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[CT191]

Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
Type : Contributed Talk
Abstract : In this paper necessary and sufficient conditions are established for the controllability of linear fractional dynamical system of the form \begin{eqnarray} ^CD^{\alpha,\rho}_{0^+}x(t)&=& Ax(t)+Bu(t), \ \ t\in J=[0,T]\\ x(0)&=&x_0 \end{eqnarray} where $0<\alpha<1,\rho>0, \rho\neq 1$ and $x\in R^n$ is the state vector, $u\in R^m$ is the control vector, $x_0\in R^n$ and $A$ is an $n\times n$ matrix and $B$ is an $n\times m$ matrix. Here the generalized fractional derivative is taken as \begin{eqnarray*} ^CD^{\alpha,\rho}_{0^+}x(t)=\frac{\rho^{\alpha}}{\Gamma(1-\alpha)} \int_0^t \frac{1}{(t^{\rho}-s^{\rho})^{\alpha}}x^{\prime}(s)ds \end{eqnarray*} Further sufficient conditions are obtained for the following nonlinear fractional system \begin{eqnarray} ^CD^{\alpha,\rho}_{0^+}x(t)&=& Ax(t)+Bu(t)+f(t,x(t)), \\ x(0)&=&x_0 \end{eqnarray} where the function $f:J\times R^n\to R^n$ is continuous. The results for linear systems are obtained by using the Mittag-Leffler function and the Grammian matrix. Controllability of nonlinear fractional system is established by means of Schauder's fixed point theorem. Examples are provided to illustrate the results.
Classification : 93B05, 34A08, Controllability, Fractional Dynamical Systems
Format : Talk at Waseda University
Author(s) :
- Balachandran Krishnan (Department of Mathematics, Bharathiar University, Coimbatore-641046)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
Type : Contributed Talk
Abstract : This work deals with some controllability results of a one-dimensional degenerate and singular parabolic equation. We provide approximate and null controllability conditions based on the moment method by Fattorini and Russel.
Classification : 93B05, 35K65, 35K67
Format : Talk at Waseda University
Author(s) :
- AMINE SBAI (Hassan 1st University and Granada University)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @A207
Type : Contributed Talk
Abstract : The Stefan problem is the quintessential macroscopic model of phase transitions in liquid-solid systems. We consider the one-phase Stefan problem with surface tension, set in two-dimensional strip-like geometry. We discuss the local null controllability of the system in any positive time, by means of control supported within an arbitrary open and non-empty subset.
Classification : 93B05, 35R35, 35Q35, 93C20, Stefan problem, free boundary problem, controllability
Author(s) :
- Debayan Maity (TIFR Centre for Applicable Mathematics)

Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : The purpose of this talk is to present our recent results on minimal control time for null and exact boundary controllability of 1-D linear hyperbolic balance laws with arbitrary internal and boundary coupling. We will show explicit and easy-to-compute formulas to completely characterize such critical quantities, which can be strictly smaller than the classical uniform lower bound. The difference between these two kinds of controllability will also be discussed.
Classification : 93B05, 35L04, Control of Partial Differential Equations; Boundary Controllability; Hyperbolic system involving balance laws (with source term (i.e. internal coupling)) and Conservation laws (without source term); Optimal control time
Format : Talk at Waseda University
Author(s) :
- Long Hu (Shandong University)
- Guillaume Olive (Jagiellonian University)

Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : At first, I shall explain the stability and stabilizability of an ODE around a periodic trajectory. A characterization of the stability of ODEs around a periodic trajectory using the Poincare map and Floquet theory will be discussed. Then, I shall explain the extension of the idea to the parabolic type of PDEs. In particular, as an application, the stabilization of the incompressible Navier-Stokes equation around a time-periodic trajectory will be discussed.
Classification : 93B52, 93D15, 35B10, 34H15, 76D55
Format : Talk at Waseda University
Author(s) :
- Debanjana Mitra (Department of Mathematics, IIT Bombay )

Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : Determining the control steering the dynamical system is equally important as it is to examine the controllability of a control system. This study computes the control for the approximately controllable nonlinear system governed by Caputo derivatives. By using operator theoretic formulations, the problem of computing the control gets converted into an ill-posed problem which is solved for stable approximations using Tikhonov regularization. An example is presented demonstrating the error and truncated control graphs using MATHEMATICA.
Classification : 93B05, 93C10, 47A52, 34K37
Format : Talk at Waseda University
Author(s) :
- Lavina Sahijwani (Indian Institute of Technology Roorkee, India)
- N. Sukavanam (Indian Institute of Technology Roorkee, India)
- D. N. Pandey (Indian Institute of Technology Roorkee, India)

Session Time & Room : 5C (Aug.25, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : The goal of this talk is to examine the regional boundary observability for time-fractional systems involving the Riemann-Liouville fractional derivative. The aim is to reconstruct the initial state of the system under considerations on a desired subregion of the evolution domains' boundary. The reconstruction problem is converted into a solvability problem with the form $AX=b$ using an adaptation of the Hilbert uniqueness method. Some successful numerical examples were simulated and provided at the end.
Classification : 93B07, 93B28, 26A33, 46F12
Format : Online Talk on Zoom
Author(s) :
- Khalid Zguaid (Higher School of Education and Training of Agadir (ESEFA), Ibn Zohr University)
- Fatima Zharae El Alaoui (Moulay Ismail University)