Controllability of dynamical systems. A survey

Bulletin of the Polish Academy of Sciences: Technical Sciences

Volumn 61, Issue 2, 2013, Pages 335-342

  Klamka, J ^a  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

control theory; controllability; dynamical systems

Indexed keywords

CHEMICAL PROCESS CONTROL; CONTROLLABILITY AND OBSERVABILITIES; CONTROLLABILITY PROBLEMS; DYNAMICAL CONTROL SYSTEMS; INFINITE DIMENSIONAL DYNAMICAL SYSTEMS; LINEAR TIME-INVARIANT CONTROL SYSTEMS; MINIMUM ENERGY CONTROL; ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS;

CONTROL THEORY; DIFFERENCE EQUATIONS; DYNAMICAL SYSTEMS; ELECTRIC POWER SYSTEMS; LINEAR CONTROL SYSTEMS; OBSERVABILITY; QUANTUM ELECTRONICS; QUANTUM OPTICS; SYSTEM THEORY;

CONTROLLABILITY;

EID: 84883474092     PISSN: 02397528     EISSN: None     Source Type: Journal    
DOI: 10.2478/bpasts-2013-0031     Document Type: Article

References (71)

1. J. Klamka, "Relative controllability and minimum energy control of linear systems with distributed delays in control", IEEE Trans. on. Automatic Control AC-21 (4), 594-595 (1976
2. J. Klamka, "Controllability of linear systems with timevariable delays in control", Int. J. Control 24 (6), 869-878 (1976
3. J. Klamka, "On the controllability of linear systems with delays in the control", Int. J. Control 25 (6), 875-883 (1977
4. J. Klamka, "Absolute controllability of linear systems with time-variable delays in control", Int. J. Control 26 (1), 57-63 (1977
5. J. Klamka, "Relative and absolute controllability of discrete systems with delays in control", Int. J. Control 26 (1), 65-74 (1977
6. J. Klamka, "Minimum energy control of discrete systems with delays in control", Int. J. Control 26 (5), 737-744 (1977
7. J. Klamka, "Relative controllability of nonlinear systems with distributed delays in control", Int. J. Control 28 (2), 307-312 (1978
8. J. Klamka, "Relative controllability of infinite-dimensional systems with delays in control", Systems Science 4 (1), 43-52 (1978
9. J. Klamka, "Minimum energy control of 2D systems in Hilbert spaces", Systems Science, 9 (1-2), 33-42 (1983
10. J. Klamka, Controllability of Dynamical Systems, PWN, Warszawa, 1990, (in Polish
11. J. Klamka, Controllability of Dynamical Systems, Kluwer Academic, Dordrecht, 1991
12. J. Klamka, "Controllability of dynamical systems -A survey", Archives of Control Sciences 2 (3/4), 281-307 (1993
13. J. Klamka, "Constrained controllability of nonlinear systems", J. Math. Analysis and Applications 201 (2), 365-374 (1996
14. J. Klamka, "Schauder's fixed point theorem in nonlinear controllability problems", Control and Cybernetics 29 (3), 377-393 (2000
15. J. Klamka, "Constrained exact controllability of semilinear systems", Systems and Control Letters 47 (2), 139-147 (2002
16. J. Klamka, "Constrained controllability of semilinear systems with multiple delays in control", Bull. Pol. Ac. Tech. 52 (1), 25-30 (2004
17. J. Klamka, "Approximate constrained controllability of mechanical systems", J. Theoretical and Applied Mechanics 43 (3), 539-554 (2005
18. J. Klamka, "Controllability of dynamical systems", Applied Mathematics 9, 57-75 (2008
19. J. Klamka, "Stochastic controllability of systems with variable delay in control", Bull. Pol. Ac. Tech. 56 (3), 279-284 (2008
20. J. Klamka, "Constrained controllability of semilinear systems with delayed controls", Bull. Pol. Ac. Tech. 56 (4), 333-337 (2008
21. J. Klamka, "Stochastic controllability and minimum energy control of systems with multiple delays in control", Applied Mathematics and Computation 206 (2), 704-715 (2008
22. J. Klamka, "Controllability of fractional discrete-time systems with delay", Scientific Notebooks of Silesian University of Technology. Series of Automatics 151, 67-72 (2008
23. J. Klamka, "Constrained controllability of semilinear systems with delays" Nonlinear Dynamics 56 (1-2), 169-177 (2009
24. J. Klamka, "Stochastic controllability of systems with multiple delays in control", Int. J. Applied Mathematics and Computer Science 19 (1), 39-47 (2009
25. J. Klamka, "Controllability and minimum energy control problem of fractional discrete-time systems", in: New Trends in Nanotechnology and Fractional Calculus, eds: D. Baleanu, Z.B. Guvenc, and J.A. Tenreiro Machado, pp. 503-509, Springer-Verlag, New York, 2010
26. J. Klamka and L. Socha, "Some remarks about stochastic controllability", IEEE Trans. on Automatic Control AC-22 (5), 880-881 (1977
27. J. Klamka and L. Socha, "Some remarks about stochastic controllability for delayed linear systems", Int. J. Control. 32 (3), CD-ROM (1980
28. J. Klamka and J. Wyrwał, "Controllability of second-order infinite-dimensional systems, Systems and Control Letters 57 (5), 386-391 (2008
29. J. Klamka and B. Sikora, "On constrained stochastic controllability of dynamical systems with multiple delays in control, Bull. Pol. Ac. Tech. 60 (2), 301-306 (2012
30. P. Gawron, J. Klamka, J. Miszczak, and R. Winiarczyk, "Extending scientific computing system with structural quantum programming capabilities", Bull. Pol. Ac. Tech. 58 (1), 77-88 (2010
31. S. Wegrzyn, J. Klamka, and S. Bugajski, "Foundation of quantum computing, Part 1", Archives of Theoretical and Applied Informatics 13 (2), 97-142 (2001
32. S. Wegrzyn J. Klamka, and S. Bugajski, "Foundation of quantum computing. Part 2", Archives of Theoretical and Applied Informatics 14 (2), 93-106 (2002
33. S. Wegrzyn, J. Klamka, L. Znamirowski, R. Winiarczyk, and S. Nowak, "Nano and quantum systems of informatics", Bull. Pol. Ac. Tech. 52 (1), 1-10 (2004
34. H.P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford, 2002
35. D. Dong and I.R. Petersen, "Quantum control theory and applications: A survey", IET Control Theory and Applications 4 (12), 2651-2671 (2010
36. N.K. Son, "A unified approach to constrained approximate controllability for the heat equations and the retarded equations", J. Mathematical Analysis and Applications 150 (1), 1-19 (1990
37. K. Balachandran and J.P. Dauer, "Controllability of nonlinear systems via fixed point theorems, J. Optimization Theory and Applications 53, 345-352 (1987
38. K. Balachandran and J.P. Dauer, "Controllability of nonlinear systems in Banach spaces. A Survey", J. Optimization Theory and Applications 115, 7-28 (2002
39. K. Balachandran, D.G. Park, and P. Manimegalai, "Controllability of second order integrodifferential evolution systems in Banach spaces", Computers and Mathematics with Applications 49, 1623-1642 (2005
40. K. Naito, "Controllability of semilinear control systems dominated by the linear part", SIAM J. on Control and Optimization 25 (3), 715-722 (1987
41. S.M. Robinson, "Stability theory for systems of inequalities. Part II. Differentiable nonlinear systems", SIAM J. on Numerical Analysis 13 (4), 497-513 (1976
42. G. Peichl and W. Schappacher, "Constrained controllability in Banach spaces", SIAM J. on Control and Optimization 24 (6), 1261-1275 (1986
43. T.I. Seidman, "Invariance of the reachable set under nonlinear perturbations", SIAM J. on Control and Optimization 25 (5), 1173-1191 (1987
44. J.Y. Park, K. Balachandran, and G. Arthi, "Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces", Nonlinear Analysis: Hybrid Systems 3, 184-194 (2009
45. Y. Lin Y. and N. Tanaka, "Nonlinear abstract wave equations with strong damping", J. Mathematical Analysis and Applications 225, 46-61 (1998
46. H.X. Zhou, "Controllability properties of linear and semilinear abstract control systems", SIAM J. on Control and Optimization 22 (3), 405-422 (1984
47. X. Fu, "Controllability of abstract neutral functional differential systems with unbounded delay", Applied Mathematics and Computation 141, 299-314 (2004
48. E. Hernandez and H.R. Henriquez, "Impulsive partial neutral differential equations", Applied Mathematical Letters 19, 215-222 (2006
49. E. Hernandez, H.R. Henriquez, and M. Rabello, "Existence of solutions for impulsive partial neutral functional differential equations", J. Mathematical Analysis and Applications 331, 1135-1158 (2007
50. X. Liu and A.R. Wilms, "Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft", Mathematical Problems in Eng. 2, 277-299 (1996
51. J.Y. Park, K. Balachandran, and G. Arthi, "Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces", Nonlinear Analysis: Hybrid Systems 3, 184-194 (2009
52. R. Sakthivel, N.I. Mahmudov, and J.H. Kim, "On controllability of second-order nonlinear impulsive differential systems", Nonlinear Analysis 71, 45-52 (2009
53. N.I. Mahmudov and A. Denker, "On controllability of linear stochastic systems", Int. J. Control 73 (2), 144-151 (2000
54. N.I. Mahmudov and S. Zorlu, "Controllability of nonlinear stochastic systems", Int. J. Control 76 (2), 95-104 (2003
55. T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002
56. T. Kaczorek, "Reachability and controllability to zero of cone fractional linear systems", Archives of Control Sciences 17 (3), 357-367 (2007
57. T. Kaczorek, "Fractional positive continuous-time linear systems and their reachability", Int. J. Applied Mathematical Computation Science 18 (2), 223-228 (2008
58. T. Kaczorek, "Positive fractional continuous time linear systems with singular pencils", Bull. Pol. Ac. Tech. 60 (1), 9-12 (2012
59. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006
60. S. Ostalczyk, Outline of Integral/Differential Calculus of Fractional Orders. Theory and Applications in Authomatics, ź University of Technology Publishing House, ź, 2008, (in Polish
61. S.S. Ge, Z. Sun, and T.H. Lee, "Reachability and controllability of switched linear discrete-time system", IEEE Trans. on Automatic Control AC-46 (9), 1437-1441 (2001
62. Z. Sun, S.S. Ge, and T.H. Lee, "Controllability and reachability criteria for switched linear system", Automatica 38 (5), 775-786 (2002
63. Z. Sun and S.S. Ge, Switched Linear Systems -Control and Design, Springer, New York, 2004
64. Z. Sun and D.Z. Zheng, "On reachability and stabilization of switched linear control systems", IEEE Trans. on Automatic Control AC-46 (2), 291-295 (2001
65. X. Liu, H. Lin and B.M. Chen, "Structural controllability of switched linear systems", ArXiv.1106.1703v2 [cs.SY] (2012
66. G. Xie and L. Wang, "Controllability and stabilizability of switched linear systems", Systems and Control Letters 48 (2), 135-155 (2003
67. Z. Sun and S.S. Ge, Stability Theory of Switched Dynamical Systems, Springer-Verlag, London, 2011
68. J. Clotet, J. Ferrer, and M.D. Magret, "Distance from a controllable switched linear system to an uncontrollable one", 2nd Meeting on Linear Algebra Matrix Analysis and Applications 1, CD-ROM (2010
69. Y. Qiao and D. Cheng, "On partitioned controllability of switched linear systems", Automatica 45 (1), 225-229 (2009
70. T. Kaczorek, "Positive fractional 2D continuous discrete time linear systems", Bull. Pol. Ac. Tech. 59 (4), 575-579 (2011
71. T. Kaczorek, "Positive switched 2D linear systems described by the Roesser models", Eur. J. Control 18 (3), 239-246 (2012