Multi-phase optimal control applied to 4D business trajectory strategic planning in air traffic management

Given the sequence of phases and flight modes that represent the flight plan of a commercial aircraft, the initial and final states, and a set of path constraints, we solve the multi-phase optimal control problem of finding control inputs, switching times between flight modes and the corresponding trajectory of the aircraft that minimizes fuel consumption. The aircraft in flight is modeled as a switched dynamical system, a subclass of hybrid dynamical system, i.e., a system that has continuous and discrete variables. The structure of the flight plan is modeled with discrete variables. The 3D motion of the aircraft over a spherical earth is described by a point variable-mass dynamic model. The multi-phase optimal control problem is converted into a conventional optimal control problem, which is solved using a collocation method. This approach provides an overall optimal solution, giving the 4D business trajectory in a constraint based paradigm towards future operational concepts in Air Traffic Management (ATM).