniques are analyzed to design the ITCG laws using the Lyapunov stability theory, and then the time-to-go estimate based on proportional navigation guidance is selected as the suitable time-to-go estimation method to develop nonlinear guidance laws considering impact time constraints. The impact time error is calculated using the current time, the designated impact time, and the time-to-go estimate. A Lyapunov candidate function is dened as the square of the impact time error. The stability and the singularity of the proposed two-dimensional Lyapunov-based ITCG law are analyzed by employing the Lyapunov stability theory. Numerical simulations demonstrate the performance of the proposed two-dimensional Lyapunov-based ITCG law.

The impact time control problem is extended to the three-dimensional environment. Conventional guidance problems are dealt with in the two-dimensional environment under the assumption that the pitch channel and the yaw channel of a missile are decoupled. However, the two channels of the missile are coupled in the real engagement situation. For this reason, the three-dimensional engagement geometry without the decoupling assumption of the pitch and yaw channels is adopted to design a three-dimensional ITCG law. The proposed three-dimensional Lyapunov-based ITCG law does not have the singularity issue, either. Numerical simulations are performed to demonstrate the performance of the proposed guidance laws in the three-dimensional environment.