Nonlinear optimal impact-time-control guidance law for stationary target

Abstract

This thesis deals with the impact-time-control guidance (ITCG) law that can maintain optimality even in nonlinear engagement situations. The ITCG law improves the mission success probability against missile defense systems, so it has been utilized for the salvo attacks and cooperative attacks. The ITCG law have been developed based on various theories such as nonlinear control theory and optimal error dynamics, but the previous studies generally cannot maintain optimality in nonlinear engagement situations. In this regard, this thesis derives the characteristics of the optimal guidance command in nonlinear engagement situations and proposes an ITCG law that can maintain optimality even in nonlinear engagement situations. The optimal solution is derived as a function of the state variable through the optimal necessary condition, then the differential equation of the optimal solution is derived. Since the optimal solution is a Jacobi elliptic function, it is impossible to derive the unknown constants that satisfy the boundary conditions analytically. To this end, in this study, the ITCG law is designed analytically by modifying the previous ITCG law so that the guidance command become similar to optimal solution. The guidance command is derived so that the cosine function follows the time-to-go polynomial function which coefficients are calculated to satisfy the boundary constraints while maintaining optimality. Through the numerical simulations and comparison between optimization results, the validity of the proposed ITCG law is verified.