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Bounds Computation for Adaptive Systems V&V
Point of Contact	Giampiero Campa campa@cemr.wvu.edu
Dates	June 2006 - December 2008
Problem	Adaptive control is quickly becoming one of the most used tools in the aerospace and control communities. In particular, adaptive approximation tools like on-line learning neural networks, are becoming widespread. However, adaptive systems often pose challenging problems from the verification and validation point of view. For example, existing proofs that the evolution of an adaptive system is bounded into a certain set, often lack generality and/or constructiveness. A first objective of this research effort is to provide a Lyapunov analysis based proof for the boundedness of a very general class of adaptive systems, while at the same time providing closed form expressions for such bounds. A MATLAB-based software capable of computing and visualizing these bounds will then be developed, together with a set of tools for adaptive on-line approximation. Finally, boundedness could be verified by a custom built automated bound testing tool for adaptive systems modeled in Simulink. Finally, the application of the above results to several case studies, with particular attention to a current NASA project using a GEN2 adaptive controller, will be fully documented and provided.
Objective	By 12/31/2006 a software library for adaptive on-line approximation should be completed and functioning. The library will include several on line learning Neural Networks as well as a manual and examples on how to use them. By 12/31/2007 we expect to have completed a general Lyapunov boundedness analysis, complete with closed form expressions for bounds and sets that limit the evolution of a general adaptive system in general, and of an on line neural network in particular. Finally by 12/31/2008 we expect to have completed the development of a software for bound computation and visualization, possibly including tools for automated general bound testing for adaptive systems. Several important case studies, including a GEN2 NASA IFCS controller will be performed as well.
Results	SAS 06 Executive Presentation.ppt SAS 06 Technical Presentation.ppt Technical Report_Lyapunov_Analysis_Adaptive_Elements_Campa.doc SAS_07_Exec_Briefing_Bounds_Computation_Campa.ppt SAS_07_Tech_Pres_Bounds_Computation_v5_Campa.ppt Technical Report-Lyapunov Analysis of Systems Containing Adaptive and Uncertain Elements.pdf SAS 2008 Executive Presentation Bounds Computation for Adaptive Systems V&V.ppt SAS 2008 Technical Presentation Bounds Computation for Adaptive Systems V&V.ppt Bounding Set Calculation for Neural Network Based Control Systems.pdf Bounds Computation for Adaptive Systems.pdf
Keywords	Adaptive Control Systems, Verification and Validation, MATLAB and Simulink, Neural Networks
Categories	Software Safety Design Analysis Dynamic Analysis Interface Analysis Requirements Analysis Software Architecture Assessment Traceability Analysis

Curator: Josh Stonestreet
NASA Official: Lisa Montgomery

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