# Optimization of Descending and Landing Trajectories of Commercial Aircraft through Optimal Control Techniques (OPTA)

Dinesh Babu Seenivasa

University of Rey Juan Carlos, Madrid, Spain

Tuesday, January 31, 2017, 11:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

In this PhD project, a solution was proposed for the problem of detecting and solving conflicts between 4D paths (3D space and time) of multiple aircraft. An example of this problem arises in the planning of multiple aircraft landing trajectories on a single runway in the presence of an obstacle, where the obstacle represents a constraint that may exist in an urban environment and situations in which it is necessary to specify Distance between aircraft landing simultaneously on adjacent runways.

In the abstract, the problem of the optimization of the landing and take-off trajectories of multiple aircraft can be considered as a restricted non-linear optimal control (OC) problem. Optimum control techniques for aircraft trajectory optimization problems involve the consideration of multiple elements, including the dynamic model of the aircraft, its aerodynamic configurations, meteorology and wind.

This main objective is addressed through 3 specific objectives, corresponding to the development of applications based on three methodologies linked to optimal control:

- Integrated Optimal Control Techniques (EOC) and with logical constraints

- Model Based Predictive Control (MPC)

- Techniques of optimum stochastic control based on Monte Carlo (MC)

The main advantage in the use of EOC techniques is that no assumption is required about the number of switching phases, i.e. they are determined by the solution of the problem. In addition, logical constraints are transformed into equality constraints and inequalities involving only continuous variables. On the other hand, MPC provides a closed-loop version of the EOC solution. MPC has been a popular approach for tracking control of system with constraints. The basic idea of MPC is to solve a finite horizon constrained optimal control problem online at each time step. Finally, to minimize the risk of loss of separation between aircraft, we must consider the uncertainty of the system as wind in the airport environment, a difficult task that can be addressed using MC-based stochastic optimization techniques, which can handle variables Such as wind. In this way, the stochastic optimum control problem becomes an affordable set of optimal deterministic control problems which in turn can be solved using traditional nonlinear programming methods, thus considerably reducing the computational complexity of finding the solution.

Regarding the objectives set out in the research plan mentioned above, in the first 20 months already three fundamental tasks have been carried out:

- Up-to-date in the state of the art on optimal control techniques

- Familiarization with Direct Collocation Techniques

- Development of preliminary results of calculation of aircraft trajectories including logic conditions using an EOC approach.

All three tasks have been performed successfully to obtain promising results from joint planning of aircraft trajectories including exclusion zones and conflict avoidance conditions. In addition, the preliminary work for the planned stay in the mobility plan to acquire advanced knowledge about MPC, subject matter of the second major objective of the plan research. After the stage period, a more realistic approach of stochastic MC control will be carry out in the third part of the PhD activity.