Mechanical Engineering - Research Publications
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ItemA note on robustness of linear spatially distributed parameter systems and their numerical approximations(IEEE, 2007-01-01)In this paper, we investigate a relationship between robust stability properties of linear spatially distributed parameter systems (LSDPS) with disturbances and robust stability properties of their numerical approximations. Since it is hard to analytically find solutions of a partial differential equation, numerical methods, such as finite-difference methods, are always used to approximately find the solutions. Moreover, it is crucial that the numerical method reproduces (approximately) the behavior of the actual system model. For instance, if the actual system is stable in some sense, then the numerical method should possess (approximately) the same stability property and vice versa. Our results show that input-to-state exponential stability (ISES) properties of the numerical approximation with respect to disturbances are equivalent to practical ISES of the LSDPS provided that: (i) the finite-difference approximation is consistent with the model; (ii) an appropriate uniform boundedness condition holds for the numerical method. Our results can be regarded as an extension of the celebrated Lax-Richtmyer theorem to systems with disturbances, as well as its application to analysis of ISES. This question is typically not considered in the numerical analysis literature and yet it is very well noticed by in control applications.
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ItemA trajectory based approach for robust stability properties of infinite-dimensional systems(International Federation of Automatic Control (IFAC), 2007-01-01)In this paper, we present a trajectory based approach to discuss the robustness of parameterized families of systems with disturbances with respect to arbitrary closed sets in a normed space. Input-to-state stability (ISS) properties are discussed. Our results are applicable to infinite-dimensional systems with disturbances.
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ItemOn automatic seeking of optimal steady-states in biochemical processes(IFAC, 2007-01-01)It is discussed how the automatic seeking of optimal steady states biochemical reactors can be achieved by using non-model based extremum-seeking control with semi-global practical stability and convergence properties. A special attention is paid to processes with multiple steady-states and multivalued cost functions.
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ItemOn global extremum seeking in the presence of local extrema(IEEE, 2006-01-01)We analyze global extremum seeking in the presence of local extrema for static nonlinear maps controlled by a scalar extremum seeking scheme that was recently proposed in [1]. Sufficient conditions are given under which it is possible to tune the controller parameters to achieve convergence to an arbitrarily small neighborhood of the global extremum in the presence of local extrema from an arbitrarily large set of initial conditions. Several examples provide insights and highlight the potential difficulties that one would face when trying to generalize our results.
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ItemOn the choice of dither in extremum seeking systems: A case study(IEEE, 2006-01-01)We discuss how the dither (excitation signal) shape affects on the performance of extremum seeking using a benchmark situation: a static scalar map; and a simple scalar extremum seeking scheme. Our comparisons are based on the performance of the system with different dithers in terms of three performance indicators: the speed of convergence, domain of attraction and accuracy (i.e. the ultimate bound on trajectories). Our analysis explicitly shows how the dither shape affects each of these performance indicators. Our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter. Computer simulations support our theoretical findings.
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ItemOn non-local stability properties of extrernum seeking control(PERGAMON-ELSEVIER SCIENCE LTD, 2006-06-01)In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.
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ItemGait analysis methods in rehabilitation(BMC, 2006-03-02)INTRODUCTION: Brand's four reasons for clinical tests and his analysis of the characteristics of valid biomechanical tests for use in orthopaedics are taken as a basis for determining what methodologies are required for gait analysis in a clinical rehabilitation context. MEASUREMENT METHODS IN CLINICAL GAIT ANALYSIS: The state of the art of optical systems capable of measuring the positions of retro-reflective markers placed on the skin is sufficiently advanced that they are probably no longer a significant source of error in clinical gait analysis. Determining the anthropometry of the subject and compensating for soft tissue movement in relation to the under-lying bones are now the principal problems. Techniques for using functional tests to determine joint centres and axes of rotation are starting to be used successfully. Probably the last great challenge for optical systems is in using computational techniques to compensate for soft tissue measurements. In the long term future it is possible that direct imaging of bones and joints in three dimensions (using MRI or fluoroscopy) may replace marker based systems. METHODS FOR INTERPRETING GAIT ANALYSIS DATA: There is still not an accepted general theory of why we walk the way we do. In the absence of this, many explanations of walking address the mechanisms by which specific movements are achieved by particular muscles. A whole new methodology is developing to determine the functions of individual muscles. This needs further development and validation. A particular requirement is for subject specific models incorporating 3-dimensional imaging data of the musculo-skeletal anatomy with kinematic and kinetic data. METHODS FOR UNDERSTANDING THE EFFECTS OF INTERVENTION: Clinical gait analysis is extremely limited if it does not allow clinicians to choose between alternative possible interventions or to predict outcomes. This can be achieved either by rigorously planned clinical trials or using theoretical models. The evidence base is generally poor partly because of the limited number of prospective clinical trials that have been completed and more such studies are essential. Very recent work has started to show the potential of using models of the mechanisms by which people with pathology walk in order to simulate different potential interventions. The development of these models offers considerable promise for new clinical applications of gait analysis.
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ItemSplice site identification using probabilistic parameters and SVM classification(BioMed Central, 2006-12-18)BACKGROUND: Recent advances and automation in DNA sequencing technology has created a vast amount of DNA sequence data. This increasing growth of sequence data demands better and efficient analysis methods. Identifying genes in this newly accumulated data is an important issue in bioinformatics, and it requires the prediction of the complete gene structure. Accurate identification of splice sites in DNA sequences plays one of the central roles of gene structural prediction in eukaryotes. Effective detection of splice sites requires the knowledge of characteristics, dependencies, and relationship of nucleotides in the splice site surrounding region. A higher-order Markov model is generally regarded as a useful technique for modeling higher-order dependencies. However, their implementation requires estimating a large number of parameters, which is computationally expensive. RESULTS: The proposed method for splice site detection consists of two stages: a first order Markov model (MM1) is used in the first stage and a support vector machine (SVM) with polynomial kernel is used in the second stage. The MM1 serves as a pre-processing step for the SVM and takes DNA sequences as its input. It models the compositional features and dependencies of nucleotides in terms of probabilistic parameters around splice site regions. The probabilistic parameters are then fed into the SVM, which combines them nonlinearly to predict splice sites. When the proposed MM1-SVM model is compared with other existing standard splice site detection methods, it shows a superior performance in all the cases. CONCLUSION: We proposed an effective pre-processing scheme for the SVM and applied it for the identification of splice sites. This is a simple yet effective splice site detection method, which shows a better classification accuracy and computational speed than some other more complex methods.