Haider Ali Biswas
Khulna University
Optimal control applied to stellar models in relativistic dynamics
Abstract
Optimal Control has its origins in practical flight mechanics problems in aerospace engineering. It emerged as a distinct field of research in the 1950s, to address in a unified fashion optimization problems arising in scheduling and the control of engineering devices, beyond the reach of traditional analytical and computational techniques. The systematic research in the optimal control problems dates from the late 1950s and a tremendous developments were occurred in the 1982s by several authors specially by F. Clarke for the development of nonsmooth optimal control and its distinct calculus. But now, 70 years on, the research in this field rests not only on aerospace applications, but on applications in new areas such as process control, resource economics, robotics, mathematical biology and epidemiology of infectious diseases. Equally significant is the stimulus optimal control has given to research in related branches of mathematics (e.g. convex analysis, nonlinear analysis, functional analysis, and dynamical systems). From a modern perspective, optimal control is an outgrowth of the calculus of variations which takes account of new kinds of constraints (e.g. differential equation constraints, pathwise constraints on control functions, etc.) encountered in advanced engineering design. A number of key recent developments in optimal control have resulted from marrying old ideas from the calculus of variations and modern analytical techniques. So, optimal control opens a new horizons in the field of calculus of variations as its modern guise and continues to be dominated as a distinct research field specially in Mathematical Physics as well as in Engineering Mathematics. Optimal control is a mathematical technique that is powerful and useful and can be applied to solve the mathematical problems in astrophysics, relativity and cosmology.
In this talk, we discuss some of the applications of optimal control theory in the form of ‘maximum principle’ to obtain the condition of hydrostatic equilibrium of relativistic stellar models, their construction, equilibrium and stability. It is shown that a straightforward application of Pontryagin’s maximum principle has led directly to the Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic equilibrium.
Bio
Dr. Md. Haider Ali Biswas is currently affiliated with Khulna University, Bangladesh as a Professor of Mathematics under Science Engineering and Technology School and he served as the Head of Mathematics Discipline from 2015 to 2018. Prof. Biswas obtained his B Sc (Honors) in Mathematics and M Sc in Applied Mathematics in the year 1993 and 1994 respectively from the University of Chittagong, Bangladesh, M Phil in Mathematics in the year 2008 from the University of Rajshahi, Bangladesh and Ph D in Electrical and Computer Engineering from the University of Porto, Portugal in 2013. He has more than 20 years teaching and research experience in the graduate and post-graduate levels at different public universities in Bangladesh. He published three books, three book chapters and more than 100 research papers in the peer reviewed journals and international conferences. Prof. Biswas has worked at several R & D projects in home and abroad as PI and/or Researcher, particularly he is conducting different research projects funded by the Ministry of Science and Technology, Bangladesh, University Grants Commission of Bangladesh and The World Academy of Science (TWAS), Trieste, Italy. His present research interests include Optimal Control with Constraints, Application of Optimal Control in Relativistic Dynamics, Nonsmooth Analysis, Mathematical Modeling, Mathematical Biology and Biomedicine, Epidemiology of Infectious Diseases. He is the life/general members of several professional societies and/or research organizations like Bangladesh Mathematical Society (BMS), Asiatic Society of Bangladesh (ASB), Institute of Mathematics and its Applications (IMA), UK, European Mathematical Society (EMS) and Society for Mathematical Biology (SMB). Dr. Biswas was the General Secretary of Mathematical Forum Khulna in 2013-2015. Dr. Biswas organized several national and international seminars/workshops/conferences in home and abroad and he has been working as editor/member of editorial boards of several international peer-reviewed journals. Professor Biswas contributed as Keynote/Invited/Plenary/Panel speaker at several international conferences/seminars/workshops in home and abroad. Professor Biswas has been nominated as the Member of the Council of Asian Science Editors (CASE) for 2017-2020 and the Associate Member of the Organization for Women in Science for the Developing World (OWSD) since 2017. Recently, Professor Biswas has been elected as a Member of Executive Committee of Bangladesh Mathematical Society (BMS) for the year 2020-2021, and also nominated as the Associate Editor of the international journal GANIT- an official journal of Bangladesh Mathematical Society (BMS) for the year 2020-2021. Dr. Biswas has been nominated as a Member of Executive Committee of the IEOM Society Int., Bangladesh Chapter (IEOM-BD) and also serving as the Treasurer of the IEOM-BD for the year 2020-2021. He has been serving as the Founder Faculty Advisor of the IEOM Society Khulna University Chapter (IEOM-KU) since 2015. Professor Biswas is presently serving as the President of Bangladesh Society for Mathematical Biology (BSMB) for the year 2020-2022.