Seminar talk of Dr. Grushkovskaya and Prof. Dr. Zuyev

 

Speakers

1. Dr. Victoria Grushkovskaya (University of Klagenfurt)

2. Prof. Dr. Alexander Zuyev (MPI Magdeburg)

Title

1. Time-varying feedback control of nonholonomic systems: full- and partial state stabilization (Dr. Victoria Grushkovskaya)

2. On periodic optimal control problems with isoperimetric constraints (Prof. Dr. Alexander Zuyev)

Abstract

1. This talk focuses on the development of stabilizing control for nonholonomic systems, i.e., systems with non-integrable constraints. Such systems describe the motion of many important industrial objects, e.g., mobile robots, wheeled systems, autonomous underwater and air vehicles, spacecrafts, robotic manipulators, rolling bodies, etc. Generally, nonholonomic systems can be represented as driftless control-affine systems of ODEs which have several significant features, such as lack of control inputs and uncontrollable linearization. One of the main results of this talk describes a novel unified control design for solving a variety of control problems such as: stabilization of an equilibrium point, tracking an arbitrary curve in the state space, and motion planning with obstacles for rather general non-autonomous systems. Moreover, a similar control approach is exploited for solving partial stabilization problem. The proposed control design scheme is illustrated with several examples.

2. An isoperimetric optimal control problem with non-strictly convex cost is considered for nonlinear systems of ordinary and partial differential equations subject to periodic boundary conditions and input constraints. This type of problems appears naturally, e.g., in the optimization of non-isothermal reaction models in chemical engineering. It is shown that the optimal controls are piecewise constant (bang-bang) in the considered case due to the Pontryagin maximum principle. We present an estimate of the number of switchings of the extremal controllers and formulate the general problem of existence and computation of periodic solutions under the discontinuous control. For small periods, an approximation of the periodic solutions with discontinuous control functions is presented based on the Chen-Fliess expansion. In the case of systems with dominating linear parts, an iterative scheme for approximating the periodic solutions is presented for arbitrary values of periods. It is shown that this scheme can be improved with the use of Newton type methods.

Bio

1. Victoria Grushkovskaya received her Master’s degree in Mathematics from Donetsk National University (Ukraine) in 2010, and her Ph.D. degree from the Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine (IAMM NASU), in 2013. In 2015, she joined the Institute for Systems Theory and Automatic Control, University of Stuttgart (Germany) as a postdoctoral researcher within the scope of the Alexander von Humboldt fellowship. In 2018, she obtained a DFG research grant for carrying out her research project at the Institute of Mathematics, Julius Maximilian University of Würzburg, where she was working as a postdoctoral researcher until November 2019. From December 2019, Victoria Grushkovskaya works as a postdoctoral assistant at the Institute of Mathematics, University of Klagenfurt. Her primary research interests are in the areas of mathematical control theory and nonlinear dynamics. Her scientific results were awarded by the Prize of the President of Ukraine for young scientists and the Honorary Medal of the National Academy of Sciences (NAS) of Ukraine “Talent, Inspiration, Work” for personal research achievements of young scientists.

2. Alexander Zuyev received his Diploma with Honors in Mathematics from Donetsk National University in 1997 and a PhD degree in 2000 from the Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine (IAMM NASU). He was a visiting scientist at the Abdus Salam International Centre for Theoretical Physics under the aegis of UNESCO and IAEA in Trieste and received the Alexander von Humboldt Research Fellowship at TU Ilmenau and the University of Stuttgart. Since his habilitation in 2008, he has been working as a Professor and Head of the Department of Mechanics at IAMM NASU. Alexander Zuyev is currently with the Otto von Guericke University Magdeburg and the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Germany. Alexander Zuyev is a Corresponding Member of the National Academy of Sciences of Ukraine (elected in 2021) and a laureate of several prestigious awards, including the State Award of Ukraine in Science and Technology and awards of the President, Cabinet of Ministers, and Parliament of Ukraine.

Time and Place

March 28, 4pm

Seminar room 333, 3rd floor in our ICT cubes