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Explanatory Notes
Instructions
Anotation:
Semidefinite programming or optimization over linear matrix inequalities (LMIs) is an extension of linear programming to the cone of positive semidefinite matrices. LMI methods are an important modern tool in systems control and signal processing.
Theory: Convex sets represented via LMIs; LMI relaxations for solution of non-convex polynomial optimization problems; Interior-point algorithms to solve LMI problems; Solvers and software; LMIs for polynomial mehods in control.
Control applications: robustness analysis of linear and nonlinear systems; design of fixed-order robust controllers with H-infinity specifications.
For more information, see
http://www.laas.fr/~henrion/courses/lmi
Výsledek studentské ankety předmětu je zde:
XP35LMI
Course outlines:
Exercises outline:
Literature:
# S. Boyd, L. Vandenberghe. Convex Optimization, Cambridge University
Press, 2005
# A. Ben-Tal, A. Nemirovskii. Lectures on modern convex optimization:
analysis, algorithms and engineering applications. SIAM, Philadelphia,
| 2001. | | Most of the material there can be found in various lecture notes and |
slides available at A. Nemirovksii's webpage at Georgia Tech.
LMI representation of semialgebraic sets and lift-and-project techniques
are described in:
# A. Ben-Tal, A. Nemirovskii. Lectures on modern convex optimization:
analysis, algorithms and engineering applications. SIAM, Philadelphia,
2001
# P. A. Parrilo, S. Lall. SDP Relaxations and Algebraic Optimization in
Control. ECC'03 and CDC'03 workshops, whose slides are available at P. A.
Parrilo's webpage at MIT.
Modern state-space LMI methods in control are nicely surveyed in:
# C. Scherer, S. Weiland. LMIs in Control, Lecture Notes at Delft
University of Technology and Eindhoven University of Technology, 2005.
Polynomials methods for robustness analysis are well described in
# B. R. Barmish. New tools for robustness of linear systems. MacMillan,
| 1994. | | Polynomial methods and LMI optimization for fixed-order robust controller |
design are described in parts III and IV of:
# D. Henrion. Course on polynomial methods for robust control, LAAS-CNRS
Toulouse, 2001
as well as in the papers
# D. Henrion, M. Sebek, V. Kucera. Positive Polynomials and Robust
Stabilization with Fixed-Order Controllers, IEEE Transactions on Automatic
Control, Vol. 48, No. 7, pp. 1178-1186, July 2003
# D. Henrion, D. Arzelier, D. Peaucelle. Positive Polynomial Matrices and
Improved LMI Robustness Conditions, Automatica, Vol. 39, No. 8, pp.
1479-1485, August 2003.
Requirements:
Subject is included into these academic programs:
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