Optimal time advance in terminal area arrivals: Throughput vs. fuel savings

Journal of Guidance, Control, and Dynamics

Speyer

2016

Self Cite

Among the premises of the Next Generation Air Transportation System initiative is the necessity for precision procedures in air traffic operations. Conformance with such procedures can help safety and the ability to accommodate higher traffic demand. The contribution of this paper is an algorithm for automating the process of speed control, aimed at separation assurance and conducted in current air traffic operations by human air traffic controllers. If a separation-compliant collective speed profile for the given set of aircraft exists, the algorithm computes this profile. If no such speed profile exists, the computer reports the nonexistence. Uncertainties such as weather are not considered, but the algorithm can be modified to include them. The algorithm proceeds in two stages. First, it finds an arrival sequence for the aircraft. The computational complexity of this stage is factorial in the number of aircraft but allows substantial parallelization. The second stage finds a collective speed profile for a given arrival sequence and has computational complexity that is polynomial in the number of aircraft. The algorithm is proved to find a solution whenever one exists and to ascertain nonexistence correctly. NomenclatureAy i = cone of attainability at y j d = intersection of all guiding hyperplane in the ordered set H e 2 = unit vector of the axis corresponding to aircraft 2 in the K-dimensional space, 0; 1; 0; : : : ; 0 H = ordered set of K − 1 guiding hyperplanes HPx; n = hyperplane that passes through state x with normal vector n HP Attain k 1 ;k 2 = attainability hyperplane associated with aircraft k 1 and k 2 , when aircraft k 1 is flying with its maximum speed and aircraft k 2 is flying with its minimum speed HP Sep k 1 ;k 2 = separation hyperplane associated with aircraft k 1 and k 2 , when aircraft k 1 is leading aircraft k 2 HSx; n = closed half-space for which n is the inner normal and HPx; n is the hyperplane boundary HS O x; n = open half-space for which n is the inner normal and HPx; n is the hyperplane boundary HS Attain k 1 ;k 2 = closed half-space associated with attainability hyperplane HP Attain k 1 ;k 2 HS CL Attain k 1 ;k 2

Section: A Three Aircraftmentioning

confidence: 98%

Section: A Three Aircraftmentioning

confidence: 99%

Section: Nomenclaturementioning

confidence: 99%

See 1 more Smart Citation

Existence and Determination of Separation-Compliant Speed Control in Terminal Airspace

Rezaei

Journal of Guidance, Control, and Dynamics

Speyer

2016

Self Cite

“…[2][3][4] An approach widely used in general Air Traffic Management (ATM) research is to cast the problem as a mixedinteger (non)linear program. [5][6][7][8] Since the sets of flights, waypoints, meter fixes, and route segments are finite, it is natural to think of the operational problems intuitively as discrete.…”

Section: Ia Backgroundmentioning

confidence: 99%

“…The model is similar to that in Ref. 2 but, by contrast, includes the inertia of the aircraft by treating the accelerations as the only control variables. The aforementioned tradeoff is analyzed numerically for one example (section III).…”

Section: Introductionmentioning

confidence: 97%

Separation-Compliant Time Advance in Terminal Area Arrivals: Tradeoff between Makespan and Fuel Burn

AIAA Guidance, Navigation, and Control (GNC) Conference

Fabien

2013

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The current operational practice in scheduling air traffic arriving at an airport is to adjust flight schedules by delay, i.e. a postponement of an aircraft's arrival at a scheduled location, to manage safely the FAA-mandated separation constraints between aircraft. To meet the observed and forecast growth in traffic demand, however, the practice of time advance (speeding up an aircraft toward a scheduled location) is envisioned for future operations as a practice additional to delay. Time advance has three potential advantageous capabilities: to increase the throughput of the arriving traffic, to reduce the total traffic delay when the traffic sample is below saturation density, and to save total fuel consumption (though perhaps at the expense of increasing it for some individual aircraft). A cost associated with time advance is the fuel expenditure required by an aircraft to speed up.The contribution of this paper is a simplified optimal control model of air traffic arriving in a terminal area that gives, as a first step toward time advance, qualitative insight into the interdependence between two competing objectives: saving fuel (total, for the entire air traffic operation) and reducing the duration (makespan) of the operation. The numerical solutions provided here were obtained using, for convenience, a software packaged based on the Pseudospectral Method with Legendre-Gauss-Radau collocation. Nomenclature . q the time derivative of quantity q A the number of aircraft in a given traffic sample A a finite set of A aircraft: A = {1, 2, . . . , A} α the index of an aircraft in the given sample: α ∈ A G = (V, E) a d i r e c t e d g r a p h w i t h v e r t e x s e t V and edge set E Downloaded by PURDUE UNIVERSITY on July 30, 2015 | http://arc.aiaa.org |

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

Journal of Dynamic Systems, Measurement, and Control

Davis

Isaacson

2014

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A class of problems in air traffic management (ATM) asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs (MIPs), hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the fully routed nominal problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively piecewise linear with finitely many vertices, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.