Relating Dynamical Systems to Software Engineering

Transcription

1 Relating Dynamical Systems to Software Engineering Some of the most exciting interactions between mathematics and engineering are occurring in the area of analysis and control of uncertain, multivariable, and nonlinear systems. While changing technology has made control and dynamical systems theory increasingly relevant to a much broader class of problems, the interdisciplinary nature of this area means that they no longer have a natural home exclusively or even primarily within any one of the traditional engineering disciplines. From CalTech s DS&C Website 1

2 Dynamical Systems Basics The change of state in a system over time Autonomous & control systems Continuous & discrete systems Characterized by some level of complexity Degrees of freedom => # of dimensions Incompleteness Godelian Dynamical Systems Basics Possible meta-states of outcomes Deterministic Vascillation Chaotic Some combination of the above 2

3 SE Basics Best practices Formalized processes & procedures Phases and iterations Possible meta-state outcomes Deterministic (hopefully) Vascillation Chaotic Decisions, decisions Is it important to be precise? π = 3.14 π = (6.4 Billion* digits and counting) Is it important to be correct? π = the constant ratio of the circumference of a circle to the diameter *American 3

4 Heisenberg Uncertainty in the Software Engineering System The more precisely you know where you are (your state), the less precisely you know where you re going (your transition) Lorenz Attractor Phase shifting between state space and transition space Tools from MOF / UML World 4

5 Outside Observer A Change of State State Start Transition Event End Requirement n Confusion Analysis Epiphany*? Understanding Over time *A sudden manifestation of the essence or meaning of something. Can Become Complex Confusion Epiphany* Mealy Moore Understanding Time *A sudden manifestation of the essence or meaning of something. 5

6 Space (The Final Frontier?) State Space Transition Space Phase Space Model Space Paper Space Defining Time & Space Iteration => Discrete time (ordered) A State Space Discrete A Transitional (Phase) Space In the state of transition? Transitional vector between State spaces State space and a Phase Space Phase Spaces => meta-phase Space Discrete 6

7 Embedding A State Space Blue => confusion White => understanding Blue => Documentary White => Analysis Yellow => Normalization Red => Synthesis Aqua => Realization Meaning of order In space A Transition Space State 1 Confusion Possible Pseudo- States? State 2 Understanding 7

8 A Phase Space Automata Rules for Transitions Rules can be expressed in mathematical, textual and graphical dimensions The iteration of rules can show behavior and meta-state evolution. Rules may be unidirectional or bidirectional => rules may be Hamiltonian or dissipative. 1

9 Possible Conclusions and Derivative concepts Methods may be formalized using concepts of space, state, transition and phase to predict meta-state behavior in software engineering systems. Replicate the space concepts discussed to include a model space of all known informational dimensions not just an abstraction. Paper space may be a projection of 2 dimensions of the model onto a traditional medium. 2

10 Contact Information Kenneth A. Lloyd, Jr. President Watt Systems Technologies, Inc Briar Place Carmel, IN USA Phone: Web: Copyright 2002, Watt Systems Technologies, Inc. Copyright Kenneth A. Lloyd, Jr. All rights reserved. The companies and individuals listed above hereby grant a royalty-free license to the Object Management Group, Inc. (OMG) for worldwide distribution of this document or any derivative works thereof within OMG and to OMG members for evaluation purposes, so long as the OMG reproduces the copyright notices and the below paragraphs on all distributed copies. The information contained in this document is subject to change with notice. UML is a trademark of the Object Management Group. 3