Attractive Ellipsoids in Robust Control

This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the “attractive ellipsoid method.” Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.

1. Introduction.- 2. Mathematical Backgrounds.- 3. Robust State Feedback Control.- 4. Robust Output Feedback Control.- 5. Control with Sample-Data Measurements.- 6. Sample Data and Quantifying Output Control.- 7. Robust Control of Implicit Systems.- 8. Attractive Ellipsoids in Sliding Mode control.- 9. Robust Stabilization of Time-Delay Systems.- 10. Robust Control of Switched Systems.- 11. Bounded Robust Control.- 12. Attractive Ellipsoid Method with Adaptation.

Alexander S. Poznyak graduated from Moscow Physical Technical Institute (MPhTI) in 1970. He earned PhD and Doctor Degrees from the Institute of Control Sciences of Russian Academy of Sciences in 1978 and 1989, respectively. He is now the head of the Automatic Control Department at CINVESTAV-IPN, and has published more than 120 papers in different international journals and 9 books. Andrey Polyakov is a researcher at NON-A team, Inria Lille-Nord Europe. He has graduated with a PhD in Physics and Mathematics from Voronezh State University, Russia in 2005. His areas of interest lie within control theory and differential equations. Vadim Azhmyakov is a Professor at University of Antonio Nariño, Colombia, in the Department of Electronic and Biomedical Engineering.