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## Mathematical Foundations of Computing

May 2020 , Volume 3 , Issue 2

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**Abstract:**

The paradigm of compressed sensing is to exactly or stably recover any sparse signal

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**Abstract:**

This research work proposes a novel triple mode sliding mode controller for a nonlinear system with measurement noise and uncertainty. The proposed control has the following goals (1) it ensures the transient and steady state robustness of the system in closed loop (2) it reduces chattering in the control signal with measurement noise. Fuzzy system is used to tune the appropriate order of the fractional operators for the proposed control system. Depending on the tuned range of the fractional operators, the proposed controller can operate effectively in the following three modes (1) classical sliding mode (SMC) (2) fractional order sliding mode (FSMC) (3) Integral sliding mode control (ISMC). With the noisy feedback, the performance of the classical SMC and SMC with boundary layer degrades significantly while ISMC shows better performance. However ISMC exhibits large transient overshoots.The proposed control method optimally selects the appropriate mode of the controller to ensure performance(transient and steady state) and suppresses the effect of noisy feedback. The proposed scheme is derived for the permanent magnet synchronous motor, s (PMSM) speed regulation problem which is subject to uncertainties, measurement noise and un-modeled dynamics as a case study. The effectiveness of proposed scheme is verified using numerical simulations.

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**Abstract:**

Recently, some weighted Durrmeyer type operators were used as research tools in Learning Theory. In this paper we introduce a class of multidimensional weighted Kantorovich operators

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**Abstract:**

Many moving-camera video processing and analysis tasks require accurate estimation of homography across frames. Estimating homography between non-adjacent frames can be very challenging when their camera view angles show large difference. In this paper, we propose a new deep-learning based method for homography estimation along videos by exploiting temporal dynamics across frames. More specifically, we develop a recurrent convolutional regression network consisting of convolutional neural network (CNN) and recurrent neural network (RNN) with long short-term memory (LSTM) cells, followed by a regression layer for estimating the parameters of homography. In the experiments, we evaluate the proposed method on both the synthesized and real-world short videos. The experimental results verify that the proposed method can estimate the homographies along short videos better than several existing methods.

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