The problem of pole configuration via periodic output feedback for linear discrete periodic systems with time-varying dimensions of states and input spaces is addressed. By some mathematical derivation, the considered problem can be reduced into solving a special Sylvester matrix equation from which the periodic output feedback gains can be separated and computed explicitly. Based on this, a detail parametric algorithm is presented, by which countless periodic output feedback gains can be generated by choosing different free parameter matrices. Furthermore, the proposed approach is used to achieve robustness performance and robust poles configuration algorithm is provided. Numerical examples are employed to illustrate the effectiveness of the proposed algorithms.
Facial expression recognition (FER) in uncontrolled environment is challenging due to various un-constrained conditions. Although existing deep learning-based FER approaches have been quite promising in recognizing frontal faces, they still struggle to accurately identify the facial expressions on the faces that are partly occluded in unconstrained scenarios. To mitigate this issue, we propose a transformer-based FER method (TFE) that is capable of adaptatively focusing on the most important and unoccluded facial regions. TFE is based on the multi-head self-attention mechanism that can flexibly attend to a sequence of image patches to encode the critical cues for FER. Compared with traditional transformer, the novelty of TFE is two-fold: (i) To effectively select the discriminative facial regions, we integrate all the attention weights in various transformer layers into an attention map to guide the network to perceive the important facial regions. (ii) Given an input occluded facial image, we use a decoder to reconstruct the corresponding non-occluded face. Thus, TFE is capable of inferring the occluded regions to better recognize the facial expressions. We evaluate the proposed TFE on the two prevalent in-the-wild facial expression datasets (AffectNet and RAF-DB) and the their modifications with artificial occlusions. Experimental results show that TFE improves the recognition accuracy on both the non-occluded faces and occluded faces. Compared with other state-of-the-art FE methods, TFE obtains consistent improvements. Visualization results show TFE is capable of automatically focusing on the discriminative and non-occluded facial regions for robust FER.
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