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In this research, we consider the commercial aircraft trajectory optimizationproblem for a general cruise model with arbitrary spatial wind fields to besolved using the Pontryagin maximum principle. The model features twofundamental controls, namely, throttle setting (which appears as a singularcontrol) and heading angle (appearing as a regular control). For a constrainedproblem with minimum time-fuel objective, we show that the optimal headingangle is fully defined through the classic Zermelo navigation identity. We alsoshow that the optimal throttle setting can be characterized through a completefeedback function. The switching-point algorithm is employed to solve a casestudy where we inspect the optimality conditions and graph the optimal controlstogether with the optimal state and co-state variables.

Time-Fuel-Optimal Navigation of a Commercial Aircraft in Cruise with Heading and Throttle Controls using Pontryagin's Maximum Principle