Miroslav Krstic, Professor of Mechanical and Aerospace Engineering and Associate Vice Chancellor for Research at the University of California, San Diego recently received an impressive gift for his 50th birthday.
Forty-six of his colleagues in the control theory and systems field – including the most prominent scholars and scientists in his area of specialty of nonlinear control and delay systems – dedicated a new 400-page special-issue volume in his honor.
The book highlights some of Krstic’s greatest contributions – as well as the legacy of those contributions – to the field of nonlinear control theory and systems.
While control systems theorists and engineers mastered nonlinear control systems approximately 15 years ago, this mastery only held up under the assumption that there are no delays in sensing, computation, actuation, or communication over a network. Delays, however, are inevitable.
In the mid-2000s, Krstic’s work on the then-active topic of control of fluid flows for aerodynamic drag reduction led to an elegant solution to this delay conundrum. The fluid flow systems Krstic was studying are not modeled by conventional ordinary differential equations but by partial differential equations. And delays are a special case of such partial differential equations.
“Few things intimidate a controls engineer as much as ‘latency’ in sensing or computation,” said Krstic. “Wrong timing of a control signal can turn stabilizing negative feedback into destabilizing positive feedback and result in potentially calamitous consequences.”
Krstic adapted his techniques developed for flow control to compensation of large delays in nonlinear control systems. He developed a method that takes any controller designed for a system without a delay and makes it work in the presence of a delay of arbitrary length, even when the delay varies with time or depends on the system's state (such as the solid-liquid interface in extruders for 3D printing), and even when the delay value is unknown.
Krstic's breakthrough occurred in the late 2000s and quickly attracted the attention of researchers looking for mathematical challenges as well as engineers looking to solve real-world challenges.
Most if not all "nonlinear control designers" have since turned their attention to nonlinear control systems under delays, and Krstic believes that the possibilities are endless.
“Now that a whole generation of researchers has been eased into control of nonlinear infinite-dimensional systems, the day will soon come when they will start conquering problems that only a few years ago they would not have imagined of even attempting,” said Krstic. “These could include coupled nonlinear partial differential equations governing plasmas in lasers and fusion, electrochemistry in batteries, congestion in road and air traffic, and control of systems over wireless networks with volatile delays.”
Much of the work done by this group of researchers to date is gathered in the volume that pays tribute to Krstic and his legacy on this and other subjects. Many of their contributions are theoretical, but some of them already deal with applications such as neuromuscular stimulation for patients with mobility disorders, stabilization of networks of compressible fluids, automotive engines, heat exchangers, population dynamics, and magnetic bearings.
“This book is dedicated to Professor Miroslav Krstic on his 50thbirthday,” says the book’s dedication, “to help honor him for his many important contributions to control theory and its applications. Through his many excellent presentations and publications, including 10 books, and his helpful discussions, Miroslav has inspired each of us to work on challenging control problems.”
Krstic said the birthday gift, hatched and completed in complete secrecy, was a real surprise.
“In my field, an honor like this is reserved for a few top people – there was previously only one in the UC system – on the occasion of their 60th or 70th birthdays, and it is typically a special issue of a journal, not a book. So it is both deeply humbling and a real honor.”
50 is the new 70, it seems.
The book, “Recent Results on Nonlinear Delay Control Systems,” will be published by Springer, a publisher of innovative academic and professional books, reference works, and journals.