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Novel fault detection criteria based on linear quadratic control performances

100%
Krokavec D., Filasová A.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
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nr 4
929-938
EN
This paper proposes a new approach to designing a relatively simple algorithmic fault detection system that is potentially applicable in embedded diagnostic structures. The method blends the LQ control principle with checking and evaluating unavoidable degradation in the sequence of discrete-time LQ control performance index values due to faults in actuators, sensors or system dynamics. Design conditions are derived, and direct computational forms of the algorithms are given. A simulation example subject to different types of failures is used to illustrate the design process and to demonstrate the effectiveness of the method.
2
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Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form

100%
Orłowski P.
International Journal of Applied Mathematics and Computer Science
|
2007
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tom 17
|
nr 4
505-513
EN
Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.
3
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An optimal sliding mode congestion controller for connection-oriented communication networks with lossy links

100%
Bartoszewicz A., Leśniewski P.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 1
87-97
EN
A new discrete-time sliding-mode congestion controller for connection-oriented networks is proposed. Packet losses which may occur during the transmission process are explicitly taken into account. Two control laws are presented, each obtained by minimizing a different cost functional. The first one concentrates on the output variable, whereas in the second one the whole state vector is considered. Weighting factors for adjusting the influence of the control signal and appropriate (state or output) errors are incorporated in both the functionals. The asymptotic stability of the closed-loop system is proved, and the conditions for 100% bottleneck node bandwidth utilization are derived. The performance of the proposed algorithm is verified by computer simulations.
4
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$H_∞$ control of discrete-time linear systems constrained in state by equality constraints

75%
Krokavec D.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 3
551-560
EN
In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.
5
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Positive partial realization problem for linear discrete-time systems

75%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2007
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tom 17
|
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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