Bi-Level Optimal Control Algorithm for Climate Optimized Cruise Trajector

Abstract

In the year 2050, global anthropogenic radiative forcing from aircraft emissions are projected to increase significantly. Recent studies have considered climate optimized flight trajectories to be a promising measure to mitigate non-CO2 emissions’ environmental impact, which is highly sensitive to locus and time of emissions. Estimating the maximum mitigation potential from these trajectories requires accounting of air traffic regulations. As designing regulated climate optimal trajectories necessitates solving a hybrid optimal control system with unknown mode sequence and associated switching times, there is a need to build an efficient and systematic control technique. In this thesis, a bi-level optimal control algorithm is proposed for designing climate optimal cruise trajectories, the lower level calculates the optimal switching times and control
inputs of a fixed mode sequence and, the upper level updates the mode sequence with mode insertion which lower the cost locally. The problem for trajectory optimization is formulated here as a hybrid optimal control problem with a switched system and with a variable mode sequence, where step-climb and descent modes are included in the mode sequence. Optimal Control problems for minimizing operating cost and climate cost with fictitious climate cost functions (CCF), varying with altitude, are solved to study the performance of the algorithm. The algorithm is implemented within the Trajectory Optimization Module (TOM) by building a bi-level framework. The framework was validated by solving the operating cost optimal control problem. The maximum error between the cost reduction estimated by the algorithm and the actual cost reduction was found to be less than 15%. With high probability it can be stated that the bi-level framework is able to calculate an optimal mode sequence as the framework allow for zero entry modes in the mode sequence i.e. modes of zero duration. Although, careful consideration is required while selecting a mode for insertion as the framework is highly dependent on the sequence of the set of modes.

Despite a satisfactory performance of the bi-level optimal control technique there are few challenges which limits the scope of this technique. The maximum error was found to increase for optimal control problems with AirClim CCFs. The dependence of the AirClim CCFs on position of the aircraft influences the locus of the trajectory at each flight level. Because of this the the trajectories calculated in each iteration of the framework are found to be inconsistent. A flight trajectory guided by waypoints is proposed as a solution for future studies to handle the inconsistency between trajectories. As future studies are expected to focus on finding optimal mode definitions for designing climate optimal trajectories, the bi-level optimal control algorithm can act as an intermediary tool with which the researchers can systematically investigate cost benefits along the trajectories.