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1
Content available remote

Behavioral systems theory: A survey

100%
Zerz E.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 3
265-270
EN
We survey the so-called behavioral approach to systems and control theory, which was founded by J. C. Willems and his school. The central idea of behavioral systems theory is to put the focus on the set of trajectories of a dynamical system rather than on a specific set of equations modelling the underlying phenomenon. Moreover, all signal components are treated on an equal footing at first, and their partition into inputs and outputs is derived from the system law, in a way that admits several valid cause-effect interpretations, in general.
2
Content available remote

Strong surjectivity of mappings of some 3-complexes into $$ M_{Q_8 } $$

80%
Aniz C.
Open Mathematics
|
2008
|
tom 6
|
nr 4
497-503
EN
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and $$ M_{Q_8 } $$ the orbit space of the 3-sphere $$ \mathbb{S}^3 $$ with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ $$ \mathbb{S}^3 $$. Given a point a ∈ $$ M_{Q_8 } $$, we show that there is no map f:K → $$ M_{Q_8 } $$ which is strongly surjective, i.e., such that MR[f,a]=min{#(g −1(a))|g ∈ [f]} ≠ 0.
3
Content available remote

Reachability of cone fractional continuous-time linear systems

80%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 1
89-93
EN
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
4
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Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems

70%
Edelmayer A., Bokor J., Szabó Z., Szigeti F.
International Journal of Applied Mathematics and Computer Science
|
2004
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tom 14
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nr 2
189-199
EN
In this paper the classical detection filter design problem is considered as an input reconstruction problem. Input reconstruction is viewed as a dynamic inversion problem. This approach is based on the existence of the left inverse and arrives at detector architectures whose outputs are the fault signals while the inputs are the measured system inputs and outputs and possibly their time derivatives. The paper gives a brief summary of the properties and existence of the inverse for linear and nonlinear multivariable systems. A view of the inversion-based input reconstruction with special emphasis on the aspects of fault detection and isolation by using invariant subspaces and the results of classical geometrical systems theory is provided. The applicability of the idea to fault reconstruction is demonstrated through examples.
5
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An approach to the analysis of observability and controllability in nonlinear systems via linear methods

70%
Zhirabok A., Shumsky A.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
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.
6
Content available remote

Predictive control for trajectory tracking and decentralized navigation of multi-agent formations

70%
Prodan I., Olaru S., Stoica C., Niculescu S.-I.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
|
nr 1
91-102
EN
This paper addresses a predictive control strategy for a particular class of multi-agent formations with a time-varying topology. The goal is to guarantee tracking capabilities with respect to a reference trajectory which is pre-specified for an agent designed as the leader. Then, the remaining agents, designed as followers, track the position and orientation of the leader. In real-time, a predictive control strategy enhanced with the potential field methodology is used in order to derive a feedback control action based only on local information within the group of agents. The main concern is that the interconnections between the agents are time-varying, affecting the neighborhood around each agent. The proposed method exhibits effective performance validated through some illustrative examples.
7
Content available remote

Zeros in linear systems with time delay in state

70%
Tokarzewski J.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 4
609-617
EN
The concept of invariant zeros in a linear time-invariant system with state delay is considered. In the state-space framework, invariant zeros are treated as triples: complex number, nonzero state-zero direction, input-zero direction. Such a treatment is strictly related to the output-zeroing problem and in that spirit the zeros can be easily interpreted. The problem of zeroing the system output is discussed. For systems of uniform rank, the first nonzero Markov parameter comprises a certain amount of information concerning invariant zeros, output-zeroing inputs and zero dynamics. General formulas for output-zeroing inputs and zero dynamics are provided.
8
Content available remote

Double fault distinguishability in linear systems

61%
Kościelny J., Łabęda-Grudziak Z.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
|
nr 2
395-406
EN
This paper develops a new approach to double fault isolation in linear systems with the aid of directional residuals. The method of residual generation for computational as well as internal forms is applied. Isolation of double faults is based on the investigation of the coplanarity of the residual vector with the planes defined by the individual pairs of directional fault vectors. Additionally, the method of designing secondary residuals, which are structured and directional, is proposed. These transformations allow achieving various isolation properties. It is shown that double fault distinguishability can be improved by decomposing the observed residual vector along the response directions. The described methods are illustrated with a simple computational example.
9
Content available remote

Positive partial realization problem for linear discrete-time systems

61%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 2
165-171
EN
A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.
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