Methods for Matrix Optimization Problems in Control
Final technical rept. 12 Jan 1997-30 Nov 2001
STANFORD UNIV CA
Pagination or Media Count:
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.
- Numerical Mathematics
- Theoretical Mathematics