Aircraft trajectory optimization for collision avoidance using stochastic optimal control. (English) Zbl 1432.93383
Summary: 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.
MSC:
| 93E20 | Optimal stochastic control |
| 93C95 | Application models in control theory |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 90B20 | Traffic problems in operations research |
Keywords:
aircraft collision avoidance; aircraft traffic management; Markov chain approximation; stochastic differential equation; stochastic optimal control; successive over-relaxation iterationReferences:
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