Generalized Homogeneity in Systems and Control Volume II
Infinite-Dimensional Systems
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Beschreibung
The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization.
The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate.
Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include:
- mathematical models of dynamical systems in infinite-dimensional spaces;
- the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);
- abstract differential equations with homogeneous operators (including differential operators);
- rewritten, reorganized chapters with the addition of substantial new material;
- robustness analysis of infinite-dimensional homogeneous systems;
- homogeneous control in a Hilbert space; and
- consistent discretization of homogeneous systems.
Illustrative examples – numerical results, computer simulations and real experiments – support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.
The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization.
The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate.
Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include:
- mathematical models of dynamical systems in infinite-dimensional spaces;
- the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);
- abstract differential equations with homogeneous operators (including differential operators);
- rewritten, reorganized chapters with the addition of substantial new material;
- robustness analysis of infinite-dimensional homogeneous systems;
- homogeneous control in a Hilbert space; and
- consistent discretization of homogeneous systems.
Illustrative examples – numerical results, computer simulations and real experiments – support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.
Provides a thorough introduction to the theory of generalized homogeneous infinite-dimensional systems Expanded discussion of mathematical models of dynamic systems in infinite-dimensions Explains homogeneous control in a Hilbert space
Autor*in
Andrey Polyakov
Themen in »Generalized Homogeneity in Systems and Control Volume II«
Infinite-dimensional Systems Infinite-dimensional Homogeneous System Homogeneous Galerkin Method Control in Hilbert Space Control in Banach Space Homogeneous Control Control in Sobolev Space Control in Lebesgue Space Fixed-time Control Linear Dilation Nonlinear Control Infinite-dimensional Control