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Miroslav Krstić

Miroslav Krstić (Serbian Cyrillic: Мирослав Крстић) is an American control theorist, Distinguished Professor at University of California, San Diego (UCSD), and Senior Associate Vice Chancellor for Research. In the list of notable researchers in systems and control, he is the youngest. ScholarGPS ranks him as the world's top control theory author, among more than 750,000 in that field.

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. For single-authored papers from his PhD, Krstić earned the O. Hugo Schuck 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 was recruited as associate professor by University of California, San Diego (UCSD) in 1997. In 2000, after receiving the NSF Career, ONR YIP, and PECASE from President Clinton, he was promoted to full professor, and in 2015 to Distinguished Professor. 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, and is the highest-published author in both of the flagship control systems journals, Automatica and IEEE Transactions on Automatic Control (according to Scopus), with more than 110 papers in each of the two journals.

  1. NONLINEAR and ADAPTIVE CONTROL. Krstić’s 1995 book with Kanellakopoulos and Kokotovic, an expanded version of his PhD dissertation, pioneered adaptive stabilization methods for nonlinear systems with unknown parameters and is the second highest-cited control monograph. 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. <u>STOCHASTIC STABILIZATION</u>. 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.
  2. 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.  <u>STOCHASTIC AVERAGING AND STOCHASTIC EXTREMUM SEEKING</u>. 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.
  3. 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. <u>CONTROL OF NAVIER-STOKES SYSTEMS</u>. For turbulent fluids, including electrically conducting flows with Maxwell’s PDEs (magnetohydrodynamic/MHD flows), Krstić and his student Vazquez developed flow control designs. <u>ISS FOR PDEs</u>. 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.
  4. 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.
  5. PRESCRIBED-TIME CONTROL. Krstić introduced time-varying techniques for the design and analysis of controllers and observers that achieve stabilization in user-prescribed time, independent of initial conditions, and even in the presence of deterministic disturbances and stochastic disturbances.
  6. SAFE, NON-OVERSHOOTING NONLINEAR CONTROL. In his 2006 paper, Krstić pioneered a backstepping procedure for guaranteeing what is now referred to as "safety" and back then as "non-overshooting" control. He provided designs for CBFs of high relative degree and for achieving, for systems with unmatched disturbances, what is now referred to as input-to-state safety (ISSf). He extended deterministic non-overshooting control to nonlinear systems with stochastic disturbances. He extended his prescribed-time (PT) idea from stabilization to safety, introducing PT safety filters,' which reduce the restrictiveness of conventional exponential safety filters. He converted his results on inverse optimal stabilization to inverse optimal safe control, where a safety filter simultaneously maximizes safety and liveness, over the entire infinite time horizon. He generalized safety control from ODEs to PDEs.
  7. MACHINE LEARNING FOR PDE CONTROL. In his 2023 IEEE Bode Lecture, 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&nbsp;nm to 13&nbsp;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

Krstić is Fellow of seven scholarly societies: Institute of Electrical and Electronics Engineers (IEEE), International Federation of Automatic Control (IFAC), Society for Industrial and Applied Mathematics (SIAM), American Society of Mechanical Engineers (ASME), American Institute of Aeronautics and Astronautics (AIAA), American Association for the Advancement of Science (AAAS), and UK's Institution of Engineering and Technology (IET).

For launching new control system directions, Krstić has been recognized by International Federation of Automatic Control (IFAC) with a quadfecta of triennial technical awards (IFAC TC Award on Non-Linear Control Systems, 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

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

Methods pioneered by Krstić

Adaptive Nonlinear Control

Source:

  1. tuning-function design
  2. * adaptive backstepping with a single parameter estimator, for unmatched parametric uncertainties
  3. modular designs
  4. * combine any parameter estimator with any ISS controller
  5. nonlinear swapping
  6. * stability analysis with nonlinear filter-based gradient and least-squares parameter estimators for nonlinear systems
  7. passivity-based identifiers
  8. * identifiers with observers and nonlinear damping
  9. adaptive CLFs and ISS-CLFs
  10. * general frameworks for Lyapunov and ISS-based adaptive nonlinear control
  11. output-feedback nonlinear and linear adaptive backstepping
  12. * adaptive observer-based controllers with K-filters

Stochastic Nonlinear Stabilization

Source:

  1. stochastic backstepping
  2. * backstepping employing Itô calculus for continuous-time stochastic systems; ensures stability in probability
  3. noise-to-state stability (NSS)
  4. * ISS in probability with respect to unknown covariance of noise
  5. inverse optimal differential games w.r.t. noise covariance
  6. * optimal assignment of integral gains from covariance to state

Extremum Seeking

  1. stability of extremum seeking for general nonlinear dynamical systems
  2. * analysis via singular perturbations and averaging of reduced model
  3. source seeking
  4. * search/navigation in space for GPS-denied autonomous vehicles and robots
  5. Nash equilibrium seeking
  6. * ES in non-cooperative game multi-agent setting
  7. Newton-based ES
  8. * 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
  9. model-free stabilization with ES
  10. * by minimum-seeking of CLFs (with Scheinker)
  11. ES for maps with large delays and PDEs
  12. * employing PDE backstepping (with Oliveira)
  13. stochastic extremum seeking
  14. * for ES with random walk perturbations, like employed by E.Coli bacteria (with Liu)
  15. generalized stochastic averaging
  16. * without restrictions (of global Lipschitzness, global exp. stability of average system, vanishing noise)

PDE Backstepping

Source:

  1. backstepping transformations, kernel PDEs
  2. * transformations into desirable target PDEs
  3. * analysis of Goursat-form PDEs for gain kernels (with Smyshlyaev)
  4. backstepping for parabolic and hyperbolic PDEs
  5. * designs of full-state stabilizing feedback law and convergent observers
  6. backstepping for PDE-ODE and PDE-PDE cascades
  7. * for cascades like ODEs with parabolic PDE input dynamic and reaction-diffusion PDEs with input delays
  8. adaptive PDE backstepping
  9. * for PDEs (parabolic and hyperbolic) with unknown functional parameters, using Lyapunov, swapping, and passive estimators
  10. traffic flow stabilization
  11. * control of ARZ PDEs (with Yu)
  12. additive manufacturing
  13. * control of Stefan PDEs (with Koga)

Navier-Stokes Stabilization and Mixing

  1. Backstepping for turbulent flows and MHD systems (with Vazquez)
  2. * Stabilizing controllers and observers at high Reynolds and Hartmann numbers
  3. Fluid mixing by optimal de-stabilization

ISS for PDEs

Source:

  1. ISS to boundary inputs (with Karafyllis)
  2. small-gain theorems for PDEs
  3. * for parabolic and hyperbolic PDEs

Predictors for Nonlinear Delay Systems

  1. nonlinear predictors
  2. * including predictors for state-dependent delays (with Bekiaris-Liberis)
  3. delay-adaptive control
  4. * for linear systems with unknown delays and other plant parameters (with Bresch-Pietri and Zhu)
  5. approximate nonlinear predictors
  6. * for real-time and sampled-data implementation (with Karafyllis)

Prescribed-Time Control

  1. PT stabilization
  2. * backstepping for driving state to setpoint by user-prescribed time regardless of initial condition (with Song)
  3. PT observers
  4. * for state estimate convergence in arbitrary finite time (with Holloway)
  5. stochastic PT control
  6. * for PT stabilization in probability (with W. Li)

Non-overshooting and Safe Nonlinear Control

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

Deep Neural Operators for PDE Control

  1. universal approximability theory for backstepping kernel PDEs
  2. stability guarantees under ML approximation of PDE backstepping
  3. * for hyperbolic and parabolic PDEs

References

External links