# Registered Data

Contents

- 1 [CT191]
- 1.1 [00520] Controllability of Generalized Fractional Dynamical Systems
- 1.2 [00100] Pointwise Controllability of Degenerate/Singular PDEs
- 1.3 [00181] Control of the Stefan problem
- 1.4 [02358] Minimal time for boundary controllability of linear hyperbolic balance laws
- 1.5 [00864] Stabilization of time-periodic flows
- 1.6 [01061] Computation of control for fractional nonlinear systems using Tikhonov regularization
- 1.7 [01995] Theoretical and Numerical Study of Regional Boundary Observability for Linear Time-Fractional Systems.

# [CT191]

**Session Time & Room****Classification**

## [00520] Controllability of Generalized Fractional Dynamical Systems

**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)

## [00100] Pointwise Controllability of Degenerate/Singular PDEs

**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)

## [00181] Control of the Stefan problem

**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)

## [02358] Minimal time for boundary controllability of linear hyperbolic balance laws

**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)

## [00864] Stabilization of time-periodic flows

**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 )

## [01061] Computation of control for fractional nonlinear systems using Tikhonov regularization

**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)

## [01995] Theoretical and Numerical Study of Regional Boundary Observability for Linear Time-Fractional Systems.

**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)