Seminar Details
2011-02-22 (15.00) : Eigenvalue based techniques for the stability analysis and robust control of linear systems with time-delay
At Euler building
Organized by Mathematical Engineering
Speaker :
Wim MICHIELS (KUL)
Abstract :
Time-delay systems are a subclass of infinite-dimensional system. They have a variety of applications in engineering,
economics and the bio-sciences. Two mainstream control design approaches for linear time-delay systems can be distinguished in the literature.
The first type is based on applying a generalization of the classical systems and control theory to infinite-dimensional systems.
It mostly results in infinite-dimensional or distributed controllers which may be hard to implement in practical applications where
the controller structure is fixed or restricted, or in controllers that include observers, requiring an on-line numerical simulation
of the systems' equations. The second approach consists of identifying approximate finite-dimensional models of low order, and applying
the existing design methods that typically yield controllers whose dimensions are larger or equal than the dimension of the plant model.
As a drawback the properties of the resulting closed-loop system may heavily depend on the accuracy of the approximation, and the design
involves a trade-off between accuracy and reliability on the one hand and the feasibility of the controller implementation on the other hand.
In my presentation I will give an overview of recent work in my group on control design methods that aim at bridging the gap between the two
types of approaches described above, by designing directly controllers for a broad class of linear time-delay systems (without starting
from a low-order approximation), where the controller structure or order is a-priori specified (e.g. imposed from practical considerations).
These methods are based on a direct optimization of appropriately defined cost functions and inspired by recent work on low-order control
design for finite-dimensional systems within an eigenvalue optimization framework. The analysis and design problems under consideration include
the stabilization problem and the computation and optimization of H2 and H-infinity type cost functions.
Many of the methods discussed heavily rely on the property that eigenvalue problems associated with linear time-delay systems, which
are usually finite-dimensional and nonlinear, can be equivalently expressed as infinite-dimensional linear eigenvalue problems.
I will point out how the underlying linearization approach can be generalized, resulting in generic computational tools for nonlinear eigenvalue
problems.