# Registered Data

Contents

- 1 [CT191]
- 1.1 [00100] Pointwise Controllability of Degenerate/Singular PDEs
- 1.2 [00181] Control of the Stefan problem
- 1.3 [00520] Controllability of Generalized Fractional Dynamical Systems
- 1.4 [00900] Controllability of fractional impulsive damped stochastic systems with distributed delays
- 1.5 [00984] TRAJECTORY CONTROLLABILITY OF FRACTIONAL LANGEVIN INTEGRO-DIFFERENTIAL SYSTEMS IN HILBERT SPACES
- 1.6 [01061] Computation of control for fractional nonlinear systems using Tikhonov regularization
- 1.7 [02358] Minimal time for boundary controllability of linear hyperbolic balance laws
- 1.8 [01204] Observer-based control for nonlinear time-delayed system under delay fractionising approach
- 1.9 [01995] Theoretical and Numerical Study of Regional Boundary Observability for Linear Time-Fractional Systems.
- 1.10 [00864] Stabilization of time-periodic flows

# [CT191]

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

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**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__**Author(s)**:**AMINE SBAI**(Hassan 1st University and Granada University)

## [00181] Control of the Stefan problem

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**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)

## [00520] Controllability of Generalized Fractional Dynamical Systems

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**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__**Author(s)**:**Balachandran Krishnan**(Department of Mathematics, Bharathiar University, Coimbatore-641046)

## [00900] Controllability of fractional impulsive damped stochastic systems with distributed delays

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: This paper investigates the controllability of nonlinear fractional impulsive damped stochastic systems with distributed delays. The fractional derivatives in the considered system are assumed to have Caputo derivatives. The sufficient conditions for controllability are derived using the Banach fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. At last, an example is given to illustrate the usefulness of the main results.**Classification**:__93B05__,__34A08__,__60H10__**Author(s)**:**Arthi Ganesan**(PSGR Krishnammal College for Women, Coimbatore)

## [00984] TRAJECTORY CONTROLLABILITY OF FRACTIONAL LANGEVIN INTEGRO-DIFFERENTIAL SYSTEMS IN HILBERT SPACES

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: In this talk, the sufficient conditions for trajectory controllability of nonlinear fractional Langevin integro-differential systems involving Caputo fractional derivative of order $0<\alpha, \beta \leq 1$ in finite-dimensional Hilbert spaces are obtained. The main results are well illustrated with examples.**Classification**:__93B05__,__93B05__,__37N35__**Author(s)**:**SURESH KUMAR P**(NATIONAL INSTITUTE OF TECHNOLOGY ANDHRA PRADESH)

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

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**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__**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)

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

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**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__**Author(s)**:**Long Hu**(Shandong University)- Guillaume Olive (Jagiellonian University)

## [01204] Observer-based control for nonlinear time-delayed system under delay fractionising approach

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: In this research, an observer-based control for a time delay system is developed. The main goal of the research is to derive tractable conditions for stability analysis with reduced conservatism. By using the Lyapunov-Krasovskii approach, delay fractionising and matrix inequality techniques, a robust observer-based control strategy is proposed so that conditions which ensures stochastic stability of the system are obtained. Finally, numerical examples provide evidence for giving the desired result with the proposed control.**Classification**:__93B07__,__93E03__,__93D05__,__93D09__**Author(s)**:**Maya Joby**(KCG College of Technology)- Srimanta Santra (Technion-Israel Institute of Technology)

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

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**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__**Author(s)**:**Khalid Zguaid**(Moulay Ismail University)- Fatima Zharae El Alaoui (Moulay Ismail University)

## [00864] Stabilization of time-periodic flows

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**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__**Author(s)**:**Debanjana Mitra**(Department of Mathematics, IIT Bombay )