LIST OF PUBLICATIONS

 

  1. with H. Schättler, Optimal and suboptimal protocols for a class of mathematical models for tumor anti-angiogenesis, J. of Theoretical Biology, accepted for publication, to appear
  2. with V. Oussa and H. Schättler, Two optimal control problems for a model of tumor anti-angiogenesis, submitted to Optimization, Methods and Software
  3. with H. Schättler, Anti-angiogenic therapy in cancer treatment as an optimal control problem, SIAM J. on Control and Optimization, Vol. 46 (3), 2007, pp. 1052-1079
  4. with H. Schättler, Analysis of a mathematical model for tumor anti-angiogenesis, Optimal Control, Applications and Methods, published online 2007, to appear.
  5. with  H. Schättler, On a class of systems describing tumor anti-angiogenesis under Gompertzian growth, WSEAS Transactions on Systems, 4, Volume 6, 2007, pp.758-766
  6. with  H. Schättler, Singular controls in systems describing tumor anti-angiogenesis, Proc. of the 5th WSEAS Conference on Systems Science and Simulation in Engineering, Tenerife, Spain, December 2006, pp. 156-161
  7. with H. Schättler, Optimal control for a system modelling tumor anti-angiogenesis, ICGST - Int. J. on Automatic Control and Systems Egineering (ACSE), 6, 2006, pp. 33-39
  8. with H. Schättler, Application of optimal control to a system describing tumor anti-angiogenesis, Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 2006, pp. 478-484
  9. with H. Schättler, Analysis of models for evolving drug resistance in cancer chemotherapy, DCDIS (Dynamics of Continuous, Discrete and Impulsive Systems),  Proceedings 2, (2006), pp. 291-304
  10. with M. de Pinho, M.M. Ferreira and H. Schättler, A model for cancer chemotherapy with state space constraints, Nonlinear Analysis,  Vol. 63 (5), 2005, pp. 2591-2602
  11.  with H. Schättler, Model of maximizing bone marrow with pharmacokinetics, Mathematical Biosciences, 2007 (in press, available electronically on journal web-site)
  12. with H. Schättler, Drug resistance in cancer chemotherapy as an optimal control problem, Discrete and Continuous Dynamical Systems, series B, Vol. 6 (1), 2006,  pp. 129-150
  13. with H. Schättler, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, Proceedings of the 44rd IEEE Conference on Decision and Control, Seville, Spain, December 12-15, 2005
  14.  with H. Schättler, The influence of PK/PD on the structure of optimal control in cancer chemotherapy models, Mathematical Biosciences and Engineering, Vol.2, No.3, August 2005
  15. with H. Schättler, A local field of extremals for single-input systems with state space constraints, to appear in the Proc. of the 43rd IEEE Conf. on Decision and Control, The Bahamas, December 2004, pp. 923-928
  16.  with H. Schättler, The structure of optimal controls for a concer chemotherapy model with PK/PD equations, to appear in the Proc. of the 43rd IEEE Conf. on Decision and Control, The Bahamas, December 2004, pp.1376-1381
  17. with H. Schättler and A.Swierniak, Finite dimensional models of drug resistant and phase specific cancer chemotherapy,  Journal of Medical Information Technology,  Vol. 8, pp.5-13,  2004
  18. with H. Schättler, Application of control theory in modeling cancer chemotherapy, ICCAS 2004, Proceedings of the Int. Conf. on Control, Automation and Systems, Bangkok, Thailand, August 2004, pp. 330-335
  19.  with H. Schättler and A.Swierniak, Singular controls are not optimal for compartmental models of cancer chemotherapy, Proceedings of X Conference on Application of Mathematics in Biology and Medicine, Jodlowy Dwor, Poland, September 2004, pp.213-218
  20. with H. Schättler, Controlling a model for bone marrow dynamics in cancer chemotherapy, Mathematical Biosciences and Engineering, Vol.1, No.1, pp.95-110, 2004
  21. with T. Brown and H. Schättler, A comparison of optimal controls for a model in cancer chemotherapy with L1- and L2-type objectives, Optimization Methods and Software,  Vol. 19. Number 3-4, (Special Issue devoted to Proceedings of the First International Conference on Optimization Methods and Software, Hangzhou, China, December 2002), pp. 351-359, 2004
  22. with H. Schättler and A. Nowakowski, Stratifiable families of extremals and sufficient conditions for optimality in optimal control problems, Journal of Optimization Theory and Applications (JOTA), Vol. 122, No.2, August 2004
  23. with H. Schättler and S. Walczak, Optimal control system governed by second-order ODEs with Dirichlet boundary data and variable parameters, Illinois Journal of Mathematics,  Vol.47, No.4, pp. 1189-1206, 2004
  24.  with H. Schättler, Optimal control for a bilinear model with recruiting agent in cancer chemotherapy, Proceedings of the 42nd IEEE Conference on Decision and Control (CDC), Maui, Hawaii, December 2003, pp.2762-2767
  25. with H. Schättler and A. Swierniak, Optimal control for a class of compartmental models in cancer chemotherapy, International Journal of Applied Mathematics and Computer Science, Vol. 13, No. 3, pp. 357-368, 2003
  26. with H. Schättler, Optimal control for a 3-compartment model for cancer chemotherapy with quadratic objective, in: Dynamical Systems and Differential Equations, (W. Feng, S, Hu and X. Lu, Eds., A supplement volume to Discrete and Continuous Dynamical Systems), Proceedings of the 4th International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, 2002, p. 544-553
  27. with H. Schättler, Sufficient conditions for optimality of controls in biomedical systems, Proceedings of the 41st IEEE Conference on Decision and Control (CDC), Las Vegas, Nevada, 2002, pp. 3524-29
  28.  with H. Schättler, Optimal controls for a two-compartment model for cancer chemotherapy with quadratic objective, Proceedings of the 5th Portuguese Conference on Automatic Control (Controlo 2002), Aveiro, Portugal, 2002, pp. 241-247
  29. with H. Schättler, Analysis of a cell-cycle specific model for cancer chemotherapy, Journal of Biological Systems, Vol. 10, No. 3, 2002, pp. 183-206
  30. with H. Schättler, On optimal controls for a general mathematical model for chemotherapy of HIV, Proceedings of the 2002 American Control Conference, Anchorage, Alaska, 2002, pp. 3454-3459
  31. with H. Schättler, Analysis of a class of optimal control problems arising in cancer chemotherapy, Proceedings of the 2002 American Control Conference, Anchorage, Alaska, 2002, pp. 3460-3465
  32.  with H. Schättler, Optimal bang-bang controls for a 2-compartment model in cancer chemotherapy, Journal of Optimization Theory and Applications, Vol. 114, No.3, 2002, pp. 609-637
  33. with S. Walczak and H. Schättler, Stability of elliptic optimal control problems, Computers and Mathematics with Applications, 41, 2001, pp. 1245-1256
  34. with H. Schättler, A high-order maximum principle for abnormal extremals, in: Encyclopedia of Optimization, Kluwer Academic Publishing Co., 2001, pp. 423-430
  35. with H. Schättler, High-order necessary conditions for abnormal points, in: Encyclopedia of Optimization, Kluwer Academic Publishing Co., 2001, pp. 431-438
  36. with H. Schättler,  On optimal controls for a 3-compartment model of cancer chemotherapy,” at Proceedings of IASTED International Conference on Control and Applications, Banff, Canada, 2001, pp. 109-114
  37. with H. Schättler, On generalizations of the Euler-Lagrange equation, Nonlinear Analysis, Vol. 47, 2001, pp. 339-350 (Proceedings of Third World Congress of Nonlinear Analysts)
  38. with H. Schättler and A. Nowakowski, A local generalized Hilbert invariant integral, Nonlinear Analysis, Vol. 47, 2001, pp. 399-310, (Proceedings of Third World Congress of Nonlinear Analysts)
  39. with H. Schättler, A high-order generalized local Maximum principle, SIAM Journal on Control and Optimization, Vol. 38, No.3, 2000, pp. 823-855
  40. with H. Schättler, Optimal control for a mathematical model of cancer chemotherapy, in: Control and Applications, Proceedings of the IASTED International Conference, Cancun, Mexico, 2000, pp. 8-14
  41. with H. Schättler, On the synthesis of controls for a mathematical model of cancer chemotherapy, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 4845-4850
  42. with H. Schättler, A high-order maximum principle for abnormal extremals - examples, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp.136-141
  43. with H. Schättler and S. Walczak, A high-order open mapping theorem in Banach spaces, Nonlinear Studies, Vol. 6, No. 1, 1999, pp. 1-10
  44. with H. Schättler and A. Nowakowski, Generalized fields of extremals, in: Mathematical Theory of Networks and Systems, Proceedings of the MTNS-98 Symposium, Padova, Italy, 1999, pp. 277-281
  45. with H. Schättler, High-order approximations in Optimal Control Theory: a comparison of normal, abnormal and singular cases, Proceedings of the MTNS-98 Symposium, Padova, Italy, 1999, pp. 282-285
  46. with H. Schättler, High-order approximations for abnormal bang-bang extremals, in: System Modelling and Optimization, P. Kall, I. Lasiecka and M. Polis, Eds., (Proceedings of the 18th IFIP Conference on Mathematical Modelling and Optimization), Addison-Wesley-Longman Publ. Co., 1999, pp. 126-135
  47. with H. Schättler, A high-order generalization of the Lyusternik theorem and its application to optimal control problems, in: Dynamical Systems and Differential Equations, Vol. II, W. Chen and S. Hu, Eds., 1998, pp. 45-59, (Proceedings of the International Conference on Dynamical Systems and Differential Equations, Springfield, Missouri, June 1996)
  48. with A. Nowakowski, Dual optimal synthesis for optimal control problems with abstract semilinear differential equations, in: Dynamical Systems and Differential Equations, Vol. II, W. Chen and S. Hu, 1998, Eds., pp. 32-44, (Proceedings of the International Conference on Dynamical Systems and Differential Equations, Springfield, Missouri, June 1996)
  49. with H. Schättler, High-order extended Maximum Principles for optimal control, in: Optimal Control: Theory, Algorithms and Applications, (W.W. Hager and P.M. Pardalos, Eds.), Kluwer Academic Publishers, 1998, pp. 298-325
  50. with H. Schättler, A high order generalization of the Lyusternik theorem, Nonlinear Analysis, Vol. 34, No. 6, 1998, pp. 793-815
  51. with H. Schättler, High-order approximations and generalized necessary conditions for optimality, SIAM Journal on Control and Optimization, Vol. 37, No. 1, 1998, pp. 33-56
  52. with H. Schättler, Analysis of abnormal extremals in optimal control, in: Proceedings of Symposia in Pure Mathematics, H. Sussmann and G. Ferreyra, Eds., Proceedings of Symposia in Pure mathematics, Vol. 64, American Mathematical Society, 1998, pp. 223-239
  53. with H. Schättler, Perturbation feedback control and neighboring extremals in the abnormal case, Proceedings of the IASTED International Conference on Control and Applications, Honolulu, Hawaii, August 1998, pp. 161-166
  54. with S. Walczak, Optimal control of systems governed by elliptic equations, Discrete and Continuous Dynamical Systems, Vol. 5, No.2, 1998, pp. 279-290
  55. with H. Schättler, Second order Dubovitskii-Milyutin theory and applications to control, Advances in Nonlinear Dynamics, (Stability and Control: Theory, Methods and Applications, Vol. 5,  S. Sivasundaram and A.A. Martynyuk, Eds.), 1997,  pp. 179-192
  56. with H. Schättler, An Extended Maximum Principle, Nonlinear Analysis, Vol.29, No.2, 1997, pp. 159-183
  57. with H. Schättler, High-order tangent cones and their application in optimization, Nonlinear Analysis, Vol. 30, No. 4, 1997, pp. 2449-2460, (Proceedings of the Second World Congress of Nonlinear Analysts, Athens, Greece, July 1996)
  58. with A. Nowakowski, Optimality conditions for control problems governed by abstract semilinear differential equations in complex Banach spaces, Journal of Applied Analysis, Vol. 3, No.1, 1997, pp. 67-91
  59. with S.Walczak, Generalizations of the Lusternik theorem and their applications to nonsmooth and abnormal problems in optimization and optimal control, Proceedings of the First  World Congress of Nonlinear Analysts, Tampa (Florida), August, 1992, Vol. III, pp. 2583-2594, Walter de Gruyter, 1996
  60. with H. Schättler, A generalization of the Lyusternik theorem and high order approximations in Optimization, Proceedings of the 2nd Portuguese Conference on Automatic Control, Porto, Portugal, September 1996, pp. 455-460
  61. with H. Schättler, Second Order  Conditions for Extremum Problems with Nonregular Equality Constraints, Journal of Optimization Theory and Applications, Vol.86, No.1, pp. 113-144, July 1996
  62. with H. Schättler, An Extended Global Maximum Principle, Proceedings of 34th IEEE Conference on Decision and Control, New Orleans, pp. 3922-3928, December 1995 
  63. with S.Walczak, On the Lusternik Theorem for Nonsmooth Operators, Nonlinear Analysis, Theory, Methods and Applications, Vol.22, No.2, pp. 121-128, 1994
  64. with H. Schättler, A theory of first and second order conditions for nonregular extremum problems, in:  Optimal Control of Differential Equations and Variational Inequalities ( editor: N. Pavel, Proceedings of the Conference on Optimal Control, Athens (Ohio), March 25-27, 1993), Lecture Notes in Pure and Applied Mathematics,  Marcel  Dekker, Vol.160, pp. 237-250, 1994
  65. with H. Schättler, Pareto optimality conditions for abnormal optimization and optimal control problems, in:  Optimal Control of Differential Equations  and Variational Inequalities  (editor: N. Pavel, Proceedings of the Conference on Optimal Control, Athens (Ohio), March 25-27, 1993), Lecture Notes in Pure and Applied Mathematics,  Marcel  Dekker, Vol.160, pp. 217-235, 1994
  66. with A. Nowakowski, Necessary and sufficient conditions for optimlity for nonlinear control problems in Banach spaces,  in:  Optimal Control of Differential Equations and Variational Inequalities ( editor: N. Pavel, Proceedings of the Conference on Optimal Control, Athens (Ohio), March 25-27, 1993), Lecture Notes in Pure and Applied Mathematics,  Marcel Dekker, Vol.160,  pp. 195-216, 1994 
  67.  with H. Schättler, Second order conditions for optimality in abnormal optimal control problems,  Proceedings of 33 IEEE Conference on Decision and Control, Orlando, December 1994, pp.2594-2599
  68. On Abnormal Optimal Control Problems with Mixed Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 173, No.1, pp. 18-42,  1993
  69. The Extremum Principle for Some Types of Distributed Parameter Control Problems, Applicable Analysis, Vol. 48, pp.1-21, 1993
  70. An Extension of the Local Maximum Principle to Abnormal Optimal Control Problems, Journal of Optimization Theory and Applications, Vol.77, No.3, pp. 661-681, 1993
  71. On Some Distributed Parameter Control Systems with Terminal Data in the Abnormal Case and in the Case of Nonoperator Equality Constraints, Journal of Applied Mathematics and Stochastic Analysis, Vol.6, No.2, pp.137-151, 1993
  72. On an Abnormal Optimal Control Problem, in: Mathematical Theory of Control  (editors: M. Joshi, A. Balakrishnan, Proceedings of the International Conference on Mathematical Control, IIT Bombay , India, December 10-15, 1990), Lecture Notes in Pure and Applied Mathematics, Vol. 142, Marcel Dekker,  pp. 255-267, 1992
  73. Optimality Conditions for Abnormal  Optimal Control Problems of Systems with Terminal Data, in: Theory of Differential Equations and Applications to Oceanography, ( editors: S.G. Deo, Y.S. Prahalad, Proceedings of International Conference on the Theory of Differential Equations and Applications to Oceanography, Goa University, India, December 17-21, 1990), Affiliated East-West Press Private Limited, New Delhi, pp. 187- 206, 1992
  74. Optimality conditions for abnormal optimal control problems with additional equality constraints, in: Partial Differential Equations, (editors: J. Wiener, J. Hale,  Proceedings of International Conference on the Theory and Applications of Differential Equations in Edinburg, Texas, May 1991),  Pitman Research Notes in Mathematics, Vol. 273, Longman Scientific and Technical, New York, pp.96-100, 1992
  75. On the Optimal Control Problems of Parabolic Equatons with an Infinite Number of Variables and with Equality Constraints, Differential and Integral Equations,Vol.4, pp. 369-381, 1991
  76. On the Euler-Lagrange Equation in the Case of Nonregular Operator Equality Constraints, Journal of Optimization Theory and Applications, Vol. 71, No.3, pp. 549-568, December 1991
  77. Optimality and Pareto Optimality Conditions for the Problems with Nonregular Operator Equality Constraints, Nonlinear Analysis , Vol 16, No.4, pp. 347-360, 1991
  78. Application of the Moser's Technique to the Tangent Direction Problem for Nonlinear  Evolution Equations, in: Differential Equations, Stability and Control, (editor: S. Elaydi, Proceeding of the International Conference of  the Differential  Equations, Theory and Applications in Stability and Control,  Colorado Springs, June 1989), Lectures Notes in Pure and Applied Mathematics, Vol.127, Marcel Dekker, pp. 363-375, 1990
  79. On the Extremum Problems in the Presence of Unbounded Operator Constraint, Journal of Mathematical Analysis and Applications, Vol.151, No.2, pp. 344-358, 1990
  80. On Some Optimal Control Problems of Differential Equations with Additional Equality Contraints. in: Modern Optimal Control (editor: E. Roxin, Proceeding of the  International Conference  in Honor of  Solomon Lefschetz and Joseph P.LaSalle, 30 Years of Modern Optimal Control Theory, Kingston,  Rhode Island, June 1988), Lecture Notes in Pure and Applied Mathematics, Vol. 119, Marcel Dekker, pp.259-271, 1989
  81. A Necessary and Sufficient Condition for Altman's Maximal Element Problem for Constraint Sets with Many Equalities, Nonlinear Analysis, Theory, Methods and Applications,Vol.13, No.7, pp. 833-840, 1989
  82. Application of Global Linearization Interative Methods to General Optimal Control Problems in Banach Spaces, in: Differential Equations and Applications, (editor: A.R. Aftabizadeh, Proceeding on the International Conference on the Theory and Applications of Differential Equations, Colmbus, Ohio, March 1988), Ohio University Press, Athens, Vol.2, pp. 103-109, 1989
  83. A Necessary Condition for the Extremal Problems under Gateaux Differentiability, Journal of Mathematical Analysis and Applications, Vol.134, No.1, pp.158-168, 1988
  84. Optimal Control Problems of Hyperbolic Systems with Operator and Nonoperator Equality Constraints, Applicable Analysis, Vol. 27, pp. 199-215, 1988
  85. On the Optimal Control Problems with Gateaux Differentiable Operator Constraints,  Journal of Mathematical Analysis and Applications, Vol. 130, No. 2, pp. 301-315, 1988
  86. Tangent Directions for a Class of Nonlinear Evolution Equations,  Differential and Integral Equations, Vol.1, No.4, pp.409-422, 1988
  87. Application of Some Specification of the Dubovitskii-Milyutin Method to Problems of Optimal Control, Nonlinear Analysis; Theory, Methods and Applications, Vol. 12, No.2, pp.101-108, 1988
  88. Application of the Method of Contractor Directions to the Dubovitskii-Milyutin Formalism, Journal of Mathematical Analysis and Applications, Vol. 125, No. 1, pp. 174-184, 1987
  89. The Extremum Principle for Problems of Optimal Control with Mixed Constraints, Acta Universitatis Lodziensis, Folia Mathematica, No. 2 , pp. 37-59, 1987
  90. Applications of the Method of Contractor Directions to Optimization Theory,  Proceedings of the Conference of Applied Mathematics, Sielpia, (Poland), pp. 168-173, 1986
  91. The Necessary and Sufficient Condition for the Problem of Optimal Control of  Parabolic Systems with Equality Constraints, Bulletin de la Societé des Science at des Lettres de Lodz,Vol. XXXVII, No. 30, pp. 1-12, 1986
  92. On Some Specification of the Dubovitskii-Milyutin Method, Nonlinear Analysis: Theory, Methods and Applications, Vol. 10, No. 12, pp. 1367-71, 1986
  93. A Necessary Condition for a Problem of Optimal Control with Equality and Inequality Constraints,  Control and Cybernetics, Vol. 14, No. 4, pp. 351-360, 1985