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As a part of my research work, I am working
on the optimal control problems for linear and nonlinear partial differential
equations and their applications with an emphasis on theory and computation. The
concept of controllability denotes the ability to move a system around in
its entire configuration space using only certain admissible manipulations, and
the time-optimal control problem under consideration consists of finding
control in an admissible set which minimizes the certain cost functional. These
problems arise naturally in various areas of science and technology, such as
controlling the heat in the electrically heated oven and reheating furnaces,
controlling the crystal growth/dissolution in the chemical process, control of the
the concentration of an activator in biochemistry and optimal portfolio selection
process in the financial market. The theory of optimal control is one of the
major areas of application of mathematics today. From its early origin to meet
the demands of the automatic control system design in engineering, it has grown
steadily in scope and now has spread to too many unrelated distinct areas such
as economics and biosciences. In my Ph.D. thesis, we focus our attention on the
optimal control problems associated with the controllability of parabolic
differential equations and parabolic integrodifferential equations by using
semi-group theory. We also carry out some numerical experiments on the
penalized optimal control problems for different target states or final states
for different control problems. Presently, I am working in the following areas:
- Theoretical
and Numerical Study of the Control Problems Involving Differential Equations
with memory terms.
- Numerical
approximation of optimal control problems involving partial differential equations by the virtual element method (VEM), which is a recently developed technique.
- Application of optimal control theory in software reliability growth modelling.
Ph. D. Guidance
-
(AS a Co-supervisor) Mr. Santosh K Bhal, “Orthogonal
Spline Collocation Methods for the Differential Equations with Interfaces”, Completed in May-2020.
- Mr. Jai Tushar, “Numerical Approximation of Optimal Control
Problems Using Virtual Element Method”, Completed in December-2022.
- Mr. Sujit Kumar Pradhan, “Application of optimal control theory in
software reliability growth modeling”, (Ongoing).
For more information see, my resume.