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Publication Hybrid Optimal Control for Aircraft Trajectory Design with a Variable Sequence of Modes(Ifac Papers Online, 2011) Kamgarpour, Maryam; Soler, Manuel; Tomlin, Claire J.; Olivares, Alberto; Lygeros, JohnThe problem of aircraft trajectory planning is formulated as a hybrid optimal control problem. The aircraft is modeled as a switched system, that is, a class of hybrid dynamical systems. The sequence of modes, the switching times, and the inputs for each mode are the control variables. An iterative bi-level optimization algorithm is employed to solve the optimal control problem. At the lower level, given a pre-de ned sequence of ight modes, the optimal switching times and the input for each mode are determined. This is achieved by extending the continuous state to include the switching times and then solving a conventional optimal control problem for the extended state. At the higher level, the algorithm modi es the mode sequence in order to decrease the value of the cost function. We illustrate the utility of the problem formulation and the solution approach with two case studies in which short horizon aircraft trajectories are optimized in order to reduce fuel burn while avoiding hazardous weather.Publication Hybrid Optimal Control Approach to Commercial Aircraft 3D Multiphase Trayectory Optimization(American Institute Of Aeronautics And Astronautics, Inc., 2010) Soler, Manuel; Olivares, Alberto; Staffetti, ErnestoGiven the sequence of phases and flights modes conforming the flight profile os a comercial aircraft, the initial and final states, a set of path constraints and real wind forecast data, we solve the multiphase problem of finding optimal control inputs, switching times between flight modes and the corresponding trajectory of the aircraft that minimizes fuel consumption. The aircraft in flight is modelled as a hybriddynamical system, i.e., a system that has contibuos and discrete dynamics, where the distinct discrete dynamics corresponds to different fight phases and swwitches betwrrn them occur either in response to control law or when the state of the system reaches prescribed regions of the state space. The three dimensional motion of the aircraft over a spherical earth is described by a point variable-mass dynamic model. The hybrid optimal control problem is converted into a conventional optimal control problem by a parameterization of the switching instants and solved using a collocation method. This approach provides an overall optimal solution for a complete fight including the optimal switching instants between phases. An application to a realistic 13-phase A-340-300 fight is solved and discussed.