Prof. Arjan van der Schaft
Johann Bernoulli Institute for Mathematics and Computer Science
University of Groningen, The Netherlands
Tuesday 2017-11-23 16:00
IST-Seminar-Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
Key constraint in the control of power networks is supply-demand matching, with the total consumed power equal to the total generated power. Optimization of the so-called social welfare function under the constraint of supply-demand matching leads to an optimal set-point for the operation of the power network. Continuous-time implementation of the primal-dual gradient algorithm converging to this optimal set-point defines a distributed dynamical controller for the physical power network. This controller also admits the interpretation of a market (pricing) dynamics. It will be shown that the optimal set-point is an asymptotically stable equilibrium of the resulting closed-loop system. Main idea in the proof is the port-Hamiltonian modeling of the physical network, as well as of the primal-dual gradient controller, leading to a natural global Lyapunov function. (joint work with Tjerk Stegink and Claudio De Persis)
Arjan van der Schaft received the (under)graduate and PhD degrees in Mathematics from the University of Groningen, the Netherlands, and joined the University of Twente, where he was appointed as full professor in Mathematical Systems and Control Theory in 2000. In September 2005 he returned to his Alma Mater as professor in Mathematics.
Books authored by him include Variational and Hamiltonian Control Systems (1987, with P.E. Crouch), Nonlinear Dynamical Control Systems (1990, 2016, with H. Nijmeijer), L2-Gain and Passivity Techniques in Nonlinear Control (1996, 2000, 2017), An Introduction to Hybrid Dynamical Systems (2000, with J.M. Schumacher), and Port-Hamiltonian Systems: An Introductory Overview (2014, with D. Jeltsema).
Arjan van der Schaft is Fellow of the Institute of Electrical and Electronics Engineers (IEEE), Fellow of the International Federation of Automatic Control (IFAC), and was the 2013 recipient of the 3-yearly awarded Certificate of Excellent Achievements of the IFAC Technical Committee on Nonlinear Systems. He was Invited Speaker at the International Congress of Mathematicians, Madrid, 2006.