Abstract: Feedback design for stabilization has been the central objective in control theory for more than 60 years. Over the last decade, inspired by applications to autonomous cars and biped robots, safety, as an objective that in some cases conflicts with stabilization to a desired equilibrium or trajectory, has opened up and thrived as a research topic, in both academia and industry. I will present feedback design ideas for safety in three directions: (1) for high relative degree control barrier functions, CBFs, such as position constraints under force inputs, which is pertinent to vehicles, (2) backstepping-based safety filter feedback designs, and (3) the notion of safety relaxed from the infinite-time notion of “safe forever” (which is conservative and sacrifices performance) to the notion of “safe over a user-prescribed time interval,” which I shorten to ‘prescribed-time safety’ (PTSf).
With safety filter feedback laws that guarantee PTSf, the system doesn’t have to be kept farther and longer away from the barrier than necessary. PTSf filters permit an operator eager to cross the barrier to do so as soon as the prohibition to cross the barrier ends. This is not achievable with exponential safety filters. Safe feedback design for high relative degree CBFs goes back to the 2006 backstepping for “non-overshooting control.” In that work I introduced chains of linear and nonlinear first-order subsystems that govern the CBFs, ensuring, by backstepping, that all the CBFs in the chain begin and remain positive. I will present PTSf versions of these 2006 designs.
Already considered in 2006, disturbances are now handled more powerfully in the PTSf framework, ensuring complete disturbance rejection by the terminal time — a full “rescue to safety” of a system that might have been thrown beyond the boundary by a very large disturbance. When disturbances are stochastic, I achieve safety in the sense of the mean, i.e., mean-PTSf.
Bio: Miroslav Krstic is Distinguished Professor of Mechanical and Aerospace Engineering, holds the Alspach endowed chair, and is the founding director of the Center for Control Systems and Dynamics at UC San Diego. He also serves as Senior 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 has been elected Fellow of EEE, IFAC, ASME, SIAM, AAAS, IET (UK), and AIAA (Assoc. Fellow) - and as a foreign member of the Serbian Academy of Sciences and Arts and of the Academy of Engineering of Serbia. He has received the Richard E. Bellman Control Heritage Award, SIAM Reid Prize, ASME Oldenburger Medal, Nyquist Lecture Prize, Paynter Outstanding Investigator Award, Ragazzini Education Award, IFAC Nonlinear Control Systems Award, Chestnut textbook prize, Control Systems Society Distinguished Member Award, the PECASE, NSF Career, and ONR Young Investigator awards, the Schuck (’96 and ’19) and Axelby paper prizes, and the first UCSD Research Award given to an engineer. Krstic has also been appointed to the Springer Professorship at UC Berkeley, as Distinguished Visiting Fellow by the Royal Academy of Engineering, the Invitation Fellow of the Japan Society for the Promotion of Science, and to four honorary professorships outside of the United States.
He serves as Editor-in-Chief of Systems & Control Letters, Senior Editor in Automatica and IEEE Transactions on Automatic Control, editor of two Springer book series, Vice President for Technical Activities of the IEEE Control Systems Society and chair of the IEEE CSS Fellow Committee. Krstic has coauthored fifteen books on adaptive, nonlinear, and stochastic control, extremum seeking, control of PDE systems including turbulent flows, and control of delay systems.