Characterizing the Performance of Nonlinear Differential Operators

Abstract

Highly complex behavior is common in both the natural and technological world. Nonlinear differential operators play an essential role in enabling accurate modeling and prediction of this behavior. Nonlinear systems theory provides a mathematical framework for the analysis and design of networks of these operators, thereby providing the foundation for scientists and engineers to understand and control this highly complex behavior. This project is primarily concerned with the development of analysis and computational tools that can accurately characterize the performance of specific classes of nonlinear differential operators in capturing specific behavioral properties of interest. A secondary concern is the development of controller synthesis tools that enable the design of networks of differential operators so as to yield specific behavioral properties. At the completion of this project after three years of funding, outcomes of this project include the development of new theoretical and computational tools for performance bound verification, tight performance bound characterization, and controller synthesis for representative behavioral properties. Integral-input-to-integral-output, integral-input-to-output, and input-to-state stability properties have been specifically considered. Substantial effort has been invested in the development of tools for the numerical approximation of solutions to the attendant optimization and optimal control problems. This includes computational tools utilizing approximating Markov chain methods and max-plus methods. The research undertaken is documented in 26 scholarly publications (17 published or accepted to be published, 9 in press or in review), and communicated via numerous presentations (including 14 invited) at internationally renowned meetings and academic institutions.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2012
Accession Number
ADA571066

Entities

People

  • Peter M. Dower

Organizations

  • University of Melbourne

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Computational Science
  • Computations
  • Control Systems
  • Differential Equations
  • Dynamic Programming
  • Engineering
  • Engineers
  • Equations
  • Integrals
  • Lyapunov Functions
  • Markov Chains
  • Mathematics
  • Nonlinear Systems
  • Optimization
  • Partial Differential Equations
  • Riccati Equation
  • Verification

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Systems Analysis and Design
  • Technical Research and Report Writing.