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mathematical complexity of running filters on semi-groups and related problems

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第7期56卷 3191-3197页

作者： Coltuc, Dinu Valahia Univ Targoviste Dept Elect Engn Bucharest Romania INP GIPSA Lab Grenoble France

This paper proves that the mathematical complexity of running filters on semi-groups is C(p) = 3 - (6/(p + 1)) operations per sample, where p is the filter window. On other algebraic structures, the mathematical complexity of the filtering can be lower. Two such cases are investigated: the running filtering on max/min lattice and on additions group. They correspond to max/min and moving average filters. It is shown that the algorithms developed for semi-groups are of interest in such cases, too. Thus, the fastest deterministic algorithm for max/min filtering known so far is based on an algorithm for running filtering on semi-groups. First, an optimized version is proposed in this paper. Then, further improvement for data-dependent max/min algorithms is proposed. Finally, the case of moving average and exponential smoothing is investigated. Their implementation by using the algorithms for semi-groups is of lower complexity than the classical recursive implementation for the particular case of small size windows (p = 3 and p = 4).

关键词： fast algorithms fast max/min filters fast moving average mathematical complexity optimal algorithms

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Improvement of dynamic performance of doubly fed induction generator-based wind turbine power system under an unbalanced grid voltage condition

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IET RENEWABLE POWER GENERATION 2012年第6期6卷 424-434页

作者： Mwasilu, F. Justo, J. J. Ro, K. -S. Jung, J. -W. Dongguk Univ Seoul Div Elect & Elect Engn Seoul 100715 South Korea

With the current increase in wind power penetration into the energy market, control and operation of wind turbine generators becomes a major research topic. Wind turbine based on doubly fed induction generator (DFIG), which is sensitive to grid disturbances, is widely used. Under an unbalanced grid voltage condition, oscillations of the DFIG's electromagnetic torque and instantaneous stator powers strongly affect the dynamic performance of the DFIG. In this study, a new configuration based on vector proportional-integral (VPI) controller is proposed to eliminate such oscillations. This new configuration is employed in the rotor side converter (RSC) of the DFIG. With the proposed VPI control strategy, decomposition of sequential components and mathematical complexity are reduced. Compared with the conventional field-oriented control based on the standard single PI controller, the VPI controller can successfully eliminate torque and stator power oscillations. The effectiveness of the proposed control strategy is validated through simulation results obtained on a 1.5 MW DFIG-based wind turbine system model built in MATLAB/Simulink.

关键词： DFIG vector proportional integral controller Control of electric power systems unbalanced grid voltage VPI controller power 1.5 MW energy market torque power oscillations Wind power plants wind turbines grid disturbances electromagnetic torque Power system control power markets MATLAB/Simulink field-oriented control doubly fed induction generator rotor side converter asynchronous generators Power system management, operation and economics power system control power convertors wind turbine power system torque Power convertors and power supplies to apparatus stators sequential components decomposition mathematical complexity power system simulation Asynchronous machines wind turbine generators instantaneous stator powers rotors wind turbine system model stator power oscillations

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A Jet Space Approach to Derive Flat Outputs

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IFAC-PapersOnLine 2015年第11 11期48卷 131-136页

作者： Schlacher, K. Schöberl, M. Kolar, B. Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz 4040 Austria

This contribution uses the representation of control systems, given by a set of ODEs, as distributions on certain jet manifolds. It is shown, there exists a sequence of systems of decreasing size, such that the system is flat, if the last system is trivial, and is not flat otherwise. Although the size decreases, these systems are defined on higher order jet spaces. We present an algorithm to construct the elements of the sequence, as well as the suitable jet spaces. Their construction uses a certain property of flat systems, which allows us to construct a simpler system. In addition normalized representations are used, to keep the mathematical complexity as small as possible. It is worth mentioning, that the presented approach degenerates to the well known one for input to state linearizable systems by static feedback. Finally, the application of the algorithm to three examples, all are not input to state linearizable by static feedback, is shown. © 2015

关键词： Fighter aircraft Feedback Geometry As distribution Cauchy Characteristics Differential geometry Flat systems Linearizable systems mathematical complexity Static feedback Symmetries

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Social Heteronomy and Contrasting Economic Epistemology a mathematical Approach

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Procedia - Social and Behavioral Sciences 2014年 140卷 27-36页

作者： Masudul Alam Choudhury Masudul Alam Choudhury Professorial Chair of Islamic Finance Institute of Islamic Banking and Finance International Islamic University Malaysia Kuala Lumpur Malaysia

An original socio-scientific theory is developed out of a contrast with the rationalist paradigm. This new worldview arises from the epistemology of unity of knowledge and its functional ontological implication of unity of the world-system. The Kantian epistemological meaning of heteronomy is shown to be one of the permanent socio-scientific problems of rationalism. The methodology is of the topological mathematical nature by virtue of the complex problem that inheres in the criticism of Kantian heteronomy and rationalism. The emergence of the new epistemological worldview of unity of knowledge and the world-system is formalized. Several theoretical constructs and applications of the episteme of unity of knowledge are pointed out in diverse fields.

关键词： epistemology rationalism unity of knowledge mathematical complexity economics and finance

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