Methods for Matrix Optimization Problems in Control

Abstract

We have developed new techniques for solving matrix optimization problems, such as bilinear matrix inequalities and matrix rank minimization problems. These techniques have enabled us to developed new extensions of Lyapunov theory, which allowed us to analyze the stability and performance of a wide variety of complex systems that could not be handled before. This includes systems with mode-switching logic, hysteresis and saturation nonlinearities and asynchronous clocks. We have also developed optimization-based frameworks for the simultaneous probing and control of uncertain systems, as well as for simultaneous control and communication resource allocation. We have also developed new tools for robust control which compute optimal uncertainty models directly from frequency domain data, and compute reduced order controllers with guaranteed stability properties.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2002
Accession Number
ADA402612

Entities

People

  • Stephen P. Boyd

Organizations

  • Stanford University

Tags

Communities of Interest

  • Human Systems
  • Materials and Manufacturing Processes
  • Sensors
  • Space

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Algorithms
  • Asynchronous Systems
  • Computations
  • Computer-Aided Design
  • Control Systems
  • Convex Programming
  • Electrical Engineering
  • Frequency
  • Frequency Domain
  • Heuristic Methods
  • Hybrid Systems
  • Hysteresis
  • Inequalities
  • Linear Systems
  • Optimization
  • Semidefinite Programming

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.