Pontryagin Principle Applied to Commercial Aircrafts Optimal Control Problem Under Physical and Energetic Constraints

The objective of this work is the development of a control and optimization flight paths model minimizing fuel consuption and noise perceived on the ground for two aircraft when flight constraints are considered. Flight dynamics, combined with the criterion to minimize noise levels generates an optimal control problem governed by nonlinear differential equations . This problem is solved using an indirect method applying the minimum principle of Pontryagin and a dynamic programming method. Obtained optimal results showed significant reductions of fuel consumption and noise levels. This model shows and confirm environmental Approach impact around airport by reduction of the gene for neighbors due to noise. Reduction of Economic cost to airlines and for builders are also confirmed. An optimal approach path when compared to standard flight path is confirmed.This model can be generalized for any type of aircraft when considering real case for airport trafic and air traffic.