Publications:

  1. “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.
  2. "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).
  3. "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).
  4. "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).
  5. ``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).
  6. “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 )
  7. “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/).
  8. “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).
  9. "Modelling Modal Based Sensors for Oscillatory Systems", Proceedings of 41st IEEE CDC Proceedings, Dec. 2002, 1725-1726, (with A. Balogh and D. S. Gilliam).
  10. ``Stationary solutions for a boundary controlled viscous Burgers' equation,'' Journal Mathematical and Computer Modeling, (2001), (with A. Balogh and D.S. Gilliam).
  11. ``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).
  12. ``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).
  13. ``Examples of output regulation for distributed parameter systems with infinte dimensional exosystem,'' Proceedings of 40th IEEE-CDC, 2001, 547-548.
  14. ``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).
  15. ``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).
  16. ``Semiglobal stabilization of a boundary controlled viscous BurgersŐ equation,'' 38th IEEE-CDC Proceedings, 1999, 680-681, (with C.I. Byrnes and D.S. Gilliam).
  17. ``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).
  18. ``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).
  19. ``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
  20. ``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  
  21. ``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).
  22. ``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).
  23. ``Global solvability for damped nonlinear hyperbolic systems,'' J. Diff. and Int. Equations, 10, 1997, 309-332, (with H.T. Banks and D.S. Gilliam).
  24. ``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).
  25. ``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).
  26. ``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).
  27. ``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
  28. ``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).
  29. ``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).
  30. ``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).
  31. ``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).
  32. ``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).
  33. ``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).
  34. ``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).
  35. ``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),
  36. ``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).
  37. ``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).
  38. ``Natural exponential families of probability distributions and exponential polynomial approximation,'' Applied Math. and Comp., 59 1993, 277-298, (with C.F. Martin).
  39. ``Probability measures, Appel polynomials and polynomial approximation. Appl. Math. Comput.'' 53, no. 2-3, 1993, 277-298. (with C.F. Martin)
  40. ``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).
  41. ``Long time behavior of infinite dimensional dissipative dynamical systems I.'' Journal of Mathematical Systems, Estimation and Control, 2, no. 4, 1992, 381-427.
  42. ``Subsets of a Hilbert space, having finite Hausdorff dimension,'' J. of Soviet Math., 49, no. 5, 1990.
  43. ``On dynamics of discrete and continuous $ \sigma$-models with values in Riemannian manifolds,'' Mathematics of Nonlinear Science, Contemporary Mathematics, 108, 1990, 139-143.
  44. ``The dynamics of infinite classical anharmonic systems with constraints,'' Proceedings of the Steklov Mathematical Institute, 179 (1988) 203-224.
  45. ``Existence of a weak solution of the BBGKY hierarchy for infinite classical anharmonic systems with constraints,'' J. of Soviet Math., 40, 1988, 690-700.
  46. On the dynamics of infinite classical anharmonic systems with constraints,'' J. of Soviet Math. 147, 1985, 190-195.
  47. ``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.
  48. ``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.
  49. ``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).
  50. ``Classification of the reductions of the equations of principal chiral fields,'' Functional Analysis and its Applications, 16, 1983, 239-240.
  51. ``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.
  52. ``On finding $ N$-soliton solutions of nonlinear equations by means of Hirota's method,'' Theoretical and Mathematical Physics, 41, 1979, 891-895, .
  53. ``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
 

  1. Fine dust limit for solutions of Navier-Stokes and Euler equations coupled through Stokes’ drag law.
  2. Generalized Donaldson-Sullivian model of a vortex flow, (with D. S. Gilliam, J. Baker, C. Mickel, and E. Vurgin).
  3. Small-scale spatial mollifiers with efficient spectral filtering properties and applications, (with J.A.Burns, C.I. Byrnes, and D.S. Gilliam).
  4. 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).
  5. ``The output regulator problem for regular linear systems,'' (with C.I. Byrnes, D.S. Gilliam and G. Weiss).
  6. “Output regulation and flows on complete metric spaces”, (with C.I. Byrnes, D.S. Gilliam and A. Isidori).


BOOK IN PREPARATION

  1. "A Mathematical Analysis of Tornado Dynamics," This book is under consideration by the SIAM Series Frontiers in Science.

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