Polynomial Based Impact-Time-Control Guidance Law Integrating Optimal Characteristics

This paper proposes a polynomial based impacttime-control guidance (ITCG) law designed to retain a degree of optimality in target interception. Building on previous research, the proposed ITCG command is formulated such that the cosine of the lead angle adheres to a time-to-go polynomial, ensuring compliance with impact time constraints. To further enhance optimality, optimal characteristics are integrated into the time-to-go polynomial function. These characteristics are derived using optimal control theory, resulting in an optimal solution represented as a Jacobi elliptic function with respect to the time. Its validation is confirmed through the comparisons with direct optimization results. This approach avoids common approximations, such as the small angle assumption without need for numerical methodologies. Numerical simulation results demonstrate that the proposed ITCG law effectively achieves target interception within the desired impact time while preserving a degree of optimality.