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This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system's state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

Robust face clustering enjoys a wide range of applications for gate passes, surveillance systems and security analysis in embedded sensors. Nevertheless, existing algorithms have limitations in finding accurate clusters when data contain noise (e.g., occluded face clustering and recognition). It is known that in subspace clustering, the ℓ 1 - and ℓ 2 -norm regularizers can improve subspace preservation and connectivity, respectively, and the elastic net regularizer (i.e., the mixture of the ℓ 1 - and ℓ 2 -norms) provides a balance between the two properties. However, existing deterministic methods have high per iteration computational complexities, making them inapplicable to large-scale problems. To address this issue, this paper proposes the first accelerated stochastic variance reduction gradient (RASVRG) algorithm for robust subspace clustering. We also introduce a new momentum acceleration technique for the RASVRG algorithm. As a result of the involvement of this momentum, the RASVRG algorithm achieves both the best oracle complexity and the fastest convergence rate, and it reaches higher efficiency in practice for both strongly convex and not strongly convex models. Various experimental results show that the RASVRG algorithm outperformed existing state-of-the-art methods with elastic net and ℓ 1 -norm regularizers in terms of accuracy in most cases. As demonstrated on real-world face datasets with different manually added levels of pixel corruption and occlusion situations, the RASVRG algorithm achieved much better performance in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

In recent years, a series of matching pursuit and hard thresholding algorithms have been proposed to solve the sparse representation problem with ℓ 0 -norm constraint. In addition, some stochastic hard thresholding methods were also proposed, such as stochastic gradient hard thresholding (SG-HT) and stochastic variance reduced gradient hard thresholding (SVRGHT). However, each iteration of all the algorithms requires one hard thresholding operation, which leads to a high per-iteration complexity and slow convergence, especially for high-dimensional problems. To address this issue, we propose a new stochastic recursive gradient support pursuit (SRGSP) algorithm, in which only one hard thresholding operation is required in each outer-iteration. Thus, SRGSP has a significantly lower computational complexity than existing methods such as SG-HT and SVRGHT. Moreover, we also provide the convergence analysis of SRGSP, which shows that SRGSP attains a linear convergence rate. Our experimental results on large-scale synthetic and real-world datasets verify that SRGSP outperforms state-of-the-art related methods for tackling various sparse representation problems. Moreover, we conduct many experiments on two real-world sparse representation applications such as image denoising and face recognition, and all the results also validate that our SRGSP algorithm obtains much better performance than other sparse representation learning optimization methods in terms of PSNR and recognition rates. [ABSTRACT FROM AUTHOR]

A demand side management technique is deployed along with battery energy-storage systems (BESS) to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study, we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand. [ABSTRACT FROM AUTHOR]