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1
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State estimation for a class of nonlinear systems

100%
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 2
383-394
EN
We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of nonlinearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.
2
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Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
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tom 26
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nr 2
277-283
EN
Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
3
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Linear adaptive structure for control of a nonlinear MIMO dynamic plant

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Bańka S., Dworak P., Jaroszewski K.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 1
47-63
EN
In the paper an adaptive linear control system structure with modal controllers for a MIMO nonlinear dynamic process is presented and various methods for synthesis of those controllers are analyzed. The problems under study are exemplified by the synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system, use is made of a set of (stable) linear modal controllers that create a linear adaptive controller with variable parameters tuned appropriately to operation conditions chosen on the basis of two measured auxiliary signals. These are the ship's current forward speed measured in reference to the water and the systematically calculated difference between the course angle and the sea current (yaw angle). The system synthesis is carried out by means of four different methods for system pole placement after having linearized the model of low-frequency motions made by the vessel at its nominal “operating points” in steady states that are dependent on the specified yaw angle and the sea current velocity. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks.
4
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Design of a multivariable neural controller for control of a nonlinear MIMO plant

100%
Bańka S., Dworak P., Jaroszewski K.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
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nr 2
357-369
EN
The paper presents the training problem of a set of neural nets to obtain a (gain-scheduling, adaptive) multivariable neural controller for control of a nonlinear MIMO dynamic process represented by a mathematical model of Low-Frequency (LF) motions of a drillship over the drilling point at the sea bottom. The designed neural controller contains a set of neural nets that determine values of its parameters chosen on the basis of two measured auxiliary signals. These are the ship's current forward speed measured with respect to water and the systematically calculated difference between the course angle and the sea current (yaw angle). Four different methods for synthesis of multivariable modal controllers are used to obtain source data for training the neural controller with parameters reproduced by neural networks. Neural networks are designed on the basis of 3650 modal controllers obtained with the use of the pole placement technique after having linearized the model of LF motions made by the vessel at its nominal operating points in steady states that are dependent on the specified yaw angle and the sea current velocity. The final part of the paper includes simulation results of system operation with a neural controller along with conclusions and final remarks.
5
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Neural network-based NARX models in non-linear adaptive control

100%
Dzieliński A.
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
235-240
EN
The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed.
6
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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
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2007
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tom 17
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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.
7
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Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

100%
Verdiere N., Denis-Vidal L., Joly-Blanchard G., Domurado D.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 4
517-526
EN
The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it a priori parameter values. Then the resulting parameter estimate is improved by using the classical least-squares method.
8
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Tracking control algorithms for a laboratory aerodynamical system

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Gorczyca P., Hajduk K.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
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nr 4
469-475
EN
The tracking control problem of a strongly nonlinear MIMO system is presented. The system shares some features with a helicopter, such as important interactions between the vertical and horizontal motions. The dedicated IO board allows for control, measurements and communication with a PC. The RTWT toolbox in the MATLAB environment is used to perform real-time experiments. The control task is to track a predefined reference trajectory. A mathematical model of the system, containing experimental characteristics, is used to design the controllers: a multidimensional PD, a suboptimal controller in the sense of a quadratic performance index and a variable gain controller.
9
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Stability of a class of adaptive nonlinear systems

100%
Dzielinski A.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 4
455-462
EN
This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.
10
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Separation principle for nonlinear systems: a bilinear approach

100%
Hammami M. A., Jerbi H.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 2
481-492
EN
In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.
11
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Actuator fault tolerance in control systems with predictive constrained set-point optimizers

100%
Marusak P., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 4
539-551
EN
Mechanisms of fault tolerance to actuator faults in a control structure with a predictive constrained set-point optimizer are proposed. The structure considered consists of a basic feedback control layer and a local supervisory set-point optimizer which executes as frequently as the feedback controllers do with the aim to recalculate the set-points both for constraint feasibility and economic performance. The main goal of the presented reconfiguration mechanisms activated in response to an actuator blockade is to continue the operation of the control system with the fault, until it is fixed. This may be even long-term, if additional manipulated variables are available. The mechanisms are relatively simple and consist in the reconfiguration of the model structure and the introduction of appropriate constraints into the optimization problem of the optimizer, thus not affecting the numerical effectiveness. Simulation results of the presented control system for a multivariable plant are provided, illustrating the efficiency of the proposed approach.
12
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Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems

88%
Edelmayer A., Bokor J., Szabó Z., Szigeti F.
International Journal of Applied Mathematics and Computer Science
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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.
13
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Time-varying time-delay estimation for nonlinear systems using neural networks

88%
Tan Y.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
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nr 1
63-68
EN
Nonlinear dynamic processes with time-varying time delays can often be encountered in industry. Time-delay estimation for nonlinear dynamic systems with time-varying time delays is an important issue for system identification. In order to estimate the dynamics of a process, a dynamic neural network with an external recurrent structure is applied in the modeling procedure. In the case where a delay is time varying, a useful way is to develop on-line time-delay estimation mechanisms to track the time-delay variation. In this paper, two schemes called direct and indirect time-delay estimators are proposed. The indirect time-delay estimator considers the procedure of time-delay estimation as a nonlinear programming problem. On the other hand, the direct time-delay estimation scheme applies a neural network to construct a time-delay estimator to track the time-varying time-delay. Finally, a numerical example is considered for testing the proposed methods.
14
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Input constraints handling in an MPC/feedback linearization scheme

88%
Deng J., Becerra V., Stobart R.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 2
219-232
EN
The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.
15
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A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model

88%
Rodriguez-Alfaro L., Alcorta-Garcia E., Lara D., Romero G.
International Journal of Applied Mathematics and Computer Science
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2015
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tom 25
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nr 1
65-76
EN
The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
16
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Determining the weights of a Fourier series neural network on the basis of the multidimensional discrete Fourier transform

88%
Halawa K.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 3
369-375
EN
This paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.
17
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Integrated design of observer based fault detection for a class of uncertain nonlinear systems

88%
Chen W., Khan A., Abid M., Ding S.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 3
423-430
EN
Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the proposed design method.
18
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Soft computing in modelbased predictive control footnotemark

88%
Tatjewski P., Ławrynczuk M.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 1
7-26
EN
The application of fuzzy reasoning techniques and neural network structures to model-based predictive control (MPC) is studied. First, basic structures of MPC algorithms are reviewed. Then, applications of fuzzy systems of the Takagi-Sugeno type in explicit and numerical nonlinear MPC algorithms are presented. Next, many techniques using neural network modeling to improve structural or computational properties of MPC algorithms are presented and discussed, from a neural network model of a process in standard MPC structures to modeling parts or entire MPC controllers with neural networks. Finally, a simulation example and conclusions are given.
19
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Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems

88%
Tong S., Liu C., Li Y.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 4
637-653
EN
In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.
20
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Controllability of nonlinear discrete systems

88%
Klamka J.
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
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.
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