A Path-following Method for Solving BMI Problems in Control

Abstract

In this paper we present a path-following (homotopy) method for (locally) solving bilinear matrix inequality (BMI) problems in control. The method is to linearize the BMI using a first order perturbation approximation, and then iteratively compute a perturbation that "slightly" improves the controller performance by solving a semidefinite program (SDP). This process is repeated until the desired performance is achieved, or the performance cannot be improved any further. While this is an approximate method for solving BMIs, we present several examples that illustrate the effectiveness of the approach.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1999
Accession Number
ADA640055

Entities

People

  • Arash Hassibi
  • Jonathan How
  • Stephen Boyd

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Sensors

DTIC Thesaurus Topics

  • Actuators
  • Air Force
  • Algorithms
  • Closed Loop Systems
  • Computational Complexity
  • Eigenvalues
  • Electronic Mail
  • Feedback
  • Inequalities
  • Information Systems
  • Iterations
  • Open Loop Systems
  • Optimization
  • Perturbations
  • Semidefinite Programming
  • Specifications
  • Topology

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Rehabilitation and Prosthetic Care for Military Service Members and Veterans with Limb Loss or Disability.