Abstract

Numerous physical systems are governed by partial differential equations or involve delays/transport. Such infinite-dimensional models have been a challenge to the ODE-accustomed control engineers who seek feedback designs that are both constructive and provide stability guarantees. About 15 years this situation changed with the emergence of “continuum backstepping” approach for PDEs. The backstepping designs, whose initial applications were for Navier-Stokes equations, yield explicit feedback laws which convert the original system into a desired well-behaved “target system” (for Navier-Stokes, the target is a heat equation system). I will present the basic methodological ideas of PDE backstepping and illustrate them with examples that come from fluid flows, phase change, 3D printing, multi-vehicle robotic swarms, microbial populations, and opinion spreading in online social networks.

Bio

Miroslav Krstic holds the Alspach endowed chair and is the founding director of the Cymer Center for Control Systems and Dynamics at UC San Diego. He also serves as Associate Vice Chancellor for Research at UCSD. As a graduate student, Krstic won the UC Santa Barbara best dissertation award and student best paper awards at CDC and ACC. Krstic is Fellow of IEEE, IFAC, ASME, SIAM, and IET (UK), Associate Fellow of AIAA, and foreign member of the Academy of Engineering of Serbia. He has received the PECASE, NSF Career, and ONR Young Investigator awards, the Axelby and Schuck paper prizes, the Chestnut textbook prize, the ASME Nyquist Lecture Prize, and the first UCSD Research Award given to an engineer. Krstic has also been awarded the Springer Visiting Professorship at UC Berkeley, the Distinguished Visiting Fellowship of the Royal Academy of Engineering, the Invitation Fellowship of the Japan Society for the Promotion of Science, and the Honorary Professorships from the Northeastern University (Shenyang), Chongqing University, and Donghua University, China. He serves as Senior Editor in IEEE Transactions on Automatic Control and Automatica, as editor of two Springer book series, and has served as Vice President for Technical Activities of the IEEE Control Systems Society and as chair of the IEEE CSS Fellow Committee. Krstic has coauthored eleven books on adaptive, nonlinear, and stochastic control, extremum seeking, control of PDE systems including turbulent flows, and control of delay systems.