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1
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Numerical analysis and systems theory

100%
Campbell S. L.
International Journal of Applied Mathematics and Computer Science
|
2001
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tom 11
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nr 5
1025-1033
EN
The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. This paper will briefly discuss some of these areas of interaction and place the papers in this volume in context.
2
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Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems

100%
Dulęba I., Jagodziński J.
International Journal of Applied Mathematics and Computer Science
|
2011
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tom 21
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nr 3
525-534
EN
In this paper, an extension of the Lafferriere-Sussmann algorithm of motion planning for driftless nilpotent control systems is analyzed. It is aimed at making more numerous admissible representations of motion in the algorithm. The representations allow designing a shape of trajectories joining the initial and final configuration of the motion planning task. This feature is especially important in motion planning in a cluttered environment. Some natural functions are introduced to measure the shape of a trajectory in the configuration space and to evaluate trajectories corresponding to different representations of motion.
3
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How to compensate a spreading disturbance for a class of nonlinear systems

88%
Qaraai Y., Bernoussi A., El Jai A.
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
171-187
EN
We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.
4
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On the constrained controllability of dynamical systems with multiple delays in the state

88%
Sikora B.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
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nr 4
469-479
EN
Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types of constraints are considered. Numerical examples illustrate the theoretical analysis. An example of a real technical dynamical system is given to indicate one of possible practical applications of the theoretical results.
5
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Enlarged exact compensation in distributed systems

88%
Afifi L., Chafiai A., Fekih A. B.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 4
467-477
EN
In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study the relationship between the notion of remediability, introduced in previous works, and that of enlarged exact remediability.
6
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Construction of sampling and interpolating sequences for multi-band signals. the two-band case

75%
Avdonin S., Bulanova A., Moran W.
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
143-156
EN
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
7
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Imitation learning of car driving skills with decision trees and random forests

63%
Cichosz P., Pawełczak Ł.
International Journal of Applied Mathematics and Computer Science
|
2014
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tom 24
|
nr 3
579-597
EN
Machine learning is an appealing and useful approach to creating vehicle control algorithms, both for simulated and real vehicles. One common learning scenario that is often possible to apply is learning by imitation, in which the behavior of an exemplary driver provides training instances for a supervised learning algorithm. This article follows this approach in the domain of simulated car racing, using the TORCS simulator. In contrast to most prior work on imitation learning, a symbolic decision tree knowledge representation is adopted, which combines potentially high accuracy with human readability, an advantage that can be important in many applications. Decision trees are demonstrated to be capable of representing high quality control models, reaching the performance level of sophisticated pre-designed algorithms. This is achieved by enhancing the basic imitation learning scenario to include active retraining, automatically triggered on control failures. It is also demonstrated how better stability and generalization can be achieved by sacrificing human-readability and using decision tree model ensembles. The methodology for learning control models contributed by this article can be hopefully applied to solve real-world control tasks, as well as to develop video game bots.
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