Stabilization of Distributed Parameter Systems: Design Methods and Applications (SEMA SIMAI Springer Series, 2)

✍ Scribed by Grigory Sklyar (editor), Alexander Zuyev (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 139
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
About the Editors
Conditions of Exact Null Controllability and the Problem of Complete Stabilizability for Time-Delay Systems
1 Introduction
2 Preliminaries
3 The Moment Problem and Completability Property
4 The Main Result
References
The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms
1 Introduction
2 Optimal Control Problems with Ordinary Differential Equation
2.1 A More General Result for Scalar Ordinary Differential Equations
3 General Results in Hilbert Spaces
3.1 Exact Controllability
3.2 An Optimal Control Problem with Max-Norm Penalization
3.3 An Optimal Control Problem for Nodal Profile Exactly Controllable Systems
3.4 An Optimal Control Problem with L1-Norm Tracking Term
4 Examples
5 Conclusion
References
On the Eigenvalue Distribution for a Beam with Attached Masses
1 Introduction
2 Spectral Problem
3 Frequency Analysis
4 Numerical Simulation Results
5 Conclusion
References
Control Design for Linear Port-Hamiltonian Boundary Control Systems: An Overview
1 Introduction
2 Distributed Port-Hamiltonian Systems
3 Energy-Shaping Design by Interconnection and State-Feedback
4 Exponential Stabilisation of Port-Hamiltonian Linear BCS
5 Conclusions and Future Works
References
Nonlinear Control of Continuous Fluidized Bed Spray Agglomeration Processes
1 Introduction
2 Process Modeling
3 Control of Fluidized Bed Spray Agglomeration
3.1 Introduction to Discrepancy Based Control
3.2 Application to Fluidized Bed Spray Agglomeration
3.2.1 Discrepancy Based Control
3.2.2 Discrepancy Based Sliding Mode Control
3.3 Robustness with Respect to Parametric Uncertainties
4 Conclusion
References
On Polynomial Stability of Certain Class of C0-Semigroups
1 Introduction
2 Asymptotic Behavior on Dense Subsets
3 Maximal Asymptotics
4 Asymptotic Behavior of a Certain Special Class of Semigroups
References
Existence of Optimal Stability Margin for Weakly Damped Beams
1 Introduction
2 Weakly Damped Rotating Timoshenko Beams
3 Spectral Properties of the Operators Ai
4 Asymptotic Spectral Analysis of Operators Ai
4.1 Operator A1
4.1.1 Case μ=0, ν>0, γ2>1
4.1.2 Case μ=0, ν>0, γ2=1
4.2 Operator A2
4.2.1 Case μ>0, ν=0, γ2=1
4.3 Operator A3
4.3.1 Case μ>0, ν>0, γ2=1
5 Stability Margin Analysis
6 Conclusions
References
Stabilization of Crystallization Models Governed by HyperbolicSystems
1 Introduction
2 Continuous Crystallization Model
3 Control Design
4 Stability Analysis
5 Preferential Crystallization Model
6 Stabilization with Scalar Input
7 Conclusions
References