This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problems” held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:
- Controllability of dynamical systems
- Information transfer in multiplier equations
- Nonparametric instrumental regression
- Control of chained systems
- The damped wave equation
Control and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.
Stabilization of one dimensional wave equation with variable potential and torque.- Controlling a dynamic system through reinforcement learning.- Landweber iterative method for an inverse source problem of space-fractional diffusion equations.- On the Spectrum Distribution of Parametric Second-order Delay Differential Equations. Perspectives in Partial Pole Placement.- Exact controllability of the linear Biharmonic Schrdinger equation with space-dependent coefficients.- Carleman estimate and application to the stabilization of a dissipative hyperbolic system.- On the transfer of information in multiplier equations.- A Global Carleman Estimates of the linearized sixth-order 1 D-Boussinesq equation Application.- Nonparametric instrumental regression via mollification.- Finite-time stabilization of some classes of infinite dimensional systems.- Dispersion on certain Cartesian products of graphs.- Tracking Control of Chained Systems: application to nonholonomic unicycle mobile robots.- A short elementary proof of the Gearhart-Pruss theorem for bounded semigroups.- Revisit the damped wave equation.
Kaïs AMMARI is full professor of mathematics at the University of Monastir (Tunisia). He got his PhD from Ecole Polytechnique in Palaiseau (France). His domain of expertise includes analysis of partial differential equations, control theory and operator semi-group theory. He has held visiting professorships at various universities in France, Italy, and Spain. He has developed a number of international cooperative projects. He is the director of the research Lab of Analysis and Control of PDE (ACEDP lab).Chaker JAMMAZI is a Professor at the University of Tunis El-Manar, Tunisia. He did his PhD, in Applied Mathematics, from the Ecole Nationale dIngénieurs de Tunis, University of Tunis El-Manar (January 2008). In April 2014, he obtained the Habilitation à Diriger des Recherches (HDR), in Applied Mathematics, from the Ecole Polytechnique de Tunisie (EPT) - Carthage University. His main research interests include nonlinear mathematical control theory in finite and infinite dimensional.
Faouzi TRIKI is an associate Professor at Grenoble Alpes University, France. He did his PhD at École Polytechnique, France (2002), after getting a Master's degree from Sorbonne University, France. He does research on mathematical modeling in optics, inverse problems focusing on multiwave, and scattering-based imaging.
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