Stabilization of Distributed Parameter Systems: Design Methods and Applications

This book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium Stabilization of Distributed Parameter Systems: Design Methods and Applications at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory,differential equations, and dynamical systems.

A systematic presentation of recent stabilizability results for control systems with infinite degrees of freedom An efficient description of polynomial stability conditions for continuous semigroups Explicit control design schemes for mathematical models in mechanical and chemical engineering

Autorentext

Alexander Zuyev received his Ph.D. degree in 2000 from the Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine (IAMM NASU). He was a visiting scientist at the Abdus Salam International Centre for Theoretical Physics under the aegis of UNESCO and IAEA in Trieste and received the Alexander von Humboldt Research Fellowship at TU Ilmenau and the University of Stuttgart. Since his habilitation in 2008, he has been working as a Professor at Donetsk National University and a Leading Researcher and Department Head at IAMM NASU. He is currently with the Max Planck Institute for Dynamics of Complex Technical Systems and the Otto von Guericke University Magdeburg in Germany. Prof. Zuyev authored 2 books and more than 50 articles in the field of mathematical control theory, stability theory, and mathematical problems of mechanics and chemical engineering.

Grigory Sklyar received his Ph.D. degree in 1983 from Kharkov State University (USSR) and habilitation in 1991 from B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Science of Ukraine. He worked as a Professor of V.N. Karazin Kharkiv National University (1992-1999). Since 1999 he is a Full Professor in Institute of Mathematics of University of Szczecin (Poland). He also has been working on visiting positions in Technical University of Darmstadt, Institut de Recherche en Communications et Cybernétique de Nantes, Institute for Advanced Study in Mathematics, Hanoi and others. Prof. Sklyar is an author of more than 100 works in the field of Functional Analysis, Differential Equations, Mathematical Control Theory.

Inhalt

1. Barkhayev, P. et al, Conditions of Exact Null Controllability and the Problem of Complete Stabilizability for Time-Delay Systems.- 2. Gugat, M. et al., The finite-time turnpike phenomenon for optimal control problems: Stabilization by non-smooth tracking terms.- 3. Kalosha, J. et al., On the eigenvalue distribution for a beam with attached masses.- 4. Macchelli, A. et al., Control design for linear port-Hamiltonian boundary control systems. An overview. 5. Otto, E. et al., Nonlinear Control of Continuous Fluidized Bed Spray Agglomeration Processes. 6. Sklyar, G. et al., On polynomial stability of certain class of C_0 semigroups.- 7. Woniak, J. et al., Existence of optimal stability margin for weakly damped beams.- 8. Zuyev, A. et al., Stabilization of crystallization models governed by hyperbolic systems.