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1
Content available remote

Servo tracking of targets at sea

100%
Ahmed A., Brdys M.
International Journal of Applied Mathematics and Computer Science
|
2006
|
tom 16
|
nr 2
197-207
EN
This paper details a proposal for the position control system of a two-axis ship-mounted tracker. Aspects of the non-linear dynamics governing Line-Of-Sight (LOS) errors between the tracker and the target are presented. It is shown that the regulation of LOS errors can be achieved by introducing a feed-forward term based on the target's velocity. This velocity is not measurable, and an estimator is required. Given that the tracking problem is non-linear, the classical separation principle does not hold, and cascading the estimator and regulator together may not lead to an optimal position control system. The 'LQAdaptive' system proposed here aims therefore to improve conformity to the separation principle. Simulation trials show that tracking is improved under the LQAdaptive system in comparison to a simple estimator-regulator structure.
2
Content available remote

On adaptive control for the continuous time-varying JLQG problem

100%
Czornik A., Świernik A.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 1
53-62
EN
In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated through strongly consistent estimators.
3
Content available remote

Neural network-based NARX models in non-linear adaptive control

100%
Dzieliński A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
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.
4
Content available remote

On adaptive control of Markov chains using nonparametric estimation

100%
Drabik E., Stettner Ł.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 2
143-152
EN
Two adaptive procedures for controlled Markov chains which are based on a nonparametric window estimation are shown.
5
Content available remote

Adaptive control of discrete time Markov processes by the large deviations method

100%
Duncan T. E., Pasik-Duncan B., Stettner Ł.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 3
265-285
EN
Some discrete time controlled Markov processes in a locally compact metric space whose transition operators depend on an unknown parameter are described. The adaptive controls are constructed using the large deviations of empirical distributions which are uniform in the parameter that takes values in a compact set. The adaptive procedure uses a finite family of continuous, almost optimal controls. Using the large deviations property it is shown that an adaptive control which is a fixed almost optimal control after a finite time is almost optimal with probability nearly 1.
6
Content available remote

A generalization of Ueno's inequality for n-step transition probabilities

100%
Nowak A. S.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 3
295-299
EN
We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.
7
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.
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
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2012
|
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
Content available remote

Recursive self-tuning control of finite Markov chains

88%
Borkar V. S.
Applicationes Mathematicae
|
1996-1997
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tom 24
|
nr 2
169-188
EN
A recursive self-tuning control scheme for finite Markov chains is proposed wherein the unknown parameter is estimated by a stochastic approximation scheme for maximizing the log-likelihood function and the control is obtained via a relative value iteration algorithm. The analysis uses the asymptotic o.d.e.s associated with these.
10
Content available remote

Bayesian parameter estimation and adaptive control of Markov processes with time-averaged cost

88%
Borkar V. S., Mundra Associate S. M.
Applicationes Mathematicae
|
1998-1999
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tom 25
|
nr 3
339-358
EN
This paper considers Bayesian parameter estimation and an associated adaptive control scheme for controlled Markov chains and diffusions with time-averaged cost. Asymptotic behaviour of the posterior law of the parameter given the observed trajectory is analyzed. This analysis suggests a "cost-biased" estimation scheme and associated self-tuning adaptive control. This is shown to be asymptotically optimal in the almost sure sense.
11
Content available remote

Discrete-time predictive control with overparameterized delay-plant models and an identified cancellation order

75%
Kowalczuk Z., Suchomski P.
International Journal of Applied Mathematics and Computer Science
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2005
|
tom 15
|
nr 1
5-34
EN
The paper presents several solutions to the discrete-time generalized predictive (GPC) controller problem, including an anticipative filtration mechanism, which are suitable for plants with nonzero transportation delays. Necessary modifications of the GPC design procedure required for controlling plants based on their non-minimal models are discussed in detail. Although inevitably invoking the troublesome pole-zero cancellation problem, such models can be used in adaptive systems as a remedy for the uncertainty or variability of the model order. The purpose of this paper is to present a complete GPC controller design for delay plants that is robust to the overparameterization of the plant model. Refined conditions for the existence and stability of GPC control solutions in terms of pertinent design parameters are given, and explicit forms of closed-loop characteristic polynomials are provided. The issue of identifying the model cancellation order is also considered, and practical solutions are proposed. The presented ideas are illustrated numerically.
12
Content available remote

Motor control neural models and systems theory

75%
Doya K., Kimura H., Miyamura A.
International Journal of Applied Mathematics and Computer Science
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2001
|
tom 11
|
nr 1
77-104
EN
In this paper, we introduce several system theoretic problems brought forward by recent studies on neural models of motor control. We focus our attention on three topics: (i) the cerebellum and adaptive control, (ii) reinforcement learning and the basal ganglia, and (iii) modular control with multiple models. We discuss these subjects from both neuroscience and systems theory viewpoints with the aim of promoting interplay between the two research communities.
13
Content available remote

On adaptive control of a partially observed Markov chain

75%
Di Masi G. B., Stettner Ł.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 2
165-180
EN
A control problem for a partially observable Markov chain depending on a parameter with long run average cost is studied. Using uniform ergodicity arguments it is shown that, for values of the parameter varying in a compact set, it is possible to consider only a finite number of nearly optimal controls based on the values of actually computable approximate filters. This leads to an algorithm that guarantees nearly selfoptimizing properties without identifiability conditions. The algorithm is based on probing control, whose cost is additionally assumed to be periodically observable.
14

Adaptive control for sequential design

63%
Gautier R., Pronzato L.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 1
97-114
EN
The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure. Several sequential schemes, corresponding to different control policies, are considered. The optimal one corresponds to closed-loop control, and is solution of a stochastic dynamic-programming problem, which is extremely difficult to solve. A suboptimal strategy is proposed, which relies ona normal approximation of the future posterior of θ, independent of future observations. The design criterion obtained involves several mathematical expectations, which are approximated by Laplace method. Finally, stochastic approximation algorithms are also suggested to determine (sub)optimal sequential experiments without having to compute expectations.
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