Powiadomienia systemowe
- Sesja wygasła!
- Sesja wygasła!
- Sesja wygasła!
- Sesja wygasła!
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The main objective of this article is to review the major progress that has been made on controllability of dynamical systems over the past number of years. Controllability is one of the fundamental concepts in the mathematical control theory. This is a qualitative property of dynamical control systems and is of particular importance in control theory. A systematic study of controllability was started at the beginning of sixties in the last century, when the theory of controllability based on the description in the form of state space for both time-invariant and time-varying linear control systems was worked out. Roughly speaking, controllability generally means, that it is possible to steer a dynamical control system from an arbitrary initial state to an arbitrary final state using the set of admissible controls. It should be mentioned, that in the literature there are many different definitions of controllability, which strongly depend on a class of dynamical control systems and on the other hand on the form of admissible controls. Controllability problems for different types of dynamical systems require the application of numerous mathematical concepts and methods taken directly from differential geometry, functional analysis, topology, matrix analysis and theory of ordinary and partial differential equations and theory of difference equations. In the paper we use mainly state-space models of dynamical systems, which provide a robust and universal method for studying controllability of various classes of systems. Controllability plays an essential role in the development of modern mathematical control theory. There are various important relationships between controllability, stability and stabilizability of linear both finite-dimensional and infinite-dimensional control systems. Controllability is also strongly related to the theory of realization and so called minimal realization and canonical forms for linear time-invariant control systems such as the Kalmam canonical form, the Jordan canonical form or the Luenberger canonical form. It should be mentioned, that for many dynamical systems there exists a formal duality between the concepts of controllability and observability. Moreover, controllability is strongly connected with the minimum energy control problem for many classes of linear finite dimensional, infinite dimensional dynamical systems, and delayed systems both deterministic and stochastic. Finally, it is well known, that controllability concept has many important applications not only in control theory and systems theory, but also in such areas as industrial and chemical process control, reactor control, control of electric bulk power systems, aerospce engineering and recently in quantum systems theory.
Słowa kluczowe
Rocznik
Tom
Strony
335--342
Opis fizyczny
Bibliogr. 71 poz.
Twórcy
autor
- Institute of Control Engineering, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland
Bibliografia
- [1] J. Klamka, “Relative controllability and minimum energy control of linear systems with distributed delays in control”, IEEETrans. 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”, AppliedMathematics 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”, AppliedMathematics 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 ComputerScience 19 (1), 39-47 (2009).
- [25] J. Klamka, “Controllability and minimum energy control problem of fractional discrete-time systems”, in: New Trends inNanotechnology 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. Węgrzyn, J. Klamka, and S. Bugajski, “Foundation of quantum computing, Part 1”, Archives of Theoretical and AppliedInformatics 13 (2), 97-142 (2001).
- [32] S. Węgrzyn J. Klamka, and S. Bugajski, “Foundation of quantum computing. Part 2”, Archives of Theoretical and AppliedInformatics 14 (2), 93-106 (2002).
- [33] S. Węgrzyn, 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 QuantumSystems, 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 andApplications 53, 345-352 (1987).
- [38] K. Balachandran and J.P. Dauer, “Controllability of nonlinear systems in Banach spaces. A Survey”, J. Optimization Theoryand 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 NumericalAnalysis 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 andComputation 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 MathematicalComputation 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 Applicationsof Fractional Differential Equations, Elsevier, Amsterdam, 2006.
- [60] S. Ostalczyk, Outline of Integral/Differential Calculus of FractionalOrders. Theory and Applications in Authomatics, Łodź University of Technology Publishing House, Łodź, 2008, (in Polish).
- [61] S.S. Ge, Z. Sun, and T.H. Lee, “Reachability and controllability of switched linear discrete-time system”, IEEE Trans. onAutomatic 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 andDesign, Springer, New York, 2004.
- [64] Z. Sun and D.Z. Zheng, “On reachability and stabilization of switched linear control systems”, IEEE Trans. on AutomaticControl 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 DynamicalSystems, 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). 342 Bull.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5d67ea4f-a3c2-4168-bf8f-643858419e7d