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1
Content available Constrained controllability of second order dynami cal systems with delay
Klamka J.
Control and Cybernetics
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2013
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Vol. 42, no. 1
111--121
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.
2
Content available remote Constrained controllability of semilinear systems with delayed controls
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 4
333-337
EN
In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient conditions for constrained global relative controllability of an associated linear dynamical system with multiple point delays in control are discussed. Simple numerical example, which illustrates theoretical considerations is also given. Finally, some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
3
Content available remote Constrained controllability of semilinear systems with multiple delays in control
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2004
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Vol. 52, nr 1
25-30
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.
4
Controllability of dynamical systems with damping term and constrained controls
Respondek J.
Zeszyty Naukowe. Automatyka / Politechnika Śląska
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2003
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z. 138
135-158
EN
In the paper presented the methodology of investigation of the controllability of an infinite dimensional second order dynamical systems with damping term. Following this aim spectral theory for linear unbounded operators is involved. In the first part of the paper the problem is stated and the methodology of transforming the second order equation to the set of the first order equations is reminded. Next the theorem on transforming considered infinite dimensional dynamical system to infinite series of finite dimensional systems is proved. Finally the theorem on necessary and sufficient conditions of constrained approximate controllability of considered system is formulated and proved.
PL
W ramach pracy przedstawiono metodykę badania sterowalności nieskończenie wymiarowych układów dynamicznych rzędu drugiego z czynnikiem tłumiącym. Do tego celu wykorzystana została spektralna teoria liniowych operatorów nieograniczonych. W pierwszej części pracy został sformułowany problem i przypomniana została metodyka sprowadzenia rozpatrywanego układu drugiego rzędu do układu równań pierwszego rzędu. Następnie udowodniono twierdzenie o sprowadzeniu wyjściowego układu nieskończenie wymiarowego do nieskończonego ciągu układów skończenie wymiarowych. Na koniec zostało sformułowane i udowodnione twierdzenie podające warunki konieczne i wystarczające aproksymacyjnej sterowalności z ograniczeniami rozpatrywanego układu.
5
Controllability of dynamical systems with constrained controls
Respondek J.
Zeszyty Naukowe. Automatyka / Politechnika Śląska
|
2003
|
z. 138
121-133
EN
In the paper presented the methodology of investigation of the controllability of an infinite dimensional second order dynamical systems with damping term. Following this aim spectral theory for linear unbounded operators is involved. In the first part of the paper the problem is stated and the methodology of transforming the second order equation to the set of the first order equations is reminded. Next the theorem on transforming considered infinite dimensional dynamical system to infinite series of finite dimensional systems is proved. Finally the theorem on necessary and sufficient conditions of constrained approximate controllability of considered system is formulated and proved.
PL
W ramach pracy przedstawiono metodykę badania sterowalności nieskończenie wymiarowych układów dynamicznych rzędu drugiego z czynnikiem tłumiącym. Do tego celu wykorzystana została spektralna teoria liniowych operatorów nieograniczonych. W pierwszej części pracy został sformułowany problem i przypomniana została metodyka sprowadzenia rozpatrywanego układu drugiego rzędu do układu równań pierwszego rzędu. Następnie udowodniono twierdzenie o sprowadzeniu wyjściowego układu nieskończenie wymiarowego do nieskończonego ciągu układów skończenie wymiarowych. Na koniec zostało sformułowane i udowodnione twierdzenie podające warunki konieczne i wystarczające aproksymacyjnej sterowalności z ograniczeniami rozpatrywanego układu.
6
Content available remote Constrained Controllability of Semilinear Delayed Systems
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2001
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vol. 49, nr 3
505-515
EN
In the paper infinite-dimensional dynamical control systems described by semilinear differential equations with delays in the state variables are considered. Using a general sufficient conditions for constrained exact controllability for infinite-dimentional dynamical systems sufficient conditions for constrained exact absolute local controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. As an illustrative example, constrained exact absolute local controllability problem for semilinear dynamical system with one constant delay in the state variable is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
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