Peak-heat-flux entry test trajectory optimization by disjunctive programming

To evaluate the heat performance of the lifting-body entry vehicle during the hypersonic gliding phase, entry flight heat tests involving the determination of the maximum peak-heat-flux entry trajectory with complex constraints are essential. A significant obstacle is the uncertainty of passage time or energy states of the maximum peak entry heat flux point and waypoints. This paper showcases an endeavour to leverage disjunctive programming and combinatorial theory for the max-max type (maximum peak-heat-flux) Entry Trajectory Optimization (ETO) problems with complex constraints such as dynamic pressure, normal load, waypoints, and no-fly zones. The concept of a “generalized waypoint” is introduced, and the maximum peak-heat-flux point is regarded as a “generalized waypoint”. Through the application of propositional calculus rules, the derivation of generalized waypoints incorporating various physical quantities and magnitudes such as heat flux density, longitude, and latitude is actualized in one disjunctive normal form, enabling resolution via a unified method. Consequently, a novel method based on combinatorial prior rules is proposed, utilizing Successive Mixed-Integer Nonlinear Programming (SMINLP) to optimize various heat entry test flight trajectories. Numerical experiments are provided to show the computational accuracy, stability, and adaptability of the proposed method in solving max-max type entry optimal control problems.