Formation Mission Design for Commercial Aircraft
In this talk, a technique to solve the formation mission design problem for commercial aircraft will be described. Given the departure times and the departure and arrival locations of several commercial flights, the relevant weather forecast, and the expected fuel savings during formation flight, the problem consists in establishing how to organize them in formation or solo flights and in finding the trajectories that minimize the overall direct operating cost of the flights. Each aircraft can fly solo or in different positions inside a formation. Therefore, the mission is modeled as a switched dynamical system, in which the discrete state describes the combination of flight modes of the individual aircraft and logical constraints in disjunctive form establish the switching logic among the discrete states of the system. The formation mission design problem has been formulated as an optimal control problem of a switched dynamical system and solved using an embedding approach, which allows switching decision among discrete states to be modeled without relying on binary variables. The resulting problem is a classical optimal control problem which has been solved using a knotting pseudospectral method. The results of several numerical experiments will be described, which demonstrate the effectiveness of this approach.
Ernesto Staffetti is an Associate Professor in System Engineering and Automation at the Rey Juan Carlos University, Madrid, Spain, where he has been since 2004. He also worked with the University of North Carolina at Charlotte, the Katholieke Universiteit Leuven, the Spanish Consejo Superior de Investigaciones Científicas, and the Universitat Politècnica de Catalunya. His research interests span robotics, astronautics and aeronautics. Much of his work has been on motion planning using optimal control techniques. In particular, he has studied the optimal control problem of stochastic switched dynamical systems. Specifically, he has explored the possibility of avoiding the use of integer of binary variables to model the switching behaviour of dynamical systems or decision-making processes in the formulation of optimal control problems. He has also investigated the possibility of employing techniques such as Generalized Polynomial Chaos and Arbitrary Polynomial Chaos for uncertainty quantification in stochastic optimal control problems. Since the COVID-19 outbreak, he has worked on modelling the SARS-CoV-2 transmission dynamics and on planning optimal vaccination and testing strategies to control the pandemic using optimal control techniques.