Entry Trajectory Optimization by Second-Order Cone Programming

Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming. This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight. The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem. Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization. This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques. Rigorous analysis is conducted to support the soundness of the approach. Numerical demonstrations are provided to show the efficacy and effectiveness of the proposed method.