Le 16 décembre 2019

On the Optimal Control of Volterra Integro-Differential Equations

  Professor Vadim Azhmyakov

Abstract:

Our talk is related to a class of optimal control problems (OCPs) involving a specific dynamics described by Volterra integro-differential equations. We study OCPs associated with the Volterra integro-differential systems and establish the solvability property of this class of problems. A special structure of the abstract dynamic optimization problem under consideration makes it possible to interpret the initially given sophisticated OCP as a separate convex optimization problem in a suitable Hilbert space. This fact implies effective splitting type solution schemes in combination with the first-order computational methods for the numerical treatment of the initially given OCPs. We concretely consider the celebrated Armijo-type gradient method for this purpose. Finally, we give a mathematically rigorous proof of the numerical consistence of splitting algorithm applied to the main OCP.

Vadim Azhmyakov graduated in 1989 from the Department of Aerospace Engineering, Technical University of Moscow. After receiving his Ph.D. in Applied Mathematics in 1994 (Russian Academy of Science, Moscow, Russia), Vadim Azhmyakov has worked as Researcher and Assistant Professor in Institute of Control Problems (Moscow, Russia), University of Bayreuth (Bayreuth, Germany) and University of Greifswald (Greifswald, Germany). At 2006, he has additionally completed his “Habilitation” in Applied Mathematics at the EMA University of Greifswald (Greifswald, Germany). Afterwards he has worked as a Senior Researcher at the University of Magdeburg (Magdeburg, Germany) and Technical University of Berlin (Berlin, Germany). Since 2007 until 2014, he was appointed as a Research Professor at the Center for Advanced Study and Research of the Mexican National Polytechnic Institute (Mexico City, Mexico) and sinse 2013 as a Senior Researcher at the Younicos AG (Berlin, Germany). Since 2014 Vadim Azhmyakov works as a Professor in various Universities in Colombia, recently he holds a Full Professor position at the Department of Mathematical Sciences the EAFIT University (Medellin, Colombia).

Vadim Azhmyakov is an author of more than 120 research papers and professional conference contributions. He is also an author of 4 professional research monographs. He has experience in Applied Mathematics, Control Engineering and Applied Mechanics.