Synthesis of Systems of Systems [SoS] is in fact the Management of System Design Complexity
Richard Schmidt
Northrop Grummon TASC Corp.
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Last modified: March 31, 2006
Abstract
Synthesis of Systems of Systems [SoS] is in Fact the
Management of System Design Complexity
Richard Schmidt Chief Modeling and Simulation Architect
TASC System Engineering Methods Group.
Los Angeles CA
The design for a system is said to be specified when the features and capabilities that constitute a description of the system can verifiably support performance that subtends the stated capabilities. A list of the descriptors and their properties that comprise an expression of these capabilities is called the system description. A dynamical system and its behavior is naturally embedded in the relations between these descriptors which also defines its bounds and initial conditions. A model of such a system is a an Information System [IS], which is to say is a description of the system in terms of objects and their attributes over a set of values [fixed/variable] and their mutual ranges; that are in turn governed exclusively by the relations that are admissible on the closure of a bounded and completed region of the space formed from the of system descriptors, ie that subtended by a design of the associated IS. Thus the system design is a process that evolutionarily maps the System Description into a complete IS.
We define two topological invariants of mapsets defined on the space that support this process. Hence the evolution and evaluation of the design of a system in the context of a given description are (i) the indeterminacy of the description, and (ii) the minimal set of maximally independent measures [Measures of Effectiveness, MoEs] that span the design space. The process [ie the collection of maps] such that no component of the design region vanishes is realized as a System Design Function [SDF]. Computational methods exist to evaluate these invariants subject to a search for a mutually consistent, concurrent and convergent attribute valueset. This paper cites these methods and briefly discusses the manner in which they provide a computational method to define a model set and a system statevector, closed with respect to measurable metrics on the state space formed by the direct product space of the system descriptors. These models are then integrated into a simulator specified to execute a set of simulation experiments. These experiments are designed to span that set of descriptors designated as the parameters in the system design that establish a Nominal Operating Range. This piecewise coverage of the statespace of the system yields a continuous set of performance evaluations. The postprocessed simulation results are then used to verify that a set of prespecified design stages [design baselines] exist that have met minimal criteria corresponding to performance as measured by the MoEs. Since the MoE set spans the entire design region subtended by the current design baseline, and each baseline complies conditionally with the entire MoE set, the design at each stage is in principle a provably correct; conceptual, feasible, realizable, integrable, implementable, and verifiable baseline design in that order. Hence the criteria applied at each stage of the design process, tests for compliance with respect to these system baseleine properties. Additional “System Level Design Maturity criteria may be added at each stage subject to selected Design Decision Criteria [DDC] that are established as a the result of a Concept Stage experiment called Analysis of Alternatives.
In this manner the SDF samples the design space via simulation on a set of experiments designed to evaluate successive subtended subspaces of the MoE set. By manipulating the IS that represents which information is intrinsic and that which is extrinsic for any particular experiment, all the information within the IS is considered in applying the design decisions that are made successively at each stage. We point out (i) how the SDF thereby regulates combinatorial explosion in the design of the search experiments, and (ii) how the dynamical space is partitioned to automatically define a set of operating regimes based on local linearization around fixed points defined on a basis comprising a subset of statevector components. These components then assume the role of “control variables” on that regime. This is the sense in which the SDF is likened to the Management of Complexity.


