International Federation of Automatic Control
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  • Plenary I

    Prof. Wim Michiels wimmichiels2

    Department of Computer Science, K.U. Leuven, Belgium

    Design of fixed-order stabilizing and H-2/ H-infinity optimal controllers: an eigenvalue optimization approach


    In the context of H-2 and H-infinity control of time-delay systems two mainstream approaches can be distinguished. The first approach 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. 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 H-2 and H-infinity type cost functions.


    Biography

    Wim Michiels (1974) obtained a MSc degree in Electrical Engineering and  a PhD degree in Computer Science from the K.U.Leuven, Belgium, in 1997 and 2002, respectively. He has been research Fellow of the Research Foundation Flanders (2002-2008) and postdoctoral research associate at
    the Eindhoven University of Technology, the Netherlands (2007). In  October 2008 he was appointed associate professor at the K.U. Leuven,  Belgium, where he leads a research team within the Numerical Analysis and Applied Mathematics Division. Among other published work, he has authored the monograph “Stability and Stabilization of Time-Delay Systems. An Eigenvalue Based Approach” (SIAM Publications, 2007, with S.-I. Niculescu), over 40 articles in international scientific journals, and he has been co-editor of three books. He has been co-organizer of several workshops and conferences in the area of numerical analysis, control and optimization, including the 5th IFAC Workshop on Time-Delay Systems (Leuven, 2004) and the 14nt Belgian-French-German Conference on Optimization (Leuven, 2009). He is member of the IFAC Technical Committee on Linear Control Systems. His research interests include control and optimization, dynamical systems, numerical linear algebra and scientific computing.  His work has focused on the analysis and control of systems described by functional differential equations and on large-scale linear algebra problms, with applications in engineering and the life sciences.