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Aircraft Trajectory Optimization for Collision Avoidance Using Stochastic Optimal Control
Author(s) -
Liu Wensheng,
Liang Xuelin,
Ma Yunzhu,
Liu Weiyi
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1855
Subject(s) - trajectory , mathematical optimization , trajectory optimization , optimal control , stochastic differential equation , control theory (sociology) , computer science , markov chain , stochastic control , collision avoidance , partial differential equation , optimization problem , collision , mathematics , control (management) , mathematical analysis , physics , computer security , astronomy , artificial intelligence , machine learning
Optimizing aircraft collision avoidance and performing trajectory optimization are the key problems in an air transportation system. This paper is focused on solving these problems by using a stochastic optimal control approach. The major contribution of this paper is a proposed stochastic optimal control algorithm to dynamically adjust and optimize aircraft trajectory. In addition, this algorithm accounts for random wind dynamics and convective weather areas with changing size. Although the system is modeled by a stochastic differential equation, the optimal feedback control for this equation can be computed as a solution of a partial differential equation, namely, an elliptic Hamilton‐Jacobi‐Bellman equation. In this paper, we solve this equation numerically using a Markov Chain approximation approach, where a comparison of three different iterative methods and two different optimization search methods are presented. Simulations show that the proposed method provides better performance in reducing conflict probability in the system and that it is feasible for real applications.