Publications:
- “Geometric theory of
output regulation for linear distributed parameter systems”, Chapter
6, Research Directions in Distributed Parameter Systems in SIAM Frontiers
in Applied Mathematics, Volume 27, Ralph C. Smith and Michael A. Demetriou, Editors, ( with C.I. Byrnes, and D.S.
Gilliam (2003), 139 - 167.
- "Generalized Donaldson -
Sullivan Model of a Vortex Flow", Proceedings of the 11th International
Conference on Wind Engineering, Lubbock, TX, June 2 - 5, 2713-2720, ( with
D.S. Gilliam, C. Mickel and E. Vugrin), (2003).
- "Set Point Boundary
Control for a Nonlinear Distributed Parameter System", Proceedings of
the 42nd IEEE CDC, (with C.I. Byrnes, A. Isidori,
and D.S. Gilliam), (2003).
- "Regular Linear Systems
Governed by Boundary Controlled Heat Equation", Journal of
Dynamical and Control Systems, Vol. 8, Issue 3, 341-370, (2002) (with C.I.Byrnes, D.S.Gilliam, and
G.Weiss).
- ``The Impact of Finte Precision Arithmetic and Sensitivity on the
Numerical Solutions of Partial Differential Equations,'' Journal Mathematical and
Computer Modeling, 35, no.
11-12, 1165-1195, (2002), (with E. Allen, J.A. Burns, D.S. Gilliam, J.
Hill).
- “Output regulation for
delay systems: tracking and disturbance rejection for an oscillator with
delay damping”, Proc. of IEEE Control Systems Society Conf. on
Control Applications, Galsgow
, Scotland
, (September 2002) (with C.I. Burnes, D.S.
Gilliam, and E. Vurgin )
- “An Example of Output
Regulation for a Distributed Parameter System with Infinite Dimensional Exosystem”, Proceedings 15th
International Conference on the Mathematical Theory of Networks and
Systems, (with C.I. Byrnes, J. Hood, and D.S. Gilliam) (conference
CDROM and at URL: http://www.nd.edu/mtns/).
- “The Regulator Equations for
Retarded Delay Differential Equations”, Proceedings of 41st
IEEE-CDC Proceedings, Dec. 2002, 973-974, (with A. Balogh
and D.S. Gilliam).
- "Modelling
Modal Based Sensors for Oscillatory Systems", Proceedings of 41st
IEEE CDC Proceedings, Dec. 2002, 1725-1726, (with A. Balogh and D. S. Gilliam).
- ``Stationary solutions for a
boundary controlled viscous Burgers' equation,'' Journal Mathematical and Computer Modeling, (2001),
(with A. Balogh and D.S. Gilliam).
- ``Input - output behavior for
stable linear systems,'' J. Franklin Inst. 338 (2001), no. 4,
497-507 (with C.I. Byrnes, X. Hu, C.F. Martin).
- ``Examples of regular linear
systems governed by partial differential equations,'' Proceedings of
40th IEEE-CDC, 2001, 129-130. (with C.I. Byrnes, D.S. Gilliam).
- ``Examples of output
regulation for distributed parameter systems with infinte
dimensional exosystem,'' Proceedings of 40th
IEEE-CDC, 2001, 547-548.
- ``Output regulation for
linear distributed parameter systems,'' IEEE Transactions of Automatic
Control, 45 (2000), no. 12, 2236-2252, (with C.I. Byrnes, I.G. Laukó, D.S. Gilliam).
- ``Boundary control,
stabilization and zero-pole dynamics for a nonlinear distributed parameter
system,'' Journal of Robust and Nonlinear Control, 9, 1999,
737-768, (with C.I. Byrnes, and D.S. Gilliam).
- ``Semiglobal
stabilization of a boundary controlled viscous BurgersŐ
equation,'' 38th IEEE-CDC Proceedings, 1999, 680-681, (with C.I.
Byrnes and D.S. Gilliam).
- ``Example of output
regulation for a system with unbounded inputs and outputs,'' 38th
IEEE-CDC Proceedings, 1999, 4280-4284, (with C.I. Byrnes and D.S.
Gilliam).
- ``On the global dynamics for
a controlled viscous Burgers' equation," J. Dynam.
Control Systems, 4, no. 4, 1998, 457-519 (with C.I. Byrnes and D.S.
Gilliam).
- ``Harmonic forcing for linear
distributed parameter systems,'' Journal of Mathematical Systems,
Estimation and Control, Summary Vol. 8, No. 2, 1998, (with C.I.
Byrnes, I. Laukó and D.S. Gilliam). Full paper
at http://scholar.lib.vt.edu/ejournals/JMSEC/jmsec.html
- ``Numerical stationary
solutions for a viscous Burgers' equation,'' Journal of Mathematical
Systems, Estimation and Control, Summary Vol. 8, No. 2, 1998, (with J.
Burns, A. Balogh and D.S. Gilliam). Full paper at
http://scholar.lib.vt.edu/ejournals/JMSEC/jmsec.html
- ``Zero dynamics for relative
degree one SISO distributed parameter systems," Proc. 37th IEEE
Conf. Decision and Control, (Tampa, FL, 1998), pp. 2390-2391, (with
C.I. Byrnes, I.G. Laukó, D.S. Gilliam).
- ``Conditions for solvability
of the output regulator problem for SISO distributed parameter
systems," Proc. 37th IEEE Conf. Decision and Control, Tampa,
FL, 1998, 2392-2393, (with C.I.
Byrnes, I.G. Laukó, and D.S. Gilliam).
- ``Global solvability for
damped nonlinear hyperbolic systems,'' J. Diff. and Int. Equations,
10, 1997, 309-332, (with H.T. Banks and D.S. Gilliam).
- ``Some recent results on
feedback regularization of Navier-Stokes equations,"
Proc. 36th IEEE Conf. Decision and Control, San
Diego, CA,1997, 2231-2236 (with A. Balogh,
and D.S. Gilliam).
- ``Output regulation for
parabolic distributed parameter systems: set point control," Proc.
36th IEEE Conf. Decision and Control, San Diego, CA, 1997, 2225-2230
(with C.I. Byrnes, I. Laukó, and D.S. Gilliam).
- ``Example of output
regulation for distributed parameter systems," 28th AIAA Fluid
Dynamics Conference/ 4th AIAA Shear Flow Control Conference, 1997,
(with C.I. Byrnes, A. Isidori, I. Laukó, and D.S. Gilliam).
- ``High gain limits of
trajectories and attractors for a boundary controlled viscous Burgers'
equation," Journal of Mathematical Systems, Estimation and Control,
Summary, V. 6, No. 4, 1996, (with C.I. Byrnes and D.S. Gilliam). Full
paper at http://scholar.lib.vt.edu/ejournals/JMSEC/jmsec.html
- ``Well-posedness
for controlled nonlinear damped membranes with fixed boundary,'' Proceedings
35th IEEE Conference on Decision and Control, December 1995,
3223-3224, (with H.T. Banks and D.S. Gilliam).
- ``Well-posedness
for a damped one dimensional nonlinear beam," Progress in Systems
and Control, Birkhäuser, 1995, 1-22, (with
H.T. Banks, and D.S. Gilliam).
- ``The steady state response
to Burgers' equation with varying viscosity,'' Progress in Systems and
Control, Birkhäuser, 1995, 75-98, (with C.I.
Byrnes, D.S. Gilliam and Z. Xu).
- ``On the dynamics of boundary
controlled nonlinear distributed parameter systems," Proc. IFAC
Nonlinear Control Systems Symposium, 62, 1995, 913-913, (with C.I.
Byrnes and D.S. Gilliam).
- ``High gain limit for
boundary controlled convective reaction diffusion equations,'' Proceedings
35th IEEE Conference on Decision and Control, 1995, 3237-3238, (with
C.I. Byrnes, D.S. Gilliam, and N. Okasha).
- ``Zero and pole dynamics for
a controlled Burger's equation," Proceedings 33rd IEEE Conference
on Decision and Control, 1994, 295-298, (with C.I. Byrnes and D.S.
Gilliam).
- ``Global Lyapunov
stabilization of a nonlinear distributed parameter system," Proceedings
33rd IEEE Conference on Decision and Control, 1994, 1769-1773, (with
C.I. Byrnes and D.S. Gilliam).
- ``Turbulent behavior for a
boundary controlled Burger's equation," Proceedings 33rd IEEE
Conference on Decision and Control, 1994, 311-315, (with D. Lee, C.F. Martin
and D.S. Gilliam),
- ``Convergence of trajectories
for a controlled viscous Burgers' equation,'' Control and Estimation of
Distributed Parameter Systems: Nonlinear Phenomena Birkhauser-Boston,
vol.118, Eds. W. Desch, F. Kappel,
K. Kunish, 1994, 61-79, (with C.I. Byrnes and
D.S. Gilliam).
- ``Boundary control for a
viscous Burgers' equation,'' Identification and control in systems
governed by partial differential equations H.T. Banks, R.H. Fabiano and K. Ito (Eds.), SIAM Frontiers in Science,
1993, 171-185, (with C.I. Byrnes and D.S. Gilliam).
- ``Natural exponential
families of probability distributions and exponential polynomial
approximation,'' Applied Math. and Comp., 59 1993, 277-298, (with
C.F. Martin).
- ``Probability measures, Appel polynomials and polynomial approximation. Appl. Math. Comput.'' 53,
no. 2-3, 1993, 277-298. (with C.F. Martin)
- ``Stochastic regularization
of the observability problem for linear and
nonlinear diffusion equations,'' Systems and Networks: Mathematical
theory and Applications, 1993, 785-788, (with C.F. Martin).
- ``Long time behavior of
infinite dimensional dissipative dynamical systems I.''
Journal of Mathematical Systems, Estimation and Control, 2, no. 4,
1992, 381-427.
- ``Subsets of a Hilbert space,
having finite Hausdorff dimension,'' J. of
Soviet Math., 49, no. 5, 1990.
- ``On dynamics of discrete and
continuous
-models with values in
Riemannian manifolds,'' Mathematics of Nonlinear Science,
Contemporary Mathematics, 108, 1990, 139-143.
- ``The dynamics of infinite
classical anharmonic systems with constraints,''
Proceedings of the Steklov Mathematical
Institute, 179 (1988) 203-224.
- ``Existence of a weak
solution of the BBGKY hierarchy for infinite classical anharmonic
systems with constraints,'' J. of Soviet Math., 40, 1988, 690-700.
- On the dynamics of infinite
classical anharmonic systems with constraints,''
J. of Soviet Math. 147, 1985, 190-195.
- ``Unique solvability of the
Cauchy problem for equations of discrete chiral
fields with values in Riemannian manifolds,'' J. of Soviet Math.,
30, 1985, 2353-2368.
- ``On the unique solvability
of the Cauchy problem for the equations of discrete multidimensional chiral fields taking values in the unit sphere, J.
of Soviet Math., 24, 1984, 633-638.
- ``Unique solvability of the
Cauchy problem for the equations of the two-dimensional relativistic chiral fields with values in Riemannian manifolds,'' J.
of Soviet Math., 25, 1984, 855-864, (with O. A. Ladyzhenskaya).
- ``Classification of the
reductions of the equations of principal chiral
fields,'' Functional Analysis and its Applications, 16, 1983,
239-240.
- ``On the unique solvability
of the Cauchy problem for the equations of motion of the discrete analogs
of multidimensional chiral fields taking values
in compact symmetric spaces,'' Theoretical and Mathematical Physics,
49, 1982, 966-974.
- ``On finding
-soliton solutions of nonlinear
equations by means of Hirota's method,'' Theoretical
and Mathematical Physics, 41, 1979, 891-895, .
- ``The decomposition of a quasiregular representation of a Lie group by the
orbit method,'' J. of Soviet Math., 8, 1977, 229-246.
PAPERS IN PREPARATION OR SUBMITTED FOR PUBLICATION
- Fine dust limit for solutions
of Navier-Stokes and Euler equations coupled
through Stokes’ drag law.
- Generalized Donaldson-Sullivian model of a vortex flow, (with D. S. Gilliam,
J. Baker, C. Mickel, and E. Vurgin).
- Small-scale spatial mollifiers with efficient spectral filtering
properties and applications, (with J.A.Burns,
C.I. Byrnes, and D.S. Gilliam).
- Output regulation for
parabolic distributed parameter systems and decay of generalized Fourier
coefficients of Gevrey class functions, (with
C.I. Byrnes and D.S. Gilliam).
- ``The output regulator
problem for regular linear systems,'' (with C.I. Byrnes, D.S. Gilliam and
G. Weiss).
- “Output regulation and
flows on complete metric spaces”, (with C.I. Byrnes, D.S. Gilliam
and A. Isidori).
BOOK IN PREPARATION
- "A Mathematical Analysis
of Tornado Dynamics," This book is under consideration by the SIAM
Series Frontiers in Science.
· Back to Main Page