Trajectory Generation for Optimized Profile Descent using Hybrid Optimal Control

This paper presents the enroute descent trajectory generation method for optimized profile descent with specified arrival time constraint. Since FMS generates vertical trajectory by combining several VNAV modes, it can be modeled as a hybrid system consisting of discrete set of VNAV modes. Therefore, fuel optimal trajectory generation in FMS is the optimal control problem of hybrid system in which mode sequence is a discrete control variable as well as continuous control inputs of each mode. To solve this problem efficiently, we propose a design method to determine trajectory structure, which is a mode sequence in FMS hybrid model. Mode free fuel optimal trajectory is considered as a base trajectory. To find the best suitable mode sequence for generating similar trajectory compared with the mode free case, trajectory partitioning and mode selection scheme is proposed. By analysis of the base trajectories with various wind conditions, general VNAV mode sequence for fuel optimized profile descent is designed. The parameters of each mode are determined by solving multiple phase optimal control problem. To evaluate the method, numerical examples with B737-500 aircraft are given and performance of trajectory with designed structure is compared to mode free fuel optimal trajectory.

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