Arthur Krener

Arthur Krener is a mathematician whose research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes.  In 1971 he received the PhD in Mathematics from the University of California, Berkeley and joined the faculty of the University of California, Davis.  He retired from UCD in 2006 as a Distinguished Professor of Mathematics and he currently is a Distinguished Visiting Professor at the Naval Postgraduate School.  He has also held visiting positions at Harvard University, Imperial College, NASA Ames Research Center, the University of California, Berkeley, the University of Paris, the University of Maryland, the University of Padua and North Carolina State University.  His research has been continuously funded since 1975 by NSF, NASA, AFOSR and ONR. 

 

He is a member of the American Mathematical Association, a Fellow of the Society for Industrial and Applied Mathematics and a Life Fellow of the Institute of Electrical and Electronics Engineers. Krener has held a variety of administrative posts, including Chair of the Department of Mathematics, UC Davis, member of the Committee on Academic Personnel, UC Davis and Chair of the SIAM Activity Group on Control and Systems Theory.  He has given numerous invited addresses at professional meetings.  He has organized several major conferences including the SIAM Conferences on Control and its Applications in 1989 and 2007 in San Francisco and the IFAC NOLCOS at Lake Tahoe in 1996.

 

Some of his more important scientific contributions are the following. The numbers refer to his publication list.

 

The modern theory of linear control and estimation began around 1960 with several important developments.  R. Kalman defined the basic synthetic concepts of this theory, controllability and observability.  These arose in the discovery of and formed the underlying foundation for the linear quadratic regulator and the Kalman-Bucy filter.  But a similar theory for nonlinear systems was lacking.

 

In his PhD thesis, Krener showed that the Lie bracket played an important role in nonlinear controllability by proving a time directed version of Chow's Theorem. Sussmann-Jurdjevic and Lobry proved similar theorems around the same time but Krener's result was the broadest and his proof was the simplest. 

 

Several years later with Hermann [10], he gave the definitive treatment of controllability and observability for nonlinear systems.  The importance of this paper was recognized immediately and it received honorable mention for Best Paper of the Year in the IEEE Transaction on Automatic Control.  This was a bit surprising, as it was one of the most mathematical papers to have appeared in this engineering journal to that time. This work was cited by the IEEE Control Systems Society as one of Twenty Five Seminal Papers in Control, published in the twentieth century, which have made a major impact on the field of control.  Since that time there has been tremendous progress in the development of nonlinear systems theory, which would not have been possible without the results of this paper.

 

Also around 1960 the well-known Pontryagin Maximum Principle was developed for optimal control problems.  These are the first order necessary conditions that a control must satisfy to be optimal.  But they are not always decisive, particularly for problems where the control enters linearly.  Krener [9] developed the High Order Maximum Principle which give additional necessary conditions for optimality.  Using this he gave a rigorous proof of the generalized Legendre-Clebsch condition.  This work stimulated tremendous interest and has been generalized and extended by many authors.

 

Perhaps the two most important approaches to controlling a nonlinear system are feedback linearization and backstepping.  Krener played a key role in the development of both.  In [2] he gave necessary and sufficient conditions for a nonlinear system to be a change of state coordinates away from a linear system.  This work was extended by Brockett, Hunt-Su and Jacubczyk-Respondek who answered the question of when a nonlinear system is a change of state coordinates and state feedback away from a linear system. 

 

With Isidori, Gori-Giorgi and Monaco [21], he gave conditions for the existence and construction of decoupling and noninteracting control laws for nonlinear systems.  This paper won the Best Paper of the Year Award of the IEEE Transactions on Automatic Control and Krener received the Medal of the University of Rome for his contributions.  It also led to the concept of the zero of a nonlinear system [20], which was subsequently developed by Byrnes and Isidori and extended to the backstepping technique of control by Kokotovic and many others.

 

The dual of control is estimation and for nonlinear systems this is usually quite difficult.   Krener and Respondek [34] showed how this could be accomplished for systems that could be linearized by change of coordinates and input/output injection.  This is the dual of feedback linearization.

 

Most systems are causal, the current output is unaffected by future inputs.  But some systems are not, e. g., those that satisfy boundary instead of initial conditions. Krener [41] gave the complete realization theory for linear acausal systems, i.e., conditions for their controllability, observability and minimality.

 

The development of controllers and estimators that are robust to noise and parameter variations was the motivation for linear H-Infinity control. Krener [64] generalized this to nonlinear systems in a particularly simple fashion.

 

The theory of Markov diffusions is a beautiful area of mathematics, involving a rich interplay between Ito stochastic differential equations and parabolic partial differential equations.  Krener developed a corresponding theory for reciprocal diffusions [72]. A reciprocal process is a Markov random field with a one-dimensional parameter.  He showed that reciprocal diffusions satisfy stochastic differential equations of second order (invented by Krener) and the conditional moments of their velocity satisfy a sequence of conservation laws similar to those of continuum mechanics.   These conservation laws can be hyperbolic or mixed type.  Krener showed that these conservation laws close for two important subclasses, the Markov diffusions and the quantum diffusions.  The latter are so named because in this case the conservation laws are equivalent to the Schroedinger equation of quantum mechanics.

 

Krener has been a leader in the development of software tools for nonlinear control.  His Nonlinear Systems Toolbox [Software 1] is a suite of MATLAB routines that implement a variety of the latest methods of nonlinear control.

 

He was a co PI on an AFOSR sponsored multicampus research project to control surge, stall and flutter in compressors and aeroengines. This was part of a  AFOSR Program for Research Excellence and Transitions (PRET) which is designed to encourage academic researchers to more closely couple their research efforts with those in industry while advancing basic research.  He worked with colleagues at UCSB, Cal Tech, MIT and United Technologies Research Center, the basic research facility of Pratt and Whitney.  With Banaszuk [74] he gave a geometric method for constructing stabilizing controllers for models of axial flow compressors.  Krener  [83] developed a method for detecting the onset of instabilities in compressors which has recently been patented [Patent 1].

 

The simplest model of a compressor exhibits a rich diversity of classical bifurcations whose behavior can be modified but not eliminated by feedback control.  Recently Krener in collaboration with Wei Kang discovered that there is a theory of bifurcations for control systems [104].  A classical bifurcation occurs in a parameterized differential equation typically when there is a change in the stability of its linear approximation; an eigenvalue or pair of eigenvalues crosses the imaginary axis. Typically a control system bifurcates when there is a loss of stabilizability of its linear approximation, there develops an unstable, uncontrollable mode. 

 

Using a newly developed theory of normal forms for control systems, Kang, Krener and colleagues have been able to classify the low codimension control bifurcations and in some cases develop truly nonlinear feedbacks to stabilize them.

 

In 2002 Krener showed that, under suitable conditions, the extended Kalman filter (the most widely used nonlinear estimator) is locally convergent [95].  He also showed that under the same conditions the minimum energy estimator is globally convergent [98].

 

More recently he has developed methods for reduction of high dimensional models of control systems [118] and methods for the numerical solution of Hamilton Jacobi Bellman PDEs [119].  He has also studied the observability of simple two dimensional flows under Eulerian and Lagrangian observations [124, 125, 127].

 

Krener has received numerous honors and awards during his career.  These include a John Simon Guggenheim Fellowship in 2002, a Statistical and Applied Mathematical Sciences Institute University Fellow in 2004, the W. T. and Idalia Reid Prize from SIAM “for fundamental contributions to the control and estimation of nonlinear dynamical systems and stochastic processes” in 2004, the IEEE Control System Society Bode Prize Lecture in 2006 “for fundamental contributions to the foundations of geometric nonlinear control theory” and a Certificate of Excellent Achievements from the IFAC Techical Commttee on Nonlinear Control in 2010.  A Symposium on New Trends in Nonlinear Dynamics and Control and Their Applications was held at the Naval Postgraduate School, October 18-19, 2002 in conjunction with his 60th birthday.

 


 

Education:     Holy Cross College, Worcester                                                    BS   1964

                        University of California, Berkeley                                                  MA   1967

                        University of California, Berkeley                                                  PhD 1971

 

Employment:

                        University of California, Davis                                                                              

                             Assistant Professor of Mathematics                                       1971-1976                           

                            Associate Professor of Mathematics                                      1976-1980                          

                            Professor of Mathematics                                                         1980-2002

                             Chair of Mathematics                                                                 1987-92

                             Distinguished Professor of Mathematics                              2002-2006

 

Visiting Positions:

                        Harvard University, Cambridge                                                   

                             Research Fellow in Decision & Control                                 1974-1975

                        Imperial College of Science & Technology,             

                             Visiting Senior Research Fellow                                             1980-1981

                             and Lecturer of Electrical Engineering

                        NASA Ames Research Center                                                     

                             Visiting Scientist, Flight Dynamics and Controls                 1983-1984

                        University of California, Berkeley                                                 

                             Visiting Professor of Electrical Engineering (6 Mo.)            1985

                        University of Paris, IX

                             Visiting Professor of Mathematics (3X1 Mo.)                        1989, 92, 98

                        University of Maryland                                                                    

                             Visiting Senior Research Scientist,                                        1992-93

                             Systems Research Center

                        University of Padua

                             Visiting Professor of Electrical Engineering                          1997

                        Statistical and Applied Mathematical Sciences Institute

                               North Carolina State University-SAMSI Fellow                   2004

                        Naval Postgraduate School

                             Distinguished Visiting Professor of Applied Mathematics    2006-present

 


 

PUBLICATIONS:

 

 

 1.        1971       Krener, A.J.  A generalization of the accessibility problem for control systems.  Institute of Electrical and Electronics Engineers Conference on Decision and Control. PDF

 

 2.        1973       Krener, A.J.  On the equivalence of control systems and the linearization of nonlinear systems.  Society for Industrial and Applied Mathematics Journal of Control 11:670‑676.  PDF

 

 3.        1973       Krener, A.J.  The high order maximal principle. Geometric Methods in System Theory, D.Q. Mayne and R.W. Brockett (eds.), D. Reidel Publishing Company, Dordrecht, Holland, pp. 174‑184.  PDF

 

 4.        1974       Krener, A.J.  A generalization of Chow's theorem and the bang bang theorem to nonlinear control problems. Society for Industrial and Applied Mathematics Journal of Control 12:43‑52.  PDF

 

 5.        1974       Krener, A.J.  Linearization and bilinearization of control systems.  Proceedings, 12th Allerton Conference on Circuits and Systems, pp. 834‑843.  PDF

 

 6.        1975       Krener, A.J.  Bilinear and nonlinear realizations of input‑output maps.  Society for Industrial and Applied Mathematics Journal of Control 13:827‑834.  PDF

 

 7.        1975       Krener, A.J.  A decomposition theory for differentiable systems.  Preprints‑International Federation of Automatic Control, 6th Triennial World Congress, August 24‑30, Part 1B, 36.5:1‑10.

 

1977       a.  ALSO appeared in Society for Industrial and Applied Mathematics

    Journal on Control and Optimization 12:813‑829.  PDF

 

8.         1975       Krener, A.J.  Local approximation of control systems. Journal of Differential Equations 19:125‑133.  PDF

 

9.         1977       Krener, A.J.  The high order maximal principle and its application to singular extremals. Society of Industrial and Applied Mathematics Journal on Control and Optimization 15:256‑293.  PDF

 

10.      1977       Hermann, R. and A.J. Krener.  Nonlinear controllability and observability.  Institute of Electrical and Electronics Engineers Transactions on Automatic Control 22:728‑740.  PDF


11.      1977       Krener, A.J. and R. Hermann.  The differential‑geometric duality between controllability and observability for nonlinear systems.  Ames Research Center Conference on Geometric Control Theory, Mathematical Sciences Press, Brookline, Massachusetts.  PDF

 

12.      1978       Lesiak, C.M. and A.J. Krener.  The existence and uniqueness of Volterra series for nonlinear systems. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 23:1090‑1095.  PDF

 

13.      1978       Krener, A.J.  A note on commutative bilinear control. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 23:1111.  PDF

 

14.      1978       Krener, A.J.  Continuous linear programming and piecewise bilinear systems.  In Recent Developments in Variable Structure Systems, R.R. Mohler and A. Ruberti (eds.), Springer‑Verlag, N.Y., pp. 158‑172.  PDF

 

15.      1978       Krener, A.J.  A formal approach to stochastic integration and differential equations. Stochastics3:105‑126. PDF

 

16.      1979       Krener, A.J.  Minimal covariance, minimax and minimum energy linear estimation.  In Stochastic Control Theory and Stochastic Differential Systems, M. Kohlman and W. Vogel (eds.), Springer‑Verlag, N.Y.  PDF

 

17.      1979       Krener, A.J.  One dimensional acausal linear systems. Institute of Electrical and Electronics Engineers Conference on Decision and Control.  PDF

 

29.          1980       Krener, A.J.  Kalman‑Bucy and minimax filtering. Institute of Electrical and Electronics Engineers Transactions on Automatic Control 25:291‑292.  PDF

 

19.      1980       Krener, A.J.  Boundary value linear systems. Asterique, pp. 75‑76, 149‑166.  PDF

 

20.      1980       Krener, A.J. and A. Isidori.  Nonlinear zero distributions.  Institute of Electrical and Electronics Engineers Conference on Decision and Control.  PDF

 

21.      1981       Isidori, A., A.J. Krener, C. Gori‑Giorgi, and S. Monaco.  Nonlinear decoupling via feedback: a differential‑geometric approach.  Institute of Electrical and Electronics Engineers Transactions on Automatic Control 26:331‑345. PDF


22.      1981       Krener, A.J. and C. Lobry.  The complexity of stochastic differential equations. Stochastics 4:193‑203.  PDF

 

23.      1981       Isidori, A., A.J. Krener, C. Gori‑Giorgi, and S. Monaco.  Locally (f,g) invariant distributions. Systems and Control Letters 1:12‑15.  PDF

 

24.      1981       Isidori, A., A.J. Krener, C. Gori‑Giorgi, and S. Monaco.  The observability of cascade connected nonlinear systems. Proceedings International Federation for Automatic Control, Triennial World Congress, Tokyo.  PDF

 

25.      1981       Krener, A.J. Smoothing of stationary cyclic processes.  Proceedings of Conference on the Mathematical Theory of Networks and Systems, Santa Monica.  PDF

 

26.      1981       Krener, A.J. (f,g) invariant distributions, connections and Pontryagin classes.  Proceedings, IEEE Conference on Decision and Control, San Diego.  PDF

 

27.      1982       Krener, A.J. and A. Isidori.  (Ad f,g) invariant and controllability distributions, in Feedback Control of Linear and Nonlinear Systems, D. Hinrichsen and A. Isidori (eds.,) Springer‑Verlag, N.Y., pp. 157‑164.  PDF

 

28.      1982       Isidori, A. and A.J. Krener.  On feedback equivalence of nonlinear systems. Systems and Control Letters 2:118‑121.  PDF

 

29.      1983       Krener, A.J. and A. Isidori.  Linearization by output injection and nonlinear observers. System and Control Letters 3:47‑52. PDF

 

30.      1983       Krener, A.J. and C.I. Byrnes.  On the existence of globally (f,g) invariant distributions.  In Differential Geometric Control Theory, R.W. Brockett, R.S. Millman, and H.J. Sussman (eds.), pp. 209‑225.  PDF

31.      1983       Krener, A.J., A. Isidori, and W. Respondek.  Partial and robust linearization by feedback. Proceedings, IEEE Conference on Decision and Control, San Antonio.  PDF

 

32.      1984       Krener, A.J. New approaches to the design of nonlinear compensators. Proceedings of Berkeley‑Ames Conference on Nonlinear Problems in Control and Fluid Dynamics. C. Martin and R. Hunt (eds.), Mathematical Sciences Press.  PDF

 

33.      1984       Krener, A.J.  Approximate linearization by state feedback and coordinate change. Systems and Control Letters 5:181‑185.   PDF


34.      1985       Krener, A.J. and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM Journal on Control and Optimization 23:197‑216.  PDF

 

35.      1985       Krener, A.J. (Adf,g) (adf,g) and locally (adf,g) invariant and controllability distributions.  SIAM Journal on Control and Optimization 23:523‑549.  PDF

 

36.      1986       Krener, A.J.  Reciprocal processes and the stochastic realization problem for acausal systems. In Modeling, Identification and Robust Control, C.I. Byrnes and A. Lindquist (eds.), North Holland, Amsterdam, pp. 197‑210.  PDF

 

37.      1986       Krener, A.J.  The asymptotic approximation of nonlinear filters by linear filters. In Theory and  Application of Nonlinear Control System, C.I. Byrnes and A. Lindquist (eds.), North Holland, Amsterdam, pp. 359‑378.  PDF

 

38.      1986       Krener, A.J. Conditioned invariant and locally conditioned invariant distributions. Systems and Control Letters 8:69‑74.  PDF

 

39.      1986       Krener, A.J.  The intrinsic geometry of dynamic observations.  In Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel (eds.), Reidel, Amsterdam, pp. 77‑87. PDF 

 

40.      1986       Krener, A.J.  Normal forms for linear and nonlinear systems.  In Differential Geometry, the Interface between Pure and Applied Mathematics, Vol. 68, American Mathematical Society, Providence, pp. 157‑189.  PDF

 

41.      1987       Krener, A.J.  Acausal realization theory, Part I; Linear deterministic systems. SIAM Journal on Control and Optimization 25:499‑525.  PDF 

 

42.      1987       Krener, A.J., S. Karahan, M. Hubbard and R. Frezza. Higher order linear approximations to nonlinear control systems.  Proceedings, IEEE Conference on Decision and Control, Los Angeles, pp. 519‑523.  PDF

 

43.      1988       Krener, A.J.  Realizations of reciprocal processes. In Modeling and Adaptive Control, C. Byrnes and A. Kurzhanski,  eds., Lecture Notes in Information and Control, No. 105, Springer‑Verlag.  PDF

 

44.      1988       Frezza, R., S. Karahan, A.J. Krener and M. Hubbard. Application of an efficient nonlinear filter.  In Nonlinear Dynamics and Control, C. Byrnes, C. Martin and R. Saeks (,eds.), North Holland.   PDF

 


45.      1988       Phelps, A.R.,  and A.J. Krener.  Computation of observer normal form using MACSYMA.  In Analysis and Control of Nonlinear Systems, C.I. Byrnes, C.F. Martin and R.E. Saeks (eds.), North Holland, Amsterdam, pp. 475-482.  PDF

 

46.      1988       Krener, A.J.  Reciprocal processes, second order stochastic differential equations and PDEs of conservation and balance. In Analysis and Control of Nonlinear Systems, C. I. Byrnes, C.F. Martin and R.E. Saeks (eds.), North Holland, Amsterdam, pp. 579-590. PDF

 

47.      1988       Krener, A.J. and H. Schaettler.  The structure of small‑time reachable

sets in low dimensions.  SIAM Journal on Control and Optimization 27:120-147.  PDF

 

48.      1988       Krener, A.J.  Reciprocal diffusions and stochastic differential equations of second order. Stochastics 24:393-422.  PDF

 

49.      1988       Krener, A.J., S. Karahan and M. Hubbard.  Approximate normal forms of nonlinear systems.  Proceedings, IEEE Conference on Decision and Control, San Antonio, pp. 1223-1229.  PDF

 

50.      1990       Krener, A.J.  Nonlinear controller design via approximate normal forms.  In Signal Processing, Part II: Control Theory and its Applications,  A. Grunbaum, J.W. Helton and P. Khargonekar (eds.), Springer-Verlag, pp. 139-154.  PDF

 

51.      1990       Levy, B.C., R. Frezza, and A.J. Krener.  Modeling and estimation of discrete-time Gaussian reciprocal processes.  IEEE Transactions on Automatic Control 35:1013-1023.  PDF

 

52.      1990       Krener, A.J. and W. Kang.  Extended normal forms of quadratic systems.  Proceedings of the 29th IEEE Conference on Decision and Control, Vol. 4.. Honolulu.  PDF

 

53.      1991       Krener, A.J., R. Frezza, and B.C. Levy.  Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order.  Stochastics 34:29-56.   PDF

 

54.      1991       Krener, A.J. and Y. Zhu.  The fractional representation of a class of nonlinear systems.  Journal of Mathematical Systems, Estimation, and Control 1:183-195.  Tampa.  PDF

 

1989       a.  Also appeared in IEEE Conference on Decision and Control.  Tampa, pp. 963-968.


55.      1991       Kang, W. and A.J. Krener.  Observation of a rigid body from measurements of a principle axis.  Journal of Mathematical Systems, Estimation and Control 1(2)197-207. 

 

1989       a.  Also appeared in IEEE Conference on Decision and Control.  Tampa, pp. 2254-2258.

 

 56.     1991       Krener, A.J. and W. Kang.  Degree two normal forms of control systems and the generalized Legendre Clebsch condition.  In Analysis of Controlled Dynamical Systems, B. Bonnard, B. Bride, J.P. Gauthier and I Kupka (eds.), Birkhauser-Boston, pp. 139-154.  PDF

 

57.      1991       Krener, A.J. and B. Maag.  Controller and observer design for cubic systems.  In Modeling, Estimation and Control of Systems with Uncertainty, G. B. DiMasi, A. Gombani and A. B. Kurzhansky (eds.), Birkhauser-Boston, pp. 224-239.  PDF

 

58.      1991       Krener, A.J., M. Hubbard, S. Karahan, A. Phelps and B. Maag.  Poincare's linearization method applied to the design of nonlinear compensators.  In Algebraic Computing in Control, G. Jacob and F. Lamnahbi-Lagarrigue (eds.), Springer, Berlin, pp. 76-114.  PDF

 

59.      1992       Krener, A.J.  The construction of optimal linear and nonlinear regulators.  In Systems, Models and Feedback: Theory and Applications.  A Isidori and T.J. Tarn (eds.), Birkhauser-Boston, pp. 301-322. PDF

 

60.      1992       Krener, A.J., and Kang, W.  Extended quadratic controller normal and dynamic state feedback linearization of nonlinear system.  SIAM Journal on Control and Optimization 30:1319-1337.  PDF

 

61.      1993       Krener, A.J., and Levy, B.C.  Dynamics and kinematics of reciprocal diffusions.  Journal of Mathematical Physics, 34, pp. 1846-1875.  PDF

 

62.      1993       Krener, A.J.  Optimal model matching controllers for linear and nonlinear systems.  In Nonlinear Control Systems Design 1992, M. Fliess, (ed.), Pergamon Press, Oxford pp. 209-214.  PDF

 

63.      1994       Krener, A.J.  Nonlinear stabilizability and detectability.  In Systems and Networks:  Mathematical Theory and Applications, U. Helmke, R. Mennicken and J. Saurer, (eds.), Akademie Verlag, Berlin, pp. 231-250.  PDF

 


64.      1994       Krener, A.J., Necessary and sufficient conditions for nonlinear worst case (H-infinity) control and estimation.  Summary appeared in Journal of Mathematical Systems, Estimation, and Control 4:485-488, full manuscript appeared in Journal of Mathematical Systems, Estimation, and Control 7:81-106.  PDF

 

65.      1995       Krener, A. J. and D.Q. Mayne, editors, Nonlinear Control Systems Design, 1995, Pergamon, 1995.

 

66.      1995       Krener, A. J.  and S. Nikitin.  Dido's problem with a fixed center of mass.. In Nonlinear Control  Systems Design, 1995, A.J. Krener and D.Q. Mayne, eds. Pergamon, pp. 317-322.  PDF

 

67.      1995       Coleman , J. M., B. C. Levy and A. J. Krener. Gaussian  reciprocal diffusions and positive definite  Sturm-Liouville operators.  Stochastics and Stochastics Reports, 55, pp.279-313.  PDF

 

68.      1996       Levy, B. C. and A. J. Krener. Stochastics mechanics of reciprocal diffusions.  Journal of Mathematical Physics, 37,  pp.769-802.  PDF

 

69.      1996       Krener, A. J. Review of  "Theory of Chattering Control" by M. I. Zelikin and V. F. Borisov.  Siam Review, 38, pp.172-173.  PDF

 

70.      1996       Krener, A. J. and A. Duarte.  A hybrid computational approach to nonlinear estimation.  Proc. of 35th Conference on Decision and Control, Kobe, Japan pp. 1815-1819.  PDF

 

71.      1997       Krener, A. J. Review of "Global Controllability and Stabilization of Nonlinear Systems" by S. Nikitin. IEEE Transactions on Automatic Control, 42, pp.129-130.  PDF

 

72.      1997       Krener, A. J.  Reciprocal diffusions in flat space. Probability Theory and Related Fields, 107, pp. 243-281.  PDF

 

73.      1997       Krener, A. J. and S. Nikitin.  Generalized isoperimetric problem. Summary appeared in Journal of Mathematical Systems, Estimation, and Control, 7, pp. 367-369.  Full manuscript available at http://www.birkhauser.com/journals/jmsec/download.html, retrevial code 49224.PDF

 

74.      1997       Banaszuk, A. and A. J. Krener, Design of controllers for MG3 compressor models with general characteristics using graph backstepping. Proc. of 1997 American Control Conference, Albuquerque, pp. 977-981. PDF


 

74.a.   1999       Banaszuk, A. and A. J. Krener, Design of controllers for MG3 compressor

                              models with general characteristics using graph backstepping. 

                             Automatica, 35, pp. 1343-1368.  PDF

 

75.      1997       Humbert, J. S. and A. J. Krener, Analysis of Higher Order Moore-Greitzer

             Compressor Models, Proceedings of IEEE Conference on Control Applications, Hartford. PDF

 

76.      1998       Humbert, J. S. and A. J. Krener, Dynamics and control of entrained

                             solutions in multi-mode Moore-Greitzer compressor models,

                             International Journal of Control,71, pp. 807-821.  PDF

 

77.      1998       Krener, A. J., The existence of optimal regulators, Proceedings of IEEE

                             Conference on Decision and Control, Tampa, FL, pp. 3081-3086.  PDF

 

78.      1998       Kang, W. and A.J. Krener, Nonlinear asymptotic observer design, a

                             backstepping approach. In Mathematical Theory of Networks and

                             Systems, A. Beghi, L. Finesso and G. Picci, eds., Il Poligrafo, Padova,

                             pp. 245-248. PDF

 

79.      1999       Krener, A. J., A Lyapunov theory of nonlinear observers, in Stochastic

                             Analysis, Control, Optimization and Applications, W. McEneaney, G.G. Yin

                             and Q. Zhang, Eds.,Birkhauser, Boston, pp. 409-420.  PDF

 

80.      1999       Krener, A. J. , Feedback linearization, in Mathematical Control Theory, J.

                             Baillieul and J. C. Willems, eds., Springer Verlag, NY, pp. 66-98.  PDF

 

81.      1999       Ball, J. A., P. Kachroo and A.J. Krener,  H-Infinity tracking control for a

                             class of nonlinear systems, IEEE Transactions on Automatic Control, 44,

                             pp. 1202-1206.  PDF

 

82.      1999       Lau, E. and A. J. Krener, LPV Control of Two Dimensional Wing Flutter,

                             Proceedings of IEEE Conference on Decision and Control, Phoenix,

                             pp. 3005-3010.  PDF

 

83.      2000       Krener, A. J., Precursors of Bifurcations , Proceedings  IFAC Symposium

                             on System Identification, SYSID 2000, Santa Barbara, CD-ROM.  PDF

 

84.      2000       Li, L. and A. J. Krener, Quadratic and Cubic Normal Forms of Discrete Time

                             Nonlinear Control Systems. Anais do XIII Congresso Brasileiro de

                             Automatica, CBA 2000, pp. 19-25.  PDF

 

85.      2000      Navasca, C. and A. J. Krener, Solution of Hamilton Jacobi Bellman Equations Proceedings of the IEEE Conference on Decision and Control, Sydney, 2000, pp. 570-574.  PDF


86.      2000     Chang, D. E., W. Kang and A. J. Krener,  Normal Forms and Bifurcations of

                           Control Systems, Proceedings of the IEEE Conference on Decision and Control, Sydney, 2000, pp. 1602-1607.  PDF

 

87.      2001       Pan, Z, K. Ezal, A. J. Krener and P. Kokotovic, Backstepping Design with

    Locally Optimal Matching.  IEEE Transactions on Automatic Control, 46,

                            pp. 1014-1027.  PDF

 

88.     2001        Krener, A. J., The Local Solvability of a  Hamilton-Jacobi-Bellman PDE

                            around a Nonhyperbolic Critical Point. SIAM Journal on Control and

                            Optimization, 39, pp.1461-1484.  PDF

 

89.      2001       Krener, A. J., Kang and D, E. Chang, Normal Forms of Linearly

                            Uncontrollable Nonlinear Systems with a Single Input. Proceedings of IFAC

                            NOLCOS 2001, St. Petersburg, pp.134-139. PDF

 

90.      2001      Krener, A. J. and L. Li, Bifurcations of Discrete Time Nonlinear Control Systems. Proceedings of IFAC NOLCOS 2001, St. Petersburg, pp. 150-155.  PDF

 

91.      2001       Krener, A. J. and M.-Q. Xiao, Nonlinear Observer Design in the Siegel

                            Domain through Coordinate Changes. Proceedings of IFAC NOLCOS 2001,

                            St. Petersburg, pp. 557-562.  PDF

 

92.       2002      Krener, A. J. and M.-Q. Xiao, Observers for Linearly Unobservable Nonlinear

                            Systems, Systems and Control Letters, 46, pp281-288.  PDF

 

93.       2002      Xiao, M.-Q., and A. J. Krener, Design of Reduced-Order Observers of

                            Nonlinear Systems through Coordinate Changes, Proceedings of the 41st

                                          Conference on Decision and Control, Las Vegas, pp. 689-694. PDF

 

 

94.       2002      Krener, A. J. and L. Li, Normal Forms and Bifurcations of  Discrete Time

                           Nonlinear Control Systems, SIAM Journal on Control and Optimization, pp.

                           1697-1723.  PDF

 

95.       2002      Krener, A. J., The Convergence of the Extended Kalman Filter, in Directions in

                             Mathematical Systems Theory and Optimization, A. Rantzer and C. I. Byrnes,

                             eds, Springer  Verlag, Berlin, pp.173-182.  PDF

 

96.       2003      Krener, A. J. and M.-Q. Xiao, Nonlinear Observer Design in the Siegel    

                          Domain, SIAM Journal on Control and Optimization, Volume 41, Number 3,

                            pp. 932-953.  PDF

 

97.        2003     Xiao, M, N. Kazantzis, C. Kravaris and A. J. Krener, Nonlinear Discrete-Time             

                          Observer Design with Linearizable Error Dynamics, IEEE Transactions on

                          Automatic Control, Volume 48. Number 4, pp. 622-626.  PDF


 

98.       2003      Krener, A. J., The Convergence of the Minimum Energy Estimator,  in "New     

    Trends in Nonlinear Dynamics and Control, and Their Applications", W.        

    Kang, M. Xiao and C. Borges, eds.  Springer Verlag, Heidelberg, pp. 187-208. PDF

 

99.       2003      Hamzi, B. and A. J. Krener, Practical Stabilization of Systems with a Fold

                            Control Bifurcation,  in "New Trends in Nonlinear Dynamics and Control, and

                            Their Applications", W. Kang, M. Xiao and C. Borges, eds.  Springer Verlag,

                            Heidelberg, pp. 33-44.  PDF

 

100.     2003      Hamzi, B., W. Kang and A. J. Krener, Control of Center Manifolds, in the

                            Proceedings of the 2003 IEEE Conference on Decision and Control, pp. 2065-

                            2070. PDF

 

101.     2003      Krener, A. J. and W. Kang, Locally Convergent Observers, SIAM Journal on

                            Control and Optimization, Volume 42, pp.155-177.  PDF

 

102.     2004      Kang, W. and  A. J. Krener, On the convergence of normal forms for analytic

                            control systems, in Unsolved Problems in Mathematical Systems and

                            Control Theory, V. Blondel and A. Megretski Eds, Princeton University

                            Press, pp. 82-86.  PDF

 

103.    2004      Krener, A. J. and M. Xiao, Erratum, Nonlinear Observer Design in the Siegel

                            Domain, SIAM J. on Control and Optimization, Volume 43, pp. 377-378. PDF

 

104.     2004      Krener, A. J., W. Kang and D. E. Chang, Control Bifurcations,  IEEE

                            Transactions on Automatic Control, pp. 1231-1246.  PDF

 

105.     2004      Kravaris, C., V. Sotiropoulos, C. Georgiou, N. Kazantzis, M. Xiao and A. J. Krener, Nonlinear Observer Design for State and Disturbance Estimation, Proceedings of the 2004

                            American  Control Conference, Boston, pp. 2931-2936 PDF

 

106.     2005      Krener, A. J., W. Kang, B. Hamzi and I. Tall, Low Codimension Control

                            Singularities, in New Directions and Applications in Control Theory,

                            W. P. Dayawansa, A. Lindquist, Y. Zhou, Eds. Springer Verlag, pp. 181-192.  PDF

 

107.     2004     Hamzi, B., W. Kang and A. J. Krener,  Stabilization of Discrete Time Systems

                           with a Fold or Period Doubling Control Bifurcation, Proceedings of the

                           Sixteenth IFAC World Congress.   PDF

 

108.     2005     Hamzi, B., W. Kang and A. J. Krener, The Controlled Center Dynamics,

                           SIAM J. on Multiscale Modeling and Simulation, 3, pp. 838-852.  PDF

 

109.     2006     Kang, W. and A. J. Krener, Normal Forms of Nonlinear Control Systems,

                            in Chaos in Automatic Control, W. Perruguetti and J.-P. Barbot, Eds.,

                            Taylor and Francis, pp. 345-376.  PDF

 

110.     2006     Krener, A. J. and M. Xiao, Nonlinear Observer Design for Smooth Systems,

                            in Chaos in Automatic Control, W. Perruguetti and J.-P. Barbot, Eds.,

                            Taylor and Francis, pp. 411-422. PDF

 

111.    2004       Krener, A. J., Nonlinear Observers, in Control Systems, Robotics and

                            Automation, edited by H. Unbehauen, in Encyclopedia of Life Support Systems (EOLSS),

                            Developed under the auspices of the UNESCO, Eolss Publishers, Oxford, UK,   [http://www.eolss.net]  PDF

 

112.     2006      Hamzi,  B. , W. Kang, and A. J. Krener, The Controlled Center Dynamics

                             of Discrete Tme Control Bifurcations,  Systems and Control Letters, 55, pp. 585-596.  PDF           

 

113.    2005       Krener, A. J., Least Squares Smoothing of Nonlinear Systems, Proceedings of  

                            SYNCOD, Springer Verlag.  PDF

 

114.    2006       Krener, A. J., W. Kang, B. Hamz and I. Tall, Control Singularities of

    Codimensions One and Two, Proceedings of First IFAC Conference on the

    Analysis and Control of Chaotic Systems.  PDF

 

 

115.    2006       Kang, W., B. Hamzi and A. J. Krener, On the Convergence and Behavior of

                           Three Dimensional Normal Forms, Proceedings of First IFAC Conference on

                            the Analysis and Control of Chaotic Systems.  PDF

 

116.    2006      Hamzi,  B. and A. J. Krener, The Controlled Center System, Proceedings of

                           the 2006 IEEE Conference on Decision and Control.  PDF

 

117.    2006      Krener, A. J. The Importance of State Coordinates of a Nonlinear System.

                             In Advances in Control Theory and Applications,C. Bonivento, A. Isisdori, L.

                           Marconi, C. Rossi, Eds., Springer Verlag, LNCIS 353, pp. 161-170. PDF

 

118.    2007      Krener, A. J. Reduced Order Models for Nonlinear Control Systems,

                              in Analysis and Design of Nonlinear Control Systems, In Honor of Alberto      

                           Isidori, A. Astolfi and L. Marconi, Eds.  Springer Verlag  PDF

 

119.    2007      Navasca, C. and A. J. Krener, Patchy Solutions of Hamilton Jacobi

                         Bellman Partial Differential Equations, In A. Chiuso, A. Ferrante and S.

                         Pinzoni,  eds, Modeling, Estimation and Control, Lecture Notes in Control and

                         Information Sciences, 364, pp. 251-270.  PDF

 

120.    2007      Kravaris, C., V. Sotiropoulos, C. Georgiou, N. Kazantzis, M. Xiao and A. J. Krener, Nonlinear Observer Design for State and Disturbance Estimation,

                          Systems & Control Letters 56 (2007) 730– 735.  PDF

 

121.    2007      Hamzi, B. and A. J. Krener, The Controlled Center System, IEEE

                         Transactions on Automatic Control. 52, 2188-2192.  PDF

 

 

122.    2008      Navasca, C. and A. J. Krener, The Patchy Cost and Feedback for the HJB

                         PDE, Proceedings of 2008 MTNS, Blacksburg, VA.  PDF

 

 

122.    2008      Zhou, H., W. Kang, A. J. Krener and H. Wang, Homogeneous flow field effect

                         on the control of Maxwell materials, J. Non-Newt. Fluid Mech. 150,104–115.  PDF

 

123.    2008      Krener, A. J.,  Observability of Vortex Flows,  in Fourty Seventh Conference on

                         Decision and Control}, Cancun, Mexico, 2008.  PDF

 

124.    2008      Krener, A. J., Eulerian and Lagrangian Observability  of Point Vortex Flows,

   Tellus A, vol. 60, pp. 1089-1102.  PDF

 

 

125.    2009      Krener, A. J.  and K. Ide, Measures of Unobservability, Proceedings of the

                           IEEE Conference on Decision and Control, Shanghai.  PDF

 

126.    2009      Hunt, T and A. J. Krener,  Principal Tangent Data Reduction, Proceedings of

                            the IEEE International Conference on Control and Automation, Christchurch. PDF

 

127.    2010     Zhou H., W. Kang, A. J. Krener and H. Wang, Observability of viscoelastic 

                           fluids, J. Non-Newtonian Fluid Mech. 165 (2010) 425–434.  PDF

 

128.   2010      Krener, A. J. The Accessible Sets of Free Nilpotent Control Systems, to appear,  

                    Communications in Information and Systems.  PDF

 

LIMITED DISTRIBUTION:

 

1.         1995       Krener, A. J.  Precursors of Bifurcations, PRET Working Paper

                             D95-8-11

 

2          1995       Krener, A. J.  The Feedbacks which Soften the Primary Bifurcation of MG 3, PRET Working Paper      D95-9-11.

 

3.         1995       Krener, A. J.  Precursors of Bifurcations II, PRET Working Paper D95-9-13

 

4.         1996       Krener, A. J.  Multi-Mode Moore Greitzer Galerkin Compressor Models PRET Working Paper D96-6-     6.

 

5.         1996       Krener, A. J.  Revised Multi-Mode Moore Greitzer Galerkin Compressor Models, PRET Working      Paper D96-8-15

 

6.         1997       Krener, A. J., Detecting Precursors to Stall in Experimental Data, PRET Working Paper D97-2-4

 

 

 

 

SOFTWARE:

 

1.             1997   Krener, A. J.   Nonlinear Systems Toolbox V. 1.0, A MATLAB based toolbox available by ftp from scad.utdallas.edu.  NST2008

 

 

PATENTS:

 

1.             2000   Krener, A. J. and M. Krstic, Method and Apparatus for Predicting and Stabilizing

                        Compressor Stall.  U. S. Patent No. 6,098,010.