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We examine the potential for a simple auction to allocate arrival slots during Ground Delay Programs (GDPs) more efficiently than the currently used system. We find that the second-price slot auction has the potential to lower social costs but further analysis is needed to determine which pre-GDP schedules are best suited for an auction. The analysis of these auctions uses Predictive Game Theory (PGT) Wolpert and Bono (2013, 2010), a new approach that produces a probability distribution over strategies instead of an equilibrium set. Furthermore, the slot auction game of this paper represents the first application of PGT to a game of imperfect information and to a pure strategy space.

The success of the Next Generation Air Transportation System (NextGen), relies strongly on the adoption of new technologies and operational procedures by airlines and operators. The adoption of technologies by one airline may depend on the decisions of other airlines as well as their perception of future benefits, uncertainty over other operators’ equipage decisions, uncertainty over the NextGen implementation timeline, asymmetry of benefits across stakeholders, and the availability of capital. Policies that affect these factors could be used to incentivize certain airline behaviors and redistribute the benefits of equipage. In order to motivate and justify such large NextGen technology implementation programs and sub-capabilities, system-level analyses of the NAS are heavily relied upon. However, there are shortcomings to current modeling techniques: (1) analyses are often treated deterministically and (2) strategic interactions between players that influence system level equipage are neglected, if not ignored. This paper presents the ongoing development of Air Carrier Behavioral Modeling techniques and their application to a test case, i.e., the implementation and equipage dynamics of Automatic Dependent Surveillance-Broadcast (ADS-B) in the high altitude Gulf of Mexico (GoMex) airspace. Game theoretic modeling and evaluation is discussed for ADS-B equipage behaviors of two airlines in the GoMex, under a best-equipped, best-served policy scenario. Using a Level-K solution concept, airline equipage rates are found to be sensitive to the airline’s own strategic level and operating costs, as well as its prediction of other airlines’ strategic level.

Airbreathing hypersonic systems offer distinct performance advantages over rocket-based systems for space access vehicles. Realization of this potential performance gain will require optimum integration of many different technology areas, including vehicle dynamics and controls. Typically detailed dynamic analysis and controls design are performed after a vehicle has completed the conceptual design phase. However, due to the complex interactions in an airbreathing hypersonic vehicle, delaying application of detailed dynamics analysis and controls design could result in suboptimal vehicle designs. The Guidance, Navigation, and Controls discipline of NASA's Fundamental Aeronautics Program Hypersonics area is applying dynamic analysis and controls design early in the vehicle conceptual design. This activity includes development of controls focused dynamic models, creation of an integrated design environment for dynamics analysis and controls design, and early evaluation of vehicle controllability aspects. This effort will provide valuable insight into the vehicle multidisciplinary design and optimization phase.

A significant body of research under the rubric of blackbox optimization addresses the problem of optimization in a design space where the designs are evaluated by a computer simulation. For many such simulations, conventional local optimization methods prove inadequate, owing to the presence of local minima, local non-smoothness, and so on. A more effective approach would learn the global characteristics of the design space, and sample from disparate regions as it progresses. Several probabilistic approaches to this problem are based on the following idea: during the course of any search process, our partial knowledge of the design space grows as we evaluate a growing number of designs, and this knowledge can be elegantly expressed in terms of probability distributions. This is usually done using surrogate models, or data fits. We would like to use this partial knowledge to lead us to promising new designs, and this involves searching the data fit for points where the uncertainty of the fit, in conjunction with the fit itself, indicates a good chance of finding a improved design. This is the basis for the well-known Efficient Global Optimization (EGO) algorithm. This task can be regarded as an auxiliary optimization problem, but one that has some undesirable characteristics, including large flat regions and multiple local optima. Previous solution approaches have included branch and bound (the EGO algorithm), and local optimization with multi-start. In this paper, we present a new approach, itself based on probability distributions. Probability Collectives (PC) is an optimization framework in which a given optimization problem is transformed to one over probability distributions. This transformation often enables us to overcome problems such as local non-smoothness and multiple local optima. One particular PC approach is closely related to function smoothing and filtering. Our formulation is a type of Monte Carlo Optimization, often encountered in machine learning algorithms. We briefly introduce this approach, and apply it to the auxiliary optimization problem described above. Finally, we compare this technique with other algorithms, including a heuristic sampling algorithm, and a genetic algorithm.

In this paper, we review an optimization technique called Probability Collectives (PC), and compare its approach with that of quadratic Response Surface Methods (RSM), on some standard continuous test functions for unconstrained minimization, both in the presence and absence of uncertainty in the function evaluations. Probability Collectives (PC) is an optimization framework where optimization is performed over probability distributions over the variables of interest, rather than the variables themselves. In order to find a solution to the original optimization problem, we sample the final solution of the transformed problem, which is a probability distribution. In other words, PC is a transform technique with the special property that the inverse transform is performed stochastically. This transformation yields algorithms that are relatively insensitive to structural properties of the underlying objective function, like continuity, convexity, and dierentiability; optimization under uncertainty becomes natural and straightforward; finally, the distributions yield sensitivity information about the original problem. Some PC algorithms bear a strong resemblance to RSM, and in this paper, we investigate these similarities, and compare performances of these techniques on some simple test functions.

Recent developments in actuator technology have resulted in small, simple devices capable of afiecting the ∞ow fleld over ∞ight vehicles su‐ciently to generate control forces. One of the devices which has been under investigation is the Miniature-Trailing Edge Efiector (MiTE), which consists of a small, 1-5% chord, moveable surface mounted at the wing trailing edge. The high bandwidth and good control authority make the device an ideal candidate for control of both the rigid body and ∞exible modes of a ∞ight vehicle. Unfortunately traditional control techniques do not address the non-linear nature of the device or the competing performance goals arising from large numbers of distributed devices. Novel approaches to control design are therefore required. To demonstrate the potential of this type of ∞ight control architecture and to explore suitable control synthesis techniques, a remotely piloted ∞ight vehicle has been developed. This paper details the ∞ight vehicle including a distributed ∞ight control system based upon MiTEs. The latter system includes distributed sensing, logic, and actuation. This paper also describes an applicable novel control synthesis technique based upon the theory of collectives. The theory and its application to the design of distributed ∞ight control systems is presented. Results of ∞ight tests with conventional control surfaces and with a MiTE based control system are provided.

Aerospace systems continue to grow in complexity while demanding optimal performance. This requires the systems to be both designed and controlled optimally. Aerospace systems are also typically comprised of many interacting components, some of which may have competing requirements. The optimization approaches used for aerospace systems usually require centralized coordination and synchronous updates. In addition, while the approaches treat the large numbers of variables, they may not take advantage of the fact that the coupling may only be between a relatively small number of the variables. Distributed optimization algorithms, such as the approach based upon collectives presented in this paper, attempt to exploit this aspect. A collective is deflned as a multi-agent system where each agent is self-interested and capable of learning. Furthermore, a collective has a specifled system objective which rates the performance of the joint actions of the agents. Although collectives have been used for a number of distributed optimization problems in computer science, recent developments based upon Probability Collectives (PC) theory enhance their applicability to discrete, continuous, mixed, and constrained optimization problems. This paper will present the theoretical underpinnings of the approach for these various problem domains. Several example problems are used to illustrate the technique and to provide insight into its behavior. The examples include discrete, constrained, and continuous problems. In particular a constrained discrete structural optimization and a continuous trajectory optimization illustrate the breadth of the collectives approach.

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).