Constrained controllability of second order dynami cal systems with delay

• Autorzy: Klamka J.
• Języki publikacji: EN

Abstrakty

EN

The paper considers finite-dimensional dynami cal control systems described by second order semilinear stationary ordinary differential state equations with delay in control. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear first-order dynamical control system. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Moreover, several remarks and comments on the existing results for controllability of semilinear dynamical control systems are also presented. Finally, a simple numerical example which illustrates theoretical considerations is also given. It should be pointed out that the results given in the paper extend for the case of semilinear second-order dynamical systems constrained controllability conditions, which were previously known only for linear second-order systems.

Słowa kluczowe

EN

controllability; second-order dynamical systems; delayed control systems; semilinear control systems; constrained controls

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 1
• Strony: 111--121
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Klamka J.

• Institute of Control Engineering, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Bibliografia

• 1. Bian W. and Webb J.R.L. (1999) Constrained open mapping theorems and applications. Journal of London Mathematical Society, 60 (2), 897-911.
• 2. Kaczorek T. (1993) Linear Control Systems. Research Studies Press and John Wiley, New York.
• 3. Kaczorek T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London.
• 4. Kaczorek T.(2006) Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn. 54 (3), 347-350.
• 5. Kaczorek T.(2007a) Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6 (4).
• 6. Kaczorek T.(2007b) Reachability and controllability to zero of cone fractional linear systems. Archives of Control Sciences, 17 (3), 357-367.
• 7. Kaczorek T. (2007c) Realization problem for positive continuous-time systems with delays. Intern. J. Comput. Intellig. and Appl., 6 (2), 289-298.
• 8. Klamka J. (1991) Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht, The Netherlands.
• 9. Klamka J.(1993) Controllability of dynamical systems – a survey. Archives of Control Sciences, 2 (3/4), 281-307.
• 10. Klamka J. (1996) Constrained controllability of nonlinear systems. Journal of Mathematical Analysis and Applications, 201 (2), 365-374.
• 11. Klamka J. (2004) Constrained controllability of semilinear systems with multiple delays in control. Bulletin of the Polish Academy of Sciences. Technical Sciences, 52 (1), 25-30.