Then on the morning of Thu 26 Oct we cover latest achievements in
semidefinite programming and real algebraic geometry:
Part I.2: classification of convex semialgebraic sets that can
be represented with LMIs, lift and project techniques (1h)
Part I.2b: non-convex BMIs (0h30)
Part I.3: Shor's relaxation, polynomial moments and sum-of-squares,
Lasserre's hierarchy of LMI relaxations to solve non-convex polynomial
optimization problems, including BMIs (1h30)
For the
labs of Thu 26 Oct afternoon, we use the YALMIP interface,
SeDuMi and PENBMI to define and solve LMI and BMI problems under the
Matlab environment (1h30).
We also briefly survey recent developments in semidefinite solvers and
software packages:
Part I.4:
basics of interior-point algorithms, latest achievements in
software and solvers for LMIs and BMIs (1h30)
On Fri 27 Oct, the end of the course focuses on the application of LMI techniques to solve several control problems traditionally deemed as difficult, such as robustness analysis of linear and nonlinear systems, or design of fixed-order robust controllers with H-infinity specifications. The originality of the approach is in the simultaneous use of algebraic or polynomial techniques (as opposed to classical state-space methods) and modern convex optimization techniques:
Part II.1 and Part II.2:
State-space methods - stability analysis: Lyapunov stability,
pole placement in LMI regions, uncertain systems and robustness
analysis - controller design: H2, Hinf, robust state-feedback and
output-feedback design (3h)
Part II.3 and Part II.4:
Polynomial methods - stability analysis: polynomials in control,
robust stability of polynomials - controller design: robust fixed-order
controller design (2h)
Last updated on 13 December 2006