Workshop on optimization and systems control

Thursday 21 January 2010
LAAS-CNRS, Toulouse, France

Scope

The workshop, funded and organized by the MAC research group at LAAS-CNRS, aims at reporting recent achievements in optimization algorithms for systems control.

Date and venue

The workshop takes place on Thursday 21 January 2010 at LAAS-CNRS, 7 avenue du colonel Roche, 31077 Toulouse, in Salle du Conseil.

Programme

10:00-11:00 - Bogdan Robu (Phd Student at LAAS-CNRS, University of Toulouse, France, under Lucie Baudouin and Christophe Prieur).
Title: Robust H-infinity vibration control of fluid/plate system using HIFOO algorithm.
Abstract: Recent developments in the aerospace applications lead to more and more flexible wings. Thus it is crucial to suppress or to attenuate the plane wing's vibration when the wing is in interaction with the movement of the fuel inside of it. In the case of the experimental setup we study this is done using colocated piezoelectric actuators and sensors. First we derive an infinite dimensional model for the fluid-flexible structure system and then we calculate a robust H-infinity controller. Two types of controllers are calculated (using Robust Control Toolbox under Matlab and HIFOO algorithm) and implemented on the experimental setup. Finally a reduced order simultaneous controller is computed and tested.

11:30-12:30 Suat Gumussoy (Post-doctorate Associate at Katholieke Universiteit Leuven, Belgium).
Title: Fixed-Order H-infinity Optimization and Numerical Computations of H-infinity Norm and Pseudospectral Abscissa of Time-Delay Systems.
Abstract: In practical implementations, robust fixed-order controllers are desired since they are cheap, non-restrictive in sampling rate, bandwidth and effective under model uncertainties, disturbances. In this talk, we present our approach to design robust fixed-order controllers by an optimization based method for a class time-delay systems. Our approach allows the user to choose the controller order and to tune controller parameters to minimize the H-infinity norm of the objective function using the norm value and its derivatives with respect to the controller parameters. Besides the controller design, we discuss computations of the H-infinity norm and pseudospectral abscissa for time-delay systems. We present two numerical methods based on a predictor-corrector algorithm.

14:00-15:00 Aude Rondepierre (Associate Professor at INSA and IMT, University of Toulouse, France).
Title: Nonsmooth optimization techniques in control system design: an alternative to LMIs.
Abstract: In this talk, we present nonsmooth optimization techniques motivated by applications in multi-objective feedback control. Based on bundle methods and trust regions techniques, we propose an algorithm computing locally optimal solutions, which may have a pre-defined structure. In contrast with the traditional oracle-based methods in nonsmooth programming, our method is model-based and can accommodate cases where several Clarke subgradients can be computed at reasonable cost. Then the proposed way to manage the proximity control parameter allows us to handle nonconvex objectives. In conclusion, applications to H-infinity and H2/H-infinity control synthesis are presented to numerically prove the benefits of the nonsmooth approach in control design.

15:30-16:30 - Wim Michiels (Professor at Katholieke Universiteit Leuven, Belgium).
Title: Optimization based control design of time-delay systems.
Abstract: While the analysis of control systems with time-delays has reached some maturity, the development of general controller synthesis methods is to a large extent unexplored. Roughly speaking two types of control design approaches for 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 (hence, an approximation is necessary), 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 (this is for instance the case for pole placement and optimal H-infinity design). 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 the ongoing 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 large 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. Attention will also be paid to the incorporation of pole location constraints in the optimization problems.

Registration

There is no registration fee, but please contact Ms Christèle Soler if you are planning to attend.