Miroslav Krstić

Education After his 5-year BSc degree from University of Belgrade's School of Electrical Engineering in 1989 and two years of teaching, Krstić moved to UC Santa Barabara, California in 1991 for PhD study with Petar Kokotovic. His first journal paper, written a few weeks upon arrival, transformed adaptive control. Krstić's 455-page 1994 PhD dissertation earned the campuswide Lancaster Best Dissertation Award, was published by Wiley in 1995, and is one of the classics of control theory. and George S. Axelby outstanding paper awards. He also received the best student paper awards at the 1993 IEEE Conference on Decision and Control and 1996 American Control Conference.

Faculty career After two years as assistant professor at University of Maryland, Krstić is the first engineering professor to receive the UC San Diego Chancellor's Award for Research, in 2005. In 2008 he founded the Cymer Center for Control Systems and Dynamics. Since 2012 he has served as Senior Associate Vice-Chancellor for Research.

Research in Control Theory Krstić is a co-author of 19 books, about 500 journal papers, ), with more than 110 papers in each of the two journals. NONLINEAR and ADAPTIVE CONTROL. Krstić’s 1995 book with Kanellakopoulos and Kokotovic, an expanded version of his PhD dissertation, Krstić introduced the tuning-function designs, modular designs, nonlinear swapping, passivity-based identifiers, adaptive CLFs and ISS-CLFs, and output-feedback adaptive nonlinear and linear controllers based on backstepping. STOCHASTIC STABILIZATION. Krstić and his student Deng developed stabilizing controllers for stochastic nonlinear systems, introduced ISS-CLFs to stochastic systems, and designed differential game controllers that achieve, with probability one, peak-to-peak gain function assignment with respect to unknown noise covariance. EXTREMUM SEEKING. Krstić pioneered, for general nonlinear dynamical systems, extremum seeking (ES) as an approach for real-time model-free optimization. To establish stability and performance guarantees, he introduced a combination of averaging and singular perturbation techniques to establish exponential stability. Among Krstić’s advances of ES is source seeking for autonomous vehicles, model-free Nash equilibrium seeking for non-cooperative games, Newton-based ES for model-free assignment of convergence rate, model-free stabilization by minimum-seeking of CLFs, and ES for maps with large delays and PDEs with Oliveira. STOCHASTIC AVERAGING AND STOCHASTIC EXTREMUM SEEKING. In introducing stochastic ES, Krstić and his postdoc Liu generalized stochastic averaging theorems by removing the restrictions of global Lipschitzness, global exponential stability of the average system, vanishing noise, and finiteness of time horizon. PDE BACKSTEPPING. Krstić generalized backstepping control from ODEs to PDEs. His IFAC Chestnut prize -winning book with his student Smyshlyaev provides an accessible introduction to PDE backstepping. PDE backstepping uses explicit and invertible Volterra-type integral transformations, with spatial integration kernels governed by linear PDEs of Goursat type on triangular domains. His general methodology stabilizes PDEs of parabolic and hyperbolic types, as well as of higher orders in space (Korteweg-De Vries, Schroedinger, Kuramoto-Sivashinsky, beams, etc.). For PDEs with unknown parameters, Krstić developed adaptive controllers. Krstic applied PDE backstepping to traffic flows with his student Yu and to additive manufacturing with his student Koga. CONTROL OF NAVIER-STOKES SYSTEMS. For turbulent fluids, including electrically conducting flows with Maxwell’s PDEs (magnetohydrodynamic/MHD flows), Krstić and his student Vazquez developed flow control designs. ISS FOR PDEs. Despite the unboundedness of input operators in PDEs with boundary inputs, Krstić and Karafyllis established ISS of PDEs, developed small-gain theorems for PDEs, and enabled analysis of interconnected PDEs from different classes. PREDICTORS FOR NONLINEAR DELAY SYSTEMS. In his single-authored 2009 Birkhäuser book Krstić extended his hyperbolic PDE results to nonlinear ODEs with delays. He introduced nonlinear predictor operators of the infinite-dimensional delay state and launched control of interconnected PDE-ODE and PDE-PDE systems. In three subsequent books, Krstić and collaborators generalized the predictors to time- and state-dependent delays, to delay-adaptive control for unknown delays, and to sampled-data implementation. PRESCRIBED-TIME CONTROL. Krstić introduced time-varying techniques for the design and analysis of controllers Krstić introduced deep neural operators for off-line learning of PDE backstepping designs for hyperbolic and parabolic PDEs, to enable online use of gain-scheduling backstepping for nonlinear PDEs and adaptive backstepping for PDEs with unknown parameters. He pioneered a roadmap for both the approximation theory for gain kernel PDEs and for stability guarantees under neural network approximations of the PDE backstepping controllers.

Krstić has served as Editor-in-Chief of Systems & Control Letters and as senior editor in Automatica. On January 1, 2026 he started tenure as Editor-in-Chief of IEEE Transactions on Automatic Control.

Industry Work Krstić has contributed to technologies in extreme ultraviolet lithography, advanced arresting gear for Ford-class carriers, laser spectroscopy on NASA's Curiosity (rover) on Mars, particle accelerators, oil drilling, nuclear fusion, and Li-ion battery systems. Among the living mechanical and aerospace engineers in the U.S., Krstić is ranked sixth by ScholarGPS and is among the ten highest cited according to Research.com and Google Scholar.

CHIP PHOTOLITHOGRAPHY: Krstić founded the Cymer Center for Control Systems and Dynamics in 2008. His extremum seeking (ES) algorithm helped stabilize EUV light sources at Cymer Inc. in 2012, forming the basis of US Patent 8598552B1 and reducing the chip resolution from 193 nm to 13 nm. Cymer was acquired by ASML in 2013.

AIRCRAFT CARRIERS: From 2014 to 2019, Krstić led development of control systems for the Advanced Arresting Gear on the USS Gerald R. Ford (CVN-78) aircraft carrier, through his consultancy with General Atomics.

ACCELERATORS: Krstić's ES methods were adopted at major accelerator labs including Los Alamos, CERN, and DESY, reducing re-tuning time significantly.

MARS ROVER: An MS thesis supervised by Krstić developed the autofocus algorithm used in the ChemCam on NASA's Curiosity (rover) on Mars.

OTHER TECHNOLOGIES: Krstić's work has been applied to downhole pressure sensing at Equinor, battery estimation with Bosch and ARPA-E, fusion control at General Atomics, HCCI engine optimization at Lawrence Livermore National Laboratory, and jet engine stabilization at United Technologies. He also developed controls for Northrop Grumman for UAV endurance and for the Navy’s T-craft vessel.

Awards IEEE Roger W. Brockett Control Systems Award French National Centre for Scientific Research (CNRS) Fellow-Ambassador IEEE Hendrik W. Bode Lecture Prize AACC Richard E. Bellman Control Heritage Award ASME Rufus Oldenburger Medal SIAM W. T. and Idalia Reid Prize A. V. "Bal" Balakrishnan Award for Research in Mathematics of Systems (inaugural recipient) AACC John R. Ragazzini Award IFAC Harold Chestnut Control Engineering Textbook Prize IFAC TC Award on Non-Linear Control Systems IFAC TC Distributed Parameter Systems Ruth F. Curtain Award (inaugural recipient) IFAC TC Award on Adaptive and Learning Systems IFAC TC Delay Systems "Lifetime Achievement" Award ASME Henry Paynter Outstanding Investigator Award ASME Nyquist Lecture IEEE Control Systems Society Distinguished Member Award First engineering recipient of the UC San Diego Chancellor's Associates Award for Excellence in Science & Engineering Research (immediately following the Nobel laureate Roger Tsien) Presidential Early Career Award for Scientists and Engineers Office of Naval Research Young Investigator Award National Science Foundation Career Award George Axelby Outstanding Paper Award (IEEE Transactions on Automatic Control) O. Hugo Schuck Best Paper Award (1996 and 2019) Foreign Member, Serbian Academy of Sciences and Arts Foreign Member, Academia Europaea Visiting Miller Professorship Award, Miller Institute for Basic Research in Science, University of California, Berkeley

Krstić is Fellow of seven scholarly societies: IFAC TC Distributed Parameter Systems Ruth F. Curtain Award, IFAC TC Award on Adaptive and Learning Systems, and IFAC TC Delay Systems "Lifetime Achievement" Award).

Books Nonlinear and Adaptive Control Design (1995), co-authored with Ioannis Kanellakopoulos and Petar Kokotovic; John Wiley and Sons. Stabilization of Nonlinear Uncertain Systems (1998), co-authored with Hua Deng; Springer. Flow Control by Feedback (2002), co-authored with Ole Morten Aamo; Springer. Real-Time Optimization by Extremum Seeking Feedback (2003), co-authored with Kartik B. Ariyur; John Wiley and Sons. Control of Turbulent and Magnetohydrodynamic Channel Flows (2007), co-authored with Rafael Vazquez; Birkhauser. Boundary Control of PDEs: A Course on Backstepping Designs (2008), co-authored with Andrey Smyshlyaev; SIAM. Delay Compensation for Nonlinear, Adaptive, and PDE Systems (2009); Birkhauser. Adaptive Control of Parabolic PDEs (2010), co-authored with Andrey Smyshlyaev; Princeton University Press. Stochastic Averaging and Stochastic Extremum Seeking (2012), co-authored with Shu-Jun Liu; Springer. Nonlinear Control Under Nonconstant Delays (2013), co-authored with Nikolaos Bekiaris-Liberis; SIAM. Predictor Feedback for Delay Systems: Implementations and Approximations (2017), coauthored with Iasson Karafyllis; Birkhauser, Model-Free Stabilization by Extremum Seeking (2017), co-authored with Alexander Scheinker; Springer. Input-to-State Stability for PDEs (2018), co-authored with Iasson Karafyllis; Springer. Delay-Adaptive Linear Control (2019), co-authored with Yang Zhu; Princeton University Press. Materials Phase Change PDE Control & Estimation: From Additive Manufacturing to Polar Ice (2020), co-authored with Shumon Koga; Springer. PDE Control of String-Actuated Motion (2022); co-authored with Ji Wang, Princeton University Press. Extremum Seeking through Delays and PDEs (2022), co-authored with Tiago Roux Oliveira, SIAM. Traffic Congestion Control by PDE Backstepping (2023), co-authored with Huan Yu, Birkhäuser. Robust Adaptive Control: Deadzone-Adapted Disturbance Suppression (2025), co-authored with Iasson Karafyllis,

Methods pioneered by Krstić

Adaptive Nonlinear Control Source: search/navigation in space for GPS-denied autonomous vehicles and robots Nash equilibrium seeking ES in non-cooperative game multi-agent setting Newton-based ES for model-free assignment of convergence rate and for equalizing convergence across input channels of multivariable maps; with inversion of Hessian estimate using Riccati ODE model-free stabilization with ES by minimum-seeking of CLFs (with Scheinker) ES for maps with large delays and PDEs and PDE-PDE cascades for cascades like ODEs with parabolic PDE input dynamic and reaction-diffusion PDEs with input delays adaptive PDE backstepping ISS for PDEs Source: (with Song) PT observers for state estimate convergence in arbitrary finite time (with Holloway) stochastic PT control for PT stabilization in probability (with W. Li)

Non-overshooting and Safe Nonlinear Control high relative degree CBFs recursive backstepping design of CBFs without shrinking the safe set ISSf gain assignment backstepping design of non-overshooting controllers that assign a desired input-to-state safety gain function stochastic non-overshooting control to guarantee safety at least in the mean prescribed-time safety filters to let the state reach the safety boundary by the time the prohibition on the unsafe set is lifted (as in robot-human handover) inverse optimal safety filters safety filters with safety-maximization and liveness-maximization along entire time horizon, under deterministic and stochastic disturbances safe control for PDEs for Stefan, liquid-tank, gas-piston, and chemostat (population dynamics) PDEs

Deep Neural Operators for PDE Control universal approximability theory for backstepping kernel PDEs stability guarantees under ML approximation of PDE backstepping'' for hyperbolic and parabolic PDEs