Exoatmospheric optimal midcourse guidance law with coasting phase optimization using linear Gauss pseudospectral model predictive control

This paper proposes an optimal midcourse guidance law for exoatmospheric interception with coasting phase, based on Linear Gauss Pseudospectral Model Predictive Control (LGPMPC). The introduction of coasting phase renders the guidance problem a challenging multi-phase nonlinear optimal control problem with free phase-switching points. To address this challenge, a decoupling approach decomposes the original problem into two subproblems: optimizing the interstage coasting time and the midcourse guidance commands. First, zero-effort interception conditions are employed to derive the desired burnout velocity using the quadratic fitting of gravitational acceleration difference. Second, the interceptor’s zero-effort flight states are also derived analytically to formulate the optimal condition and its analytical gradient, which minimize the deviation between the desired and zero-effort burnout relative velocities. Then, a univariate iterative algorithm is proposed for determining the optimal interstage coasting time with high efficiency. Next, LGPMPC is applied to solve the optimal midcourse guidance problem with the optimal interstage coasting time so as to obtain the analytical optimal guidance commands on the space of orthogonal polynomial. Finally, numerical simulations are conducted to demonstrate the validity of the proposed decoupling method. Comparative and Monte Carlo simulations are performed to validate the optimality, efficiency, and robustness of the proposed method.