This monograph introduces the theory of generalized homogeneous systems governed by differential equations in both Euclidean (finite-dimensional) and Banach/Hilbert (infinite-dimensional) spaces. It develops methods of stability and robustness analysis, control design, state estimation and discretization of homogeneous control systems. Generalized Homogeneity in Systems and Control is structured in two parts. Part I discusses various models of control systems and related tools for their analysis, including Lyapunov functions. Part II deals with the analysis and design of homogeneous control systems. Some of the key features of the text include: mathematical models of dynamical systems in finite-dimensional and infinite-dimensional spaces; the theory of linear dilations in Banach spaces;homogeneous control and estimation;simple methods for an "upgrade" of existing linear control laws; numerical schemes for a consistent digital implementation of homogeneous algorithms; and experiments confirming an improvement of PID controllers. The advanced mathematical material will be of interest to researchers, mathematicians working in control theory and mathematically oriented control engineers.

Provides a thorough introduction to the theory of generalized homogeneous systems Discusses mathematical models of dynamic systems in finite- and infinite-dimensions Supports all theory with illustrations, examples and simulations Shows engineers how to enhance the precision of PID control

Autorentext

Andrey Polyakov received his PhD in Systems Analysis and Control from the Voronezh State University, Russia in 2005. Until 2010 he was an associate professor with the same university. In 2007 and 2008, he was also a research associate with the CINVESTAV-IPN center in Mexico City. From 2010 up to 2013 he was a leader researcher of the Institute of the Control Sciences, Russian Academy of Sciences. In 2013 he joined Inria, Lille, France as a researcher. He hasco-authored more than 100 papers in peer-reviewed journals and three books Attractive Ellipsoids in Robust Control, Road Map for Sliding Mode Control Design and Generalized Homogeneity in Systems and Control 1st Ed. His research interests include various aspects of nonlinear control and estimation theory such as finite-time/fixed-time control, generalized homogeneity and Lyapunov methods for both finite-dimensional and infinite-dimensional systems.

Inhalt

Chapter 1. Introduction.- Part I: Models of Control Systems and Stability Analysis.- Chapter 2. Finite-Dimensional Models.- Chapter 3. Innite-Dimensional Models.- Chapter 4. Stability and Convergence Rate.- Chapter 5. Method of Lyapunov Functions.- Part II: Homogeneous Control Systems.- Chapter 6. Dilation Groups in Banach, Hilbert and Euclidean Spaces.- Chapter 7. Homogeneous Mappings.- Chapter 8. Analysis of Homogeneous Dynamical Systems.- Chapter 9. Homogeneous Stabilization.- Chapter 10. Consistent Discretization of Homogeneous Models.- Chapter 11. Homogeneous State Estimation.- Chapter 12. Homogeneous Optimal Control.- Appendix.- Index.