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# Multiphase Optimal Control Framework for Commercial Aircraft Four-Dimensional Flight-Planning Problems

Published Online:https://doi.org/10.2514/1.C032697

The calculation of a flight plan involves the consideration of multiple elements. They can be classified as either continuous or discrete, and they can include nonlinear aircraft performance, atmospheric conditions, wind forecasts, airspace structure, amount of departure fuel, and operational constraints. Moreover, multiple differently characterized flight phases must be considered in flight planning. The flight-planning problem can be regarded as a trajectory optimization problem. A natural way to address a trajectory optimization problem is using optimal control techniques. The multiphase nature of the problem and the nonlinear dynamics of the aircraft lead to the formulation of a multiphase optimal control problem. A Hermite–Simpson collocation method is employed to transcribe the infinite-dimensional optimal control problem into a finite-dimensional optimization one, which is solved using a nonlinear programming solver. An application to the optimal takeoff weight, minimum fuel consumption trajectory planning problem is presented. Aircraft performances, flight procedures, and the resulting fuel consumption are analyzed. The problem is also solved for different takeoff weights and different cost indices. Their effects in the optimal performances are presented and discussed.

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