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 Òfor fundamental contributions to the control and estimation of nonlinear dynamical systems and stochastic processesÓ in 2004, the IEEE Control System Society Bode Prize Lecture in 2006 Òfor fundamental contributions to the foundations of geometric nonlinear control theoryÓ 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
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.