Guidance law with terminal time constraint using lyapunov stability theorem

Abstract

This paper proposes the nonlinear guidance laws satisfying terminal time constraint for two- and three-dimensional problems. A salvo attack problem of missiles and a formation flight problem of UAVs are considered for two- and three-dimensional cases, respectively. In two-dimensional problem, each missile should simultaneously impact the target at a designated impact time to enhance the survivability of the anti-ship missile group against CIWS. In three-dimensional problem, also, UAVs have to precisely complete the desired formation shape at a specified formation time and maintain the formation shape. To derive the guidance law, appropriate Lyapunov function candidates, i.e., positive definite function consisting of an expected terminal collision error and the zero-effort-miss, are selected for each problem. The guidance commands are finally determined to ensure the negative definiteness of the time derivative of the proposed Laypunov function. The previous guidance laws to control impact time in two-dimensional case are mostly derived by solving the optimal control problem based on the linearized governing equation under the small angle assumption. Hence, the time-to-go estimation process is basically required for real application and the guidance performance depends on the accuracy of the time-to-go estimation. However, this main drawback is eliminated in the guidance law proposed in this paper because it is obtained by using Lyapunov stability theorem and directly applied the full nonlinear governing equation. Furthermore, the proposed guidance law for salvo attack to impact a stationary target at the designated impact time is also extended to a slowly moving target. The guidance law for three-dimensional problem, i.e, formation flight of UAVs, is determined in the similar manner as two-dimensional problem and its final guidance command is a velocity vector. The velocity vector command can be easily transformed into the typical autopilot commands of an UAV...