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1

Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces

Mabel Lizzy R., Balachandran K.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

123--133

EN

Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

2

Trajectory planning for kinematically redundant robots using jacobi matrix – an industrial implementation

Walther M., Sewohl A., Schlegel H., Neugebauer R.

Journal of Machine Engineering

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2017

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Vol. 17, No. 3

24--35

EN

The widespread use of robots in industry contributes significantly to high productivity. Serial 6-axis robots are used in large quantities, e.g. for assembly or welding. A current emerging trend is the use of robots for classic tasks of a machine tool like finishing of milled workpieces. For such applications, standard robots are usually extended by additional axes like linear axes or rotary tilting tables. Therefore, the overall system becomes kinematically redundant. To be able to calculate the axis quantities via inverse kinematics for a given path, additional degrees of freedom must be bound. In order to automatically and optimally consider the additional axis motion a method, using the pseudoinverse of the Jacobian matrix, is discussed. Due to the dependence of the Jacobi matrix on the robot's current joint position, numerical inaccuracies, which in turn reflect a path error, are inherent to this method. By feedback control of the path error, in the form of a classic control loop, the error can be reduced so that a practical implementation on industrial robot controller is possible. In the article possibilities for parameterisation of the algorithm as well as proof of stability of the closed loop are presented. The results obtained are verified by a concrete application.

3

Zastosowanie macierzy pseudo odwrotnej w metodach alokacji pędników układu dynamicznego pozycjonowania statku

Witkowska A.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2014

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Nr 40

145--148

PL

Układy kontroli alokacji pędników stanowią ważną część systemów dynamicznego pozycjonowania na statku. Określają one sygnały sterujące nastawami pędników, na podstawie uogólnionego wektora sił wzdłużnej, poprzecznej i momentu skręcającego, uzyskiwanych z prawa sterowania. W artykule przedstawiono wybrane algorytmy kontroli alokacji pędników, różniące się sposobem wyznaczania macierzy pseudo odwrotnej oraz algorytm bezpośredniej alokacji. Omówiono wpływ zastosowanych metod na wydajność ekonomiczną oraz jakość regulacji układu dynamicznego pozycjonowania statkiem

EN

Control allocation systems are an important part of the dynamic positioning of ships. They define the control signals based on generalized vector of forces longitudinal, transverse and torque derived from the control law. The article presents selected control allocation algorithms, based on different ways of determining the pseudo inverse matrix to optimize the operation of these devices, and discusses the economic efficiency and control quality of the dynamic positioning system.

4

Iterative Learning Control for Over-Determined, Under-Determined, and Ill-Conditioned Systems

Avrachenkov K. E., Longman R. W.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 1

113-122

EN

This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization technique is discussed for computing the pseudoinverse to handle numerical instability. It is shown that for over-determined systems, the minimum error is never reached by a repetition invariant learning controller unless one knows the system exactly. For discrete time uniquely determined systems it is indicated that the inverse is usually ill-conditioned, and hence an approximate inverse based on a pseudoinverse is appropriate, treating the system as over-determined. Using the structure of the system matrix, an enhanced Tikhonov regularization technique is developed which converges to zero tracking error. It is shown that the Tikhonov regularization is a form of linear quadratic ILC, and that the regularization approach solves the important practical problem of how to intelligently pick the weighting matrices in the quadratic cost. It is also shown how to use a modification of the Tikhonov-based quadratic cost in order to produce a frequency cutoff. This robustifies good learning transients, by reformulating the problem as an over-determined system.