A Pseudospectral Model Predictive Solution to Midcourse Guidance for Multistage Interceptor

This paper presents an enhanced pseudospectral model predictive static programming (EPS-MPSP) approach to address the midcourse guidance problem for an endoatmospheric multistage interceptor. The proposed algorithm incorporates a nonlinear, state-dependent cost function to maximize terminal velocity while solving a multi-phase optimization problem featuring interior-point constraints and free coasting time. Compared to convex optimization or conventional MPSP methods, contributions of the proposed approach are threefold: 1) it employs a variational linearization technique to handle complex multi-phase optimization, significantly improving computational efficiency; 2) it implicitly treats interior-point constraints and eliminates state variables during the process, reducing the number of the optimization variables; and 3) it establishes a direct relationship between the state-dependent performance index and the control protocol, obviating the need for partial derivative computations of intermediate variables. The performance of the method is demonstrated through its application to a midcourse guidance scenario that involves a two-stage interceptor. Numerical results show that the proposed approach delivers optimal solutions with high computational efficiency and robustness, accommodating both specified and free terminal time conditions, as well as uncertainties in the operational environment.