Constrained controllability of semilinear systems with multiple delays in control

• Autorzy: Klamka J.
• Języki publikacji: EN

Abstrakty

EN

In the present paper finite-dimensional, stationary dynamical control systems described by semi linear ordinary differential state equations with multiple point delays in control are considered. Infinite-dimensional semi linear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, sufficient conditions for constrained local relative controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.

Słowa kluczowe

EN

controlability; nonlinear control systems; semilinear control system; constrained controls; delayed control systems

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 25--30
• Opis fizyczny: Bibliogr. 11 poz., 2 rys.

Twórcy

autor

Klamka J.

• Institute of Control Engineering, Silesian Technical University, 16 Akademicka St., 44-100 Gliwice, Poland

Bibliografia

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• [2] J. Klamka, Controllability of Dynamical Systems, Dordrecht: Kluwer Academic Publishers, 1991.
• [3] J. Klamka, “Controllability of dynamical systems — a survey”, Archives of Control Sciences 2(3/4), 281–307 (1993).
• [4] G. Peichl and W. Schappacher, “Constrained controllability in Banach spaces”, SIAM J. Contr. and Optimization 24(6), 1261–1275 (1986).
• [5] T. I. Seidman, “Invariance of the reachable set under nonlinear perturbations”, SIAM J. Contr. and Optimization 25(5), 1173–1191 (1987).
• [6] H. X. Zhou, “Controllability properties of linear and semilinear abstract control systems”, SIAM J. Contr. and Optimization 22(3), 405–422 (1984).
• [7] N. Fujii and Y. Sakawa, “Controllability for nonlinear differential equations in Banach space”, Automat. Contr. Theory and Appl. 2(2), 44–46 (1974).
• [8] J. Klamka, “Constrained controllability of nonlinear systems”, J. Math. Anal. and Applications 201(2), 365–374 (1996).
• [9] N. K. Son, “A unified approach to constrained approximate controllability for the heat equations and the retarded equations”, J. Math. Anal. and Applications 150(1), 1–19 (1990).
• [10] K. Naito, “Controllability of semilinear control systems dominated by the linear part”, SIAM J. Contr. and Optimization 25(3), 715–722 (1987).
• [11] S. M. Robinson, “Stability theory for systems of inequalities. Part II. Differentiable nonlinear systems”, SIAM J. Numerical Anal. 13(4), 497–513 (1976).