Hyperbolic tangent function weighted optimal intercept angle guidance law

In this paper, a new optimal guidance law with terminal constraints on miss distance and intercept angle is proposed for a missile with time-varying velocity against a maneuvering target. The proposed optimal guidance law is obtained by solving a linear quadratic optimal control problem. Miss distance and intercept angle costs are weighted by variants of hyperbolic tangent function and energy cost is weighted by a power of time-to-go. The rule for determining a key parameter in the variant of hyperbolic tangent function is studied using the theory of second order differentiation, and its validity is verified by numerical simulation. In the purpose of easy implementation, an analytical solution of the proposed optimal guidance law is derived using assumption of constant velocity when calculating integral of missile's velocity from current time to final time. The significant contribution of this paper lies in that it is the first time a variant of hyperbolic tangent function is developed and employed as weighting coefficients of constraints on miss distance and intercept angle. Therefore, the proposed optimal guidance law can reduce acceleration command at the initial phase and increase missile's terminal velocity. Nonlinear numerical simulations clearly demonstrate effectiveness of the proposed optimal guidance law.