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1
Content available remote

Data probes, vertical trajectories and classification: a tentative study

100%
Pearson D. W.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 1
107-112
EN
In this paper we introduce a method of classification based on data probes. Data points are considered as point masses in space and a probe is simply a particle that is launched into the space. As the probe passes by data clusters, its trajectory will be influenced by the point masses. We use this information to help us to find vertical trajectories. These are trajectories in the input space that are mapped onto the same value in the output space and correspond to the data classes.
2
Content available remote

Nonlinear controller design of a ship autopilot

100%
Tomera M.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 2
271-280
EN
The main goal here is to design a proper and efficient controller for a ship autopilot based on the sliding mode control method. A hydrodynamic numerical model of CyberShip II including wave effects is applied to simulate the ship autopilot system by using time domain analysis. To compare the results similar research was conducted with the PD controller, which was adapted to the autopilot system. The differences in simulation results between two controllers are analyzed by a cost function composed of a heading angle error and rudder deflection either in calm water or in waves. Simulation results show the effectiveness of the method in the presence of nonlinearities and disturbances, and high performance of the proposed controller.
3
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Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions

100%
Armaou A., Christofides P. D.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 2
287-317
EN
This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is constructed by computing and solving a high-order discretization of the PDE. Then, the Karhunen-Loaève expansion is directly applied to the ensemble of solutions to derive a small set of empirical eigenfunctions (dominant spatial patterns) that capture almost all the energy of the ensemble of solutions. The empirical eigenfunctions are subsequently used as basis functions within a Galerkin model reduction framework to derive low-order ordinary differential equation (ODE) systems that accurately describe the dominant dynamics of the PDE system. The ODE systems are subsequently used for the synthesis of nonlinear output feedback controllers using geometric control methods. The proposed control method is used to stabilize an unstable steady-state of a diffusion-reaction process with nonlinearities, spatially-varying coefficients and time-dependent spatial domain, and is shown to lead to the construction of accurate low-order models and the synthesis of low-order controllers. The performance of the low-order models and controllers is successfully tested through computer simulations.
4
Content available remote

Global linearization of nonlinear systems - A survey

100%
Čelikovský S.
Banach Center Publications
|
1995
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tom 32
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nr 1
123-137
EN
A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.
5
Content available remote

Modeling and control of induction motors

88%
Delaleau E., Louis J.-P., Ortega R.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 1
105-129
EN
This paper is devoted to the modeling and control of the induction motor. The well-established field oriented control is recalled and two recent control strategies are exposed, namely the passivity-based control and the flatness-based control.
6
Content available remote

An adaptive output feedback motion tracking controller for robot manipulators: uniform global asymptotic stability and experimentation

88%
Yarza A., Santibanez V., Moreno-Valenzuela J.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 3
599-611
EN
This paper deals with two important practical problems in motion control of robot manipulators: the measurement of joint velocities, which often results in noisy signals, and the uncertainty of parameters of the dynamic model. Adaptive output feedback controllers have been proposed in the literature in order to deal with these problems. In this paper, we prove for the first time that Uniform Global Asymptotic Stability (UGAS) can be obtained from an adaptive output feedback tracking controller, if the reference trajectory is selected in such a way that the regression matrix is persistently exciting. The new scheme has been experimentally implemented with the aim of confirming the theoretical results.
7
Content available remote

A backstepping approach to ship course control

88%
Witkowska A., Tomera M., Smierzchalski R.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
|
nr 1
73-85
EN
As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear control structures are tuned to optimise the operation of the control system. The optimisation is performed using genetic algorithms. The quality of operation of the designed control algorithms is checked in simulation tests performed on the mathematical model of a tanker. In order to obtain reference results to be used for comparison with those recorded for nonlinear controllers designed using the backstepping method, a control system with the PD controller is examined as well.
8
Content available remote

Designing a ship course controller by applying the adaptive backstepping method

88%
Witkowska A., Śmierzchalski R.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
|
nr 4
985-997
EN
The article discusses the problem of designing a proper and efficient adaptive course-keeping control system for a seagoing ship based on the adaptive backstepping method. The proposed controller in the design stage takes into account the dynamic properties of the steering gear and the full nonlinear static maneuvering characteristic. The adjustable parameters of the achieved nonlinear control structure were tuned up by using the genetic algorithm in order to optimize the system performance. A realistic full-scale simulation model of the B-481 type vessel including wave and wind effects was applied to simulate the control algorithm by using time domain analysis.
9
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A novel method for the design of switching surfaces for discretized MIMO nonlinear systems

88%
Luis-Delgado J., Al-Hadithi B., Jiménez A.
International Journal of Applied Mathematics and Computer Science
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2017
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tom 27
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nr 1
5-17
EN
Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.
10
Content available remote

Supervisory predictive control and on-line set-point optimization

75%
Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 3
483-495
EN
The subject of this paper is to discuss selected effective known and novel structures for advanced process control and optimization. The role and techniques of model-based predictive control (MPC) in a supervisory (advanced) control layer are first shortly discussed. The emphasis is put on algorithm efficiency for nonlinear processes and on treating uncertainty in process models, with two solutions presented: the structure of nonlinear prediction and successive linearizations for nonlinear control, and a novel algorithm based on fast model selection to cope with process uncertainty. Issues of cooperation between MPC algorithms and on-line steady-state set-point optimization are next discussed, including integrated approaches. Finally, a recently developed two-purpose supervisory predictive set-point optimizer is discussed, designed to perform simultaneously two goals: economic optimization and constraints handling for the underlying unconstrained direct controllers.
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