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1
Content available remote

Controllability and reconstructability of a system described by the N-D Roesser model

100%
Kurek J. E.
International Journal of Applied Mathematics and Computer Science
|
2003
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tom 13
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nr 1
55-60
EN
The controllability and reconstructability (global) of the system described by a digital N-D Roesser model are defined. Then, necessary and sufficient conditions for system controllability and reconstructability are given. The conditions constitute a generalization of the corresponding conditions for 1-D systems.
2
Content available remote

Exact boundary controllability of coupled hyperbolic equations

100%
Avdonin S., Choque Rivero A., de Teresa L.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
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nr 4
701-710
EN
We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.
3
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Controllability of right invariant systems on semi-simple Lie groups

100%
El Assoudi R., Gauthier J. P., Kupka I. A. K.
Banach Center Publications
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1995
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tom 32
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nr 1
199-208
EN
We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.
4
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Controllability theorem for nonlinear dynamical systems

100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
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tom 22
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nr 2
225-232
EN
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
5
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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

100%
Benchohra M., Górniewicz L., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
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tom 21
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nr 2
261-282
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
6
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On the controllability of fractional dynamical systems

100%
Balachandran K., Kokila J.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
523-531
EN
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
7
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Controllability of nonlinear implicit fractional integrodifferential systems

100%
Balachandran K., Divya S.
International Journal of Applied Mathematics and Computer Science
|
2014
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tom 24
|
nr 4
713-722
EN
In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.
8
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Approximate controllability of infinite dimensional systems of the n-th order

88%
Respondek J.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 2
199-212
EN
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.
9
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An approach to the analysis of observability and controllability in nonlinear systems via linear methods

88%
Zhirabok A., Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
507-522
EN
The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g., Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.
10
Content available remote

Spatial compensation of boundary disturbances by boundary actuators

88%
Afifi L., Chafiai A., Jai A. E.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 4
899-920
EN
In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance, we give the optimal control ensuring its compensation.
11
Content available remote

Monomial subdigraphs of reachable and controllable positive discrete-time systems

88%
Bru R., Caccetta L., Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
12
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Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

88%
Ezzinbi K., Degla G., Ndambomve P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2015
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tom 35
|
nr 1
25-46
EN
This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.
13
Content available remote

Controllability, observability and optimal control of continuous-time 2-D systems

88%
Jank G.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 2
181-195
EN
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data. The optimal control problem with a quadratic cost functional is also solved.
14
Content available remote

Stochastic controllability of systems with multiple delays in control

88%
Klamka J.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
|
nr 1
39-47
EN
Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.
15
Content available remote

Stochastic controllability of linear systems with state delays

88%
Klamka J.
International Journal of Applied Mathematics and Computer Science
|
2007
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tom 17
|
nr 1
5-13
EN
A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
16
Content available remote

Controllability of nonlinear discrete systems

88%
Klamka J.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
173-180
EN
Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.
17
Content available remote

On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question

88%
Przyłuski K.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
723-733
EN
In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.
18
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Content available

Controllability criteria for time-delay fractional systems with a retarded state

75%
Sikora B.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
521-531
EN
The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
19
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Content available

Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

75%
Benedetti I., Obukhovskii V., Zecca P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2011
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tom 31
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nr 1
39-69
EN
We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.
20
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Content available

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

75%
Abada N., Benchohra M., Hammouche H., Ouahab A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
|
nr 2
329-347
EN
In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
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