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The phrase "System of Systems" (SoS) has been in use for at least the past ten years. As customers of the aerospace and defense industries began asking for broad capabilities rather than for single systems to meet specific requirements, the notion of a system comprised of multiple, independently operating systems has become more important as the way to meet the desired set of capabilities. Recently, systems of systems have been identified in many other domains, such as health care, energy, logistics, and transportation. Because individual systems can operate independently within an SoS, many engineering methods and tools used to design large-scale, but monolithic, systems do not appear to work for designing systems of systems. This paper presents a three-axis taxonomy that can guide design method development and use for systems of systems. Based on this perspective, two experimental methods applications are presented for SoS problems.

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Morphing aircraft are multi-role aircraft that use innovative actuators, effectors, and mechanisms to change their state to perform select missions with substantially improved system performance. State change in this study means a change in the cross-sectional shape of the wing itself, not chord extension or span extension. Integrating actuators and mechanisms into an effective, light weight structural topology that generates lift and sustains the air loads generated by the wing is central to the success of morphing, shape changing wings and airfoils. The objective of this study is to explore a process to link analytical models and optimization tools with design methods to create energy efficient, lightweight wing/structure/actuator combinations for morphing aircraft wings. In this case, the energy required to change from one wing or airfoil shape to another is used as the performance index for optimization while the aerodynamic performance such as lift or drag is constrained. Three different, but related, topics are considered: energy required to operate articulated trailing edge flaps and slats attached to flexible 2D airfoils; optimal, minimum energy, articulated control deflections on wings to generate lift; and, deformable airfoils with cross-sectional shape changes requiring strain energy changes to move from one lift coefficient to another. Results indicate that a formal optimization scheme using minimum actuator energy as an objective and internal structural topology features as design variables can identify the best actuators and their most effective locations so that minimal energy is required to operate a morphing wing. BackgroundA morphing aircraft is a multi-role aircraft that, through the use of morphing technologies such as innovative actuators, effectors or mechanisms, changes its state substantially to complete all roles -with superior system performance.1 For instance, for a hunter-killer aircraft, role A is long-duration loiter while role B is high-speed dash and role C is some form of energy deposition to neutralize the target. Morphing aircraft are a major part of a system that requires technology integration to manipulate geometric, mechanical electromagnetic or other mission critical features -on the ground or in-flight -to match vehicle performance to a well-defined environment and mission objective.

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High reliability is a primary design goal in commercial communication satellite systems because they require large capital investment and are inaccessible after launch. Spacecraft system reliability is typically computed using standard parallel-series combination techniques based upon component and subsystem failure rates provided by suppliers. Component failure rates are empirically determined and, as such, are nondeterministic parameters. Treating these failure rates as uncertain parameters in spacecraft design may avoid unnecessary high redundancy. However, probabilistic methods in reliability evaluation are often ignored because handling uncertain parameters associated with discrete or categorical design variables, such as technology choices and redundancy levels, requires computationally expensive sampling techniques. The computational cost of optimization approaches becomes prohibitive when considering discrete technology and redundancy choices as variables. This work presents a genetic algorithm with Monte Carlo sampling for probabilistic reliability-based design optimization of satellite systems. In this approach, confidence-level constraints ensure that system reliability requirements are met with high probability. The genetic algorithm-Monte Carlo sampling approach is compared to a deterministic margin-based approach that enforces margins or safety factors on the reliability of individual components. The comparison shows that the genetic algorithm-Monte Carlo sampling approach produces satellite designs that have low launch mass (a surrogate for cost) while achieving reliability requirements at specified high confidence levels, while the genetic algorithmdeterministic margin-based approach produces heavy satellite designs with excessive redundancy. Based on this work, extensions of a genetic algorithm-based approach for discrete optimization under uncertainty that may require less computational effort appear possible. Nomenclature c = penalty multiplier E = expected value of f = fitness function G = uncertain inequality constraint g = inequality constraint M = mass N samples = number of samples P = probability of R = reliability x = design vector = failure rate = mean = uncertain parameters vector = standard deviation = Gaussian probability density function = objective function

Aircraft design optimization and airline allocation problems are two separate and wellresearched disciplines, but very little literature exists that solved the design and allocation problems simultaneously. Among the limited number of related efforts that combine them, most follow a sequential decomposition strategy. This sequential strategy has been successful in addressing the combined large-scale problem but the approach does not capture the coupling that exists between the aircraft design and airline allocation disciplines. Solving the aircraft design and airline allocation as a monolithic problem makes it a Mixed Integer Non-Linear Programming problem which is very difficult to solve for large numbers of integer variables. Because no existing generalized MINLP solver can address this problem, this work proposes a new algorithm combining branch and bound, Efficient Global Optimization, Kriging Partial Least Squares, and gradient-based optimization to solve MINLP problems with 100's of integer design variables, 1000's of continuous design variables. The algorithm was applied to an 8 route coupled aircraft design and allocation problem with the 19 allocation variables and solving a 6000 variable aircraft design optimization problem using an Euler CFD simulation. This test problem provides several key challenges for a MINLP problem: a moderate integer design space, a large continuous design space, and expensive analysis models.