- Journal Details
- Format
- Journal
- eISSN
- 2083-8492
- ISSN
- 1641-876X
- First Published
- 05 Apr 2007
- Publication timeframe
- 4 times per year
- Languages
- English
Search
- Open Access
Design of unknown input fractional-order observers for fractional-order systems
Page range: 491 - 500
Abstract
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
Keywords
- fractional calculus
- fractional-order systems
- fractional-order observers
- existence condition
- linear matrix inequality
- unknown input
- stability
- Open Access
Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems
Page range: 501 - 506
Abstract
Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
Keywords
- Padé approximation
- fractional system
- linear positive system
- Open Access
A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets
Page range: 507 - 520
Abstract
A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewise- Lipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine.
Keywords
- Hammerstein system
- non-parametric recursive identification
- Haar orthogonal expansion
- convergence analysis
- numerical stability
- Open Access
Nonparametric instrumental variables for identification of block-oriented systems
Page range: 521 - 537
Abstract
A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence is analyzed. Also, the form of optimal instrumental variables is established and the method of their approximate generation is proposed. The idea of nonparametric generation of instrumental variables guarantees that the I.V. estimate is well defined, improves the behaviour of the least-squares method and allows reducing the estimation error. The method is simple in implementation and robust to the correlated noise.
Keywords
- system identification
- instrumental variables
- NARMAX system
- Hammerstein system
- Wiener system
- Lur’e system
- nonparametric methods
- Open Access
Nonlinear state observers and extended Kalman filters for battery systems
Page range: 539 - 556
Abstract
The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging.
The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.
Keywords
- observers
- state estimation
- Riccati equations
- extended Kalman filters
- parameter estimation
- Open Access
Robust nonlinear observer design for actuator fault detection in diesel engines
Page range: 557 - 569
Abstract
This paper is concerned with actuator fault detection in nonlinear systems in the presence of disturbances. A nonlinear unknown input observer is designed and the output estimation error is used as a residual for fault detection. To deal with the problem of high Lipschitz constants, a modified mean-value theorem is used to express the nonlinear error dynamics as a convex combination of known matrices with time-varying coefficients. Moreover, the disturbance attenuation is performed using a modified H∞ criterion. A sufficient condition for the existence of an unknown input observer is obtained using a linear matrix inequality formula, and the observer gains are obtained by solving the corresponding set of inequalities. The advantages of the proposed method are that no a priori assumption on the unknown input is required and that it can be applied to a large class of nonlinear systems. Performances of the proposed approach are shown through the application to a diesel engine model.
Keywords
- diesel engine
- fault diagnosis
- nonlinear unknown input observers
- LMI
- Open Access
A biochemical multi-species quality model of a drinking water distribution system for simulation and design
Page range: 571 - 585
Abstract
Drinking Water Distribution Systems (DWDSs) play a key role in sustainable development of modern society. They are classified as critical infrastructure systems. This imposes a large set of highly demanding requirements on the DWDS operation and requires dedicated algorithms for on-line monitoring and control to tackle related problems. Requirements on DWDS availability restrict the usability of the real plant in the design phase. Thus, a proper model is crucial. Within this paper a DWDS multi-species quality model for simulation and design is derived. The model is composed of multiple highly inter-connected modules which are introduced to represent chemical and biological species and (above all) their interactions. The chemical part includes the processes of chloramine decay with additional bromine catalysis and reaction with nitrogen compounds. The biological part consists of both heterotrophic and chemo-autotrophic bacteria species. The heterotrophic bacteria are assumed to consume assimilable organic carbon. Autotrophs are ammonia oxidizing bacteria and nitrite oxidizing bacteria species which are responsible for nitrification processes. Moreover, Disinfection By-Products (DBPs) are also considered. Two numerical examples illustrate the derived model’s behaviour in normal and disturbance operational states.
Keywords
- multi-species
- chloramine
- quality
- drinking water distribution system
- critical infrastructure system
- Open Access
Controlling a non-homogeneous Timoshenko beam with the aid of the torque
Page range: 587 - 598
Abstract
Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C0-continuous semigroups may be applied.
Keywords
- Timoshenko beam
- rotating beam control
- approximate control
- stabilizability
- Open Access
An adaptive output feedback motion tracking controller for robot manipulators: Uniform global asymptotic stability and experimentation
Page range: 599 - 611
Abstract
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.
Keywords
- adaptive control
- robot control
- nonlinear control
- output feedback
- Lyapunov UGAS stability
- Open Access
A fuzzy approach to option pricing in a Levy process setting
Page range: 613 - 622
Abstract
In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.
Keywords
- option pricing
- Levy processes
- minimal entropy martingale measure
- fuzzy sets
- Monte Carlo simulation
- Open Access
Epoch-incremental reinforcement learning algorithms
Page range: 623 - 635
Abstract
In this article, a new class of the epoch-incremental reinforcement learning algorithm is proposed. In the incremental mode, the fundamental TD(0) or TD(λ) algorithm is performed and an environment model is created. In the epoch mode, on the basis of the environment model, the distances of past-active states to the terminal state are computed. These distances and the reinforcement terminal state signal are used to improve the agent policy.
Keywords
- reinforcement learning
- epoch-incremental algorithm
- grid world
- Open Access
Parametric logarithmic type image processing for contrast based auto-focus in extreme lighting conditions
Page range: 637 - 648
Abstract
While most of state-of-the-art image processing techniques were built under the so-called classical linear image processing, an alternative that presents superior behavior for specific applications comes in the form of Logarithmic Type Image Processing (LTIP). This refers to mathematical models constructed for the representation and processing of gray tones images. In this paper we describe a general mathematical framework that allows extensions of these models by various means while preserving their mathematical properties. We propose a parametric extension of LTIP models and discuss its similarities with the human visual system. The usability of the proposed extension model is verified for an application of contrast based auto-focus in extreme lighting conditions. The closing property of the named models facilitates superior behavior when compared with state-of-the-art methods.
Keywords
- logarithmic image processing
- digital camera
- auto-focus
- Open Access
Pipelined language model construction for Polish speech recognition
Page range: 649 - 668
Abstract
The aim of works described in this article is to elaborate and experimentally evaluate a consistent method of Language Model (LM) construction for the sake of Polish speech recognition. In the proposed method we tried to take into account the features and specific problems experienced in practical applications of speech recognition in the Polish language, reach inflection, a loose word order and the tendency for short word deletion. The LM is created in five stages. Each successive stage takes the model prepared at the previous stage and modifies or extends it so as to improve its properties. At the first stage, typical methods of LM smoothing are used to create the initial model. Four most frequently used methods of LM construction are here. At the second stage the model is extended in order to take into account words indirectly co-occurring in the corpus. At the next stage, LM modifications are aimed at reduction of short word deletion errors, which occur frequently in Polish speech recognition. The fourth stage extends the model by insertion of words that were not observed in the corpus. Finally the model is modified so as to assure highly accurate recognition of very important utterances. The performance of the methods applied is tested in four language domains.
Keywords
- automatic speech recognition
- hidden Markov model
- adaptive language model
- Open Access
On a matching distance between rooted phylogenetic trees
Page range: 669 - 684
Abstract
The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs, the values of similarity between clusters are transformed to the final MC-score of the dissimilarity of trees. The analyzed properties give insight into the structure of the metric space generated by MC, its relations with the Matching Split (MS) distance of unrooted trees and asymptotic behavior of the expected distance between binary n-leaf trees selected uniformly in both MC and MS (Θ(n3/2)).
Keywords
- phylogenetic tree
- phylogenetic tree metric
- phylogenetic tree comparison
- matching cluster distance
- matching split distance
- Open Access
A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics
Page range: 685 - 695
Abstract
The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution and product theorem in the LCT domain derived by a representation transformation in quantum mechanics, which seems a convenient and concise method. It is compared with the existing convolution theorem for the LCT and is found to be a better and befitting proposition. Further, an application of filtering is presented by using the derived results.
Keywords
- linear canonical transform
- convolution and product theorem
- quantum mechanical representation