New Tools in Nonlinear System Analysis
Abstract
This project was aimed at developing novel theories for the analysis and design of systems exhibiting essentially nonlinear behavior, such as systems utilizing quantized decision making, periodic orbits, switching, etc. The original primary directions of research were extending the framework of Integral Quadratic Constraints (IQC); studying the robustness of periodic trajectories subject to unmodeled dynamical perturbations; efficient analysis of switching piecewise linear systems; and model order reduction for linear and nonlinear subsystems. The primary result of the project, the IQC system analysis package "iqcBeta," is finished and is now available on the Web. New IQC for handling specific nonlinearities were discovered and used to make IQC analysis more accurate. A new methodology for robustness analysis of forced and self-induced oscillations in dynamically uncertain nonlinear systems was developed and tested. A new unconventional methodology of constructive global analysis of piecewise-linear systems (PLS) was developed, based on using surface Lyapunov functions instead of ordinary Lyapunov functions. The method was shown to work extremely well in the analysis of benchmark switching systems. Also, several new methods for linear system model order reduction (MOR) were discovered, providing error bounds that are superior to those of Hankel MOR and Balanced Truncation. A procedure for applying these methods in model reduction of nonlinear systems has been proposed. A new major research direction has emerged as a result of this work: the development of an alternative robust control framework in which finite state stochastic automata serve as nominal system models. (9 refs.)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 31, 2003
- Accession Number
- ADA421507
Entities
People
- Alexandre Megretski
Organizations
- Massachusetts Institute of Technology