Finding the optimal entry trajectory with maximum peak normal load is important to assess the maneuverability of hypersonic glide vehicles for mission flexibility and large footprint generations. This paper investigates the utilization of mixed-integer programming methods for solving the problem of maximum-normal-load entry trajectory optimization under the heat rate and dynamic pressure constraints. The maximum-normal-load entry problem is formulated as a nonconvex discrete-event optimal control problem subject to various state and control constraints, path constraints, and terminal constraints. A Big-M method is used to relax the problem into a mixed-integer nonlinear programming problem, which is proved to be equivalent to the original MaxMax problem. Through successive convex approximations of the nonlinear dynamics and nonconvex path constraints, a sequential mixed-integer convex programming method is developed to find the solution. There are efficient mixed-integer convex programming solvers that can solve each relaxed subproblem with a global optimum if the feasible set of the subproblem is nonempty. The convergence of the proposed methodology is demonstrated by numerical simulations.
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