1
CURRICULUM VITAE ET STUDIORUM
STAVROS A. BELBAS
1. Address:Mathematics Department, University of Alabama,
Tuscaloosa, AL., 35487-0350. USA.
Telephone(205) 348-1992
FAX(205) 348-7067
2. Citizenship:USA.
3. Graduate education:Ph.D. in Applied Mathematics, Brown University,
Providence, R.I.; 1980.
4. Research expertise
4.1 Optimal control, dynamic game theory, analytical and numerical methods in systems analysis and control.
4.2Numerical solution of partial differential equations.
4.3Mathematical modeling and analysis of systems involving continuum mechanics and related issues.
4.4Optimal control and identification for systems governed by partial differential equations, with applications to environmental problems.
4.5Analysis, stability and control of stochastic systems, with applications.
4.62-D and N-D systems, learning systems, neural networks.
4.7Control systems with non-local operators: integral equations, mathematical model of hysteresis; smart materials, magnetostriction.
4.8Optimal control with non-additive cost functionals, Wiener-Volterra series.
4.9Biochemistry and neurocomputing.
4.10.Counterterrorism.
5. Research papers.
5.1. Research papers in refereed journals.
5.1.1.(with A.N. Kounadis) On the parametric resonance of columns carrying concentrated masses, J. Struct. Mech., 5, 1977, 283-394.
5.1.2.Weak solutions of the Hamilton-Jacobi-Bellman equation, Systems and Control Letters, 1, 1981, 168-172.
5.1.3.Nonlinear stochastic integral equations over partially ordered topological spaces, J. Integral Equations, 4, 1982, 323-338.
5.1.4. (with S.M. Lenhart) A system of nonlinear partial differential equations arising in the optimal control of stochastic systems with switching costs, SIAM J. Appl. Math., 1983, 323-338.
5.1.5.A remark on dynamic programming with final state constraints, Systems and Control Letters, 4, 1984, 343-346.
5.1.6.(with I.D. Mayergoyz) Applications des methodes du point fixe aux equations de Bellman discretes et a des inequations quasi-variationnelles discretes, Comptes Rendus Acad. Sciences de Paris, Serie I, T. 299, 1984, 233-236.
5.1.7.(with S.M. Lenhart) Nonlinear partial differential equations for stochastic optimal control with switchings and impulses, Appl. Math. Optimization, 14, 1986, 215- 225.
5.1.8.(with T.I. Seidman) Periodic solutions of quasi-linear parabolic variational inequalities, Appl. Analysis, 29, 1988, 301-327.
5.1.9(with I.D. Mayergoyz) Applications of fixed-point methods to discrete variational and quasi-variational inequalities, Numerische Mathematik, 51, 1987, 631-654.
5.1.10.The dynamic programming equations for stochastic games with discrete actions, Systems and Control Letters, 11, 1988, 235-242.
5.1.11.(with I.D. Mayergoyz) Iterative schemes for certain time-dependent problems of optimal control, Int. J. Control, 50, 1989, 1681-1698.
5.1.12.Dynamic programming approach to the optimal control of systems governed by Goursat-Darboux equations, Int. J. Control, 51, 1990, 1279-1294.
5.1.13.Dynamic programming and maximum principle for discrete Goursat systems, J. Math. Analysis and Applic., 161, 1991, 57-77.
5.1.14.(with I.D. Mayergoyz) Numerical solution of quasi-variational inequalities arising in stochastic game theory, Appl. Math. Optimiz., 31, 1995, 19-39.
5.1.15.Multi-time dynamic programming and Riccati equations, "International Journal of Control 1998, Vol. F1, No. 1, pp. 61-78:
5.1.16.(with I. D. Mayergoyz) Optimal control of dynamical systems with hysteresis, "International Journal of Control", Vol. 73, 2000, pp. 22-29.
5.1.17.Iterative schemes for optimal control of Volterra integral equations, Nonlinear Analysis, 37 (1999), 57-79.
5.1.18.Dynamic programming for systems with Preisach hysteresis (with I. D. Mayergoyz ) , Physica-B (Condensed Matter Physics), Vol. 306, 2001, pp. 200-205.
5.1.19.Optimal control of dynamical systems with Preisach hysteresis (with I. D. Mayergoyz), "International Journal of Non-linear Mechanics", Volume 37, Issue 8, December 2002, Pages 1351-1361.
5.1.20. Intertwined dynamic programming for hybrid Roesser systems, "Optimalsteureungsprobl. Luft- u. Raumfahrt", 2003, pp. 107-116..
5.1.21. Set-valued mappings in optimal control of hysteretic systems (with I. D. Mayergoyz), to appear in "Physica-B: condensed matter Physics".
5.1.22. Optimal control of Goursat systems in irregular domains, WSEAS Transactions on Applied Mathematics, Vol. 3, 2004, pp. 581-585.
5.1.23. A general model of vector hysteresis, WSEAS Transactions on Systems, Vol. 3, 2004, pp. 1763-1769.
5.1.24. (with W. H. Schmidt) Optimal control of Volterra equations with impulses, Applied Mathematics and Computation, Vol. 166, pp. 696-723.
5.1.25. New hysteresis operators with applications to counterterrorism, Applied Mathematics and Computation, Vol. 170, 2005, pp. 425-439.
5.1.26. Control of systems with hysteresis, Science of Hysteresis, Vol. I, 2005, pp. 605-637.
5.1.27. (with I. D. Mayergoyz) Identification in modified Preisach models, "Preisach Memorial Book", Budapest, 2005, pp. 65-75.
5.1.28. (with I. D. Mayergoyz) Hadamard-like derivatives in hysteresis modelling and control, Physica B: Condensed Matter Physics, Vol. 372, 2006, pp. 87-90.
5.1.29. On series solutions of Volterra equations, Applied Mathematics and Computation, Vol. 181, 2006, pp. 1287--1304.
5.1.29. Optimal control of Goursat-Darboux systems with discontinuous co-state, Applied Mathematics and Computation, Vol. 186, 2007, pp. 101-116.
5.1.30. A new method for optimal control of Volterra integral equations, Applied Mathematics and Computation, Vol. 189, 2007, pp. 1902-1915.
5.1.31. (with J. S. Park). A hybrid Volterra-type equation with two types of impulses, J. Korea Soc, Math, Edu., Ser. B -- Pure and Applied Mathematics, Vol. 13, 2006, pp. 121-136.
5.1.32. Volterra systems with impulses and delays, accepted in "Dynamic Systems and Applications", 2007. Abstract has been published.
5.1.33. A reduction method for optimal control of Volterra integral equations, Applied Mathematics and Computation, Vol. 197, 2008, pp. 880-890.
5.1.34. Optimal control of Volterra integral equations in two independent variables, Applied Mathematics and Computation, Vol. 202, 2008, pp. 647-665.
5.1.35. (with W. H. Schmidt) Optimal control of impulsive Volterra equations with variable impulse times, Applied Mathematics and Computation, Vol. 214, 2009, pp. 353-369.
5.1.36. S. A. Belbas and Y. H. Kim, A model of hysteresis with two inputs, Journal of Mathematical Analysis and Applications, Vol. 366, 2010, pp. 181-194.
5.1.37. S. A. Belbas, Y. Bulka, Numerical solution of multiple nonlinear Volterra integral equations, Applied Mathematics and Computation, Vol. 217, 2011, pp. 4791-4804.
5.1.38. S. A. Belbas, Theoretical basis of parallel computing for multiple Volterra integral equations, Proc. Neural, Parallel, and Scientific Computations, Vol. 4, 2010, pp. 54-58.
5.2.Research papers in refereed books published by commercial publishers.
5.2.1.Numerical solution of certain nonlinear parabolic partial differential equations, Springer-Verlag Lecture Notes in Mathematics, Vol. 1248, 1987, 4-15.
5.2.2.Non-classical dynamic programming in optimal control, invited 1-hour lecture at the 1993 International Colloquium on Differential Equations; Abstract published in 1993; Complete paper published in 1994, VSP Publishers, Zeist, The Netherlands, pp. 39-43.
5.2.3.Optimal control of Goursat systems over general domains, Sixth International Colloquium on Differential Equations, 1995, pp. 55-63.
5.2.4.Approximate solution of optimal control problems for Goursat systems, Fourth International Colloquium on Numerical Analysis, 1995, pp. 11-15.
5.2.5.Optimal control of certain Volterra integral equations with special constraints on the control, invited 30 minute lecture at the 1996 Volterra Centennial Symposium; published in 1999 by Gordon and Breach in the book “Volterra equations and applications” (C. Corduneanu, ed.)
5.2.6.Forward dynamic programming for numerical solution of optimal control problems for parabolic systems, Proceedings of the Seventh International Colloquium on Differential Equations, Zeist, The Netherlands, VSP Publishers, 1997, pp. 9-15.
5.2.7.Optimal control of Goursat systems over variable domains, Proceedings of the Seventh International Colloquium on Differential Equations, Zeist, The Netherlands, VSP Publishers, 1997, pp. 17-21.
5.2.8.(with I. D. Mayergoyz) Optimal Control of discrete-time approximations to systems with hysteresis, Proc. 8th International Colloquium on Diff. Eq., VSP Publishers, Zeist, The Netherlands, 1998, pp. 457-459.
5.2.9.Optimal control of certain M-D systems, Proc. of Eight Int. Colloq. on Diff. Eq., VSP Publishers, Zeist, The Netherlands, 1998, pp. 451-455.
5.2.10.Impulsive Hamilton-Jacobi equations for hybrid control systems, in “Proc. Ninth Int. Colloquium on Differential Equations” , VSP Publishers, Utrecht, The Netherlands, 1999, pp. 29-34.
5.2.11.Numerical solution of multi-time dynamic programming problems, in “Proc. Ninth Int. Colloquium on Differential Equations”, VSP Publishers, Zeist, The Netherlands, 1999, pp. 35-38.
5.2.12.A variational framework for groundwater remediation, in the book “Modern Applied Mathematics Techniques in Circuits, Systems and Control” (World Scientific Eng, Soc., 1999), pp. 100-105 (selected papers from the Third International Multiconference on Circuits, Systems, Communications, and Computers).
5.2.13.Optimal control of 2-D systems with non-local terms, accepted in IEEE Int.
Multiconference on Circuits, Systems, Communications and Computers, July
2000.
5.2.14.Optimal control and identification in integral equations, accepted in Proc. Third Int. Congress Of Nonlinear Analysts, July 2000.
5.2.15. (with I. D. Mayergoyz) Dynamic programming for systems with hysteresis, accepted in 2001 workshop on Hysteresis and Micromagnetics.
5.2.16. Modelling of hysteretic oscillations via impulsive differential equations,
in 2001 Int Colloq. on Differential Equations.
5.2.17. Numerical models of systems with hysteresis, in 2001 Int. Colloq. on
Numerical Analysis.
5.2.18. Hybrid systems modelling in neurophysiology, "Proc. 2003 International Conference on Dynamical Systems and Applications".
5.3.Research papers in refereed conference proceedings.
5.3.1.(with A. Sulem) Explicit solution of certain deterministic optimal control problems with costly switching, 1983 Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, MD.
5.3.2.(with S. M. Lenhart) Stochastic optimal control with forced switching actions, 1983 Allerton Conference on Communications, Control, and Computing, 1983, 734-743.
5.3.3.Modeling of a mechanical system with discontinuous state, 1984 Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, MD.
5.3.4.Variational formulation of the optimality conditions for stochastic systems of variable structure, 1985 Conference on Decision and Control, 285-286.
5.3.5.(with I.D. Mayergoyz) Numerical solution of certain minimax problems of stochastic control, 1987 Conference on Decision and Control, 771-776.
5.3.6.Dynamic and semi-dynamic programming for optimal control of certain distributed systems, in 1989 American Control Conference.
5.3.7.(with M. Sun) Optimal observation schedule for identification of nonlinear distributed systems with applications, 1993, IEEE Southeastern Symposium on Systems Theory, 301-305.
5.3.8.Cascaded Hamiltonian equations and dynamic programming, 1996 Southeastern Symposium on Systems Theory, pp. 180-183.
5.3.9.Dynamic programming equations in mixed continuous-discrete time scales, accepted in 1998 International Congress on Nonlinear Analysis and Applications, Academy of Nonlinear Sciences, Moscow, Russia; abstarct has been published.
5.3.10. Optimal control of discrete stochastic 2-D systems, Proceedings of the 29th Southeastern Symposium on System Theory (Session on Image Processing), IEEE
Computer Society Press, Los Alamitos, CA., 1997, pp. 493-497.
5.3.11.Neural networks in 2-D continuous time, published in Electronic Proc. of 1999 International Joint Conference on Neural Networks.
5.3.12. (with S. Kim) Impulsive modelling in neurobiology, 2003 Intrnat. Conf. Dyn. Systems and Applications, Atlanta, GA., 2003, pp. 581-585.
5.3.13. Volterra series with impulses and delays, presented at 2007 Int. Conference on dynamical systems and Applications, Atlanta, GA., 2007; abstract has been published.
5.3.14. Binary control of Volterra integral equations, Proc. of IFAC 2008 World Congress, 2008, pp. 15411-15414.
5.3.15. S. A. Belbas, Models with memory and hysteresis in groundwater modelling and remediation, Proc. 3-rd International Conference on Experiments/Process/System Modelling/Simulation and Optimization, 8 pp, 2009.
5.3.16. S. A. Belbas, Adjoint theory for integro-partial differential equations and applications, accepted in 2011 ICIAM International Conference (Vancouver, Canada), 2011.
5.4.Refereed abstracts.
5.4.1.Optimal continuous and impulsive control of Goursat systems, invited 1-hour lecture at the 1994 International Colloquium on Differential Equations; Abstract has been published.
5.4.2.Iterative schemes for the numerical solution of optimal control problems for Volterra equations, invited 1-hour lecture at the 1995 International Colloquium on Numerical Analysis; Abstract has been published.
5.4.3.Iterative schemes for optimal control of certain integral equations, invited 1-hour lecture at the 1996 World Congress of Nonlinear Analysts; abstract has been published.
5.4.4.Generators of nonlinear Goursat-Darboux systems and their applications, invited 30-minute lecture at the 1995 International Conference on Dynamic Systems and Applications; Abstract has been published.
5.4.5.New problems in the optimal control of Volterra equations, abstract for invited talk in special session of the 2000 Meeting of the American Mathematical Society (Washington, DC).
5.4.6. New optimal control problems with non-local operators, November 2000 meeting
of the American Mathematical Society in Birmingham, AL.
5.4.7.(with R. Ahangar) Optimal control solution to integro-differential operator systems using dynamic programming", AMS 2002 Meeting, San Diego, January 2002.
5.4.8. Modal dynamic programming for groundwater remediation, 2003 Water Resources Conference, Perdido Beach, AL., September 2003.
5.4.9. New models in groundwater remediation, 2004 Water Resources Conference, Perdido Beach, AL., September 2004.
5.4.10. New issues in groundwater modelling and remediation, 2005 Water Resources Conference, Perdido Beach, AL., October 2005.
5.4.11. Non-Darcy models in groundwater identification and optimization, 2006 Water Resources Conference, Perdido Beach, AL., September 2006.
5.4.12. Optimal control of truncated Volterra integral equations, in Fourth International Conference on applied Mathematics and Computing, Plovdiv, Bulgaria, August 2008.
6.Service to the Mathematics Department.
6.1Library representative for the academic year 1995-1996.
6.2Advisor for a M. Sc. thesis in Applied Mathematics. Student: E.P. Sarris. Degree awarded in 1994. Thesis title: Issues in the optimal control of Goursat systems.
6.3Advisor for a Ph.D. thesis in Mechanical Engineering (co-advisor: Prof. Joey Parker of Mech. Eng.). Student: W.S. Choi. Degree awarded in 1991. Thesis title: Numerical solution of two classes of stochastic optimal control problems.
6.4Examiner for several M.Sc. and Ph.D. thesis in Mechanical Engineering, and for one M.Sc. thesis in Mineral Engineering.
6.5Office Building Committee, Spring 1997.
6.6Committee for modifications in the Ph.D. programs, Spring 1998
6.7Committee for computer-aided instruction in pre-calculus Mathematics.
6.8. Undergraduate mathematics contest committee, Fall 2002 and Spring 2003.
6.9. Calculus committee, Fall 2002 to Fall 2003.
6.10. Committee for Mathematics Dept. Mission Statement, Fall 2002 and Spring 2003.
6.11. Ph.D. thesis advisor for Mr. Yuriy Bulka, Fall 2002 to October 2006.
6.12.Ph. D. thesis advisor for Ms. Younghee Kim, Spring 2003 to date.
6.13. M.Sc. advisor for Mr. Wenan Fei, Fall 2003 to date.
6.14. Member of Ph. D. Committee in the Joint Program (advisor: N. Chernov, UAB), Fall 2003 to summer 2005.
6.15. Qualifying exams committee for Numerical Analysis, summer 2003.
6.16. Qualifying exams committee for Mathematical Statistics, summer 2003.
6.17. Qualifying exams committee for Numerical Analysis, summer 2004.
6.18. Qualifying exams committee for Mathematical Statistics, summer 2004.
6.19. Qualifying exams committee for Mathematical Statistics, summer 2005.
6.20. Qualifying exams committee for Optimization, summer 2005.
6.21. Qualifying exams committee for Mathematical Statistics, summer 2006.
6.22. Qualifying exams committee for Optimization, summer 2006.
6.23. Qualifying exam min Numerical Analysis for the Mechanical Engineering Department, Univ. of Alabama, December 2006.
6.24. Recruiting Committee, 2007-08 academic year.
6.25. Qualifying exam in Mathematical Statistics, summer 2007.
6.26. Qualifying exam in Numerical Analysis, summer 2007.
6.27. Qualifying exam in Mathematical Statistics, summer 2008.
6.28. Qualifying exam in Numerical Analysis, summer 2008.
6.29. Ph.D. Committee for Insuk Shim, Spring 2009.
6.30. Ph.D. Committee for Xiaohua Zheng, Spring 2009.
7.Service to the scientific community.
7.1Referee for several journals, including “Transactions of the American Mathematical Society”, “Systems and Control Letters”, “Applied Mathematics and Optimization”, “Computers and Mathematics with Applications” "Nonlinear Analysis", "Journal of Math . Analysis and Applic.", "J. of Risk Theory", "Applied Mathematical Modelling", "Applied Numerical Mathematics".
7.2Referee for several conferences, including the “IEEE Conference on Decision and Control”, the “Conference on Information Sciences and Systems”, and the “Allerton Conference”.
7.3Reviewer for “Mathematical Reviews”.
8.Invited presentations at international conferences.
8.1.Invited one-hour talk at the 1993 International Colloquium on Differential Equations.
8.2. Invited one-hour talk at the 1994 International Colloquium on Differential Equations.
8.3.Invited one-hour talk at the 1994 International Colloquium on Numerical Analysis.
8.4. Invited one-hour talk at the 1995 International Colloquium on Differential Equations.
8.5.Invited one-hour talk at the 1995 International Colloquium on Numerical Analysis.
8.6.Invited 30-minute talk at 1995 International Conference on Dynamical Systems
and Applications .
8.7.Invited one-hour talk at the 1996 World Congress of Nonlinear Analysts.
8.8.Invited one-hour talk at the 1996 International Colloquium on Differential Equations.
8.9.Invited one-hour talk at the 1996 International Colloquium on Numerical Analysis.
8.10.Invited 30-minute talk at the 1996 Volterra Centennial Symposium .
8.11.Invited one-hour talk at the 1998 International Colloquium on Differential Equations.
8.12.Invited one-hour talk at the 1998 International Colloquium on Numerical Analysis.
8.13.Invited 40-minute talk at 1998 International Conference on Nonlinear Analysis and its Applications, of the Russian Academy of Nonlinear Sciences.
8.14.Invited 30-minute talk at the 1999 International Multi-Conference on Circuits, Systems, Communications and Computers (CSCC ’99).
8.15. Invitation for 45-minute talk at the 2000 World Congress of Nonlinear Analysts.
8.16.Invited 20-minute lecture at special session of the 2000 Annual Meeting of the American Mathematical Society.
8.17.Invitation for 20-minute talk to 2000 International Multi-Conference on Circuits, Systems, Communications and Computers.
8.18.Invitation for 30-minute talk at 2001 Workshop on Hysteresis and Micromagnetics.
8.19.Invitation for one-hour talk at 2001 International Colloquium on Differential Equations.
8.20.Invitation for one-hour talk at 2001 International Colloquium on Numerical Analysis.
8.21.Invitation to 2002 International Colloquium on Numerical Analysis, for one-hour lecture.
8.22.Invitation to 2002 International Colloquium on Differential Equations, for one-hour invited talk.
8.23.Invited talk at International Conference on Optimal Control in Aerospace Problems, Greifswald, Germany, October 2002.
8.24.Invited talk at the 2004 WSEAS International Conference on Applied Mathematics, April 2004.
8.25. Invited one-hour talk at "International Conference on Applied Mathematics" (August 2007 in Plovdiv, Bulgaria).
9.External funding
9.1.Augmentation of optimal management policy selections to groundwater transport model MT3D, 2 years (1994, 1995), with C. Zheng (Geology) and M.Sun (Math). Funded by the US Geological Survey, via the Water Resources Research Institute at Auburn University; amounts $72,900 for 1994, $77,200 for 1995.
10.Proposals submitted
10.1.Collaborative research on analysis, control and identification of systems with hysteresis and their applications (w/ Teik Lim and I. D. Mayergoyz), submitted to NSF (DMS) for $286,348.00. Not funded.
10.2. Research on optimal control for hybrid systems and systems with nonlocal operators, submitted to NSF (DMS) in 2004-2005 academic year. Not funded.
10.3. Research on control of hysteretic and hereditary systems, submitted to NSF in 2005-2006; not funded.
10.4. (w/ J. Sharifov of Baku State U., Azerbaijan) Optimal control of Goursat systems with nonlocal conditions, not funded.
10.5. Numerical solution of optimal control problems for Volterra integral equations, submitted to NSF in 2006-2007 academic year; not funded.
10.6. Analytical and numerical investigation of optimal control problems for non-local hyperbolic systems (jointly with Aleksandr Handzel, University of Stavropol, Russia), submitted to CRDF in the 2006-2007 academic year; not funded.