The distributed AC microgrid (MG) voltage restoration problem has been extensively studied. Still, many existing secondary voltage control strategies neglect the co-regulation of the voltage at the point of common coupling (PCC) in the AC multi-MG system (MMS). When an MMS consists of sub-MGs connected in series, power flow between the sub-MGs is not possible if the PCC voltage regulation relies on traditional consensus control objectives. In addition, communication faults and sensor faults are inevitable in the MMS. Therefore, a resilient voltage regulation strategy based on containment control is proposed. First, the feedback linearization technique allows us to deal with the nonlinear distributed generation (DG) dynamics, where the PCC regulation problem of an AC MG is transformed into an output feedback tracking problem for a linear multi-agent system (MAS) containing nonlinear dynamics. This process is an indispensable pre-processing in control algorithm design. Moreover, considering the unavailability of full-state measurements and the potential faults present in the sensors, a novel follower observer is designed to handle communication faults. Based on this, a controller based on containment control is designed to achieve voltage regulation. In regulating multiple PCC voltages to a reasonable upper and lower limit, a voltage difference exists between sub-MGs to achieve power flow. In addition, the secondary control algorithm avoids using global information of directed communication network and fault boundaries for communication link and sensor faults. Finally, the simulation results verify the performance of the proposed strategy.

In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown external disturbances. A safety protection algorithm is proposed to keep the constrained states within the given safe-set. A second-order disturbance observer technique is utilized to estimate the external disturbances. It is shown that the desired tracking performance of the controlled unmanned helicopter can be achieved with the application of the backstepping approach, dynamic surface control technique, and Lyapunov method. Finally, the availability of the proposed control scheme has been shown by simulation results.

This paper studies a novel distributed optimization problem that aims to minimize the sum of the non-convex objective functionals of the multi-agent network under privacy protection, which means that the local objective of each agent is unknown to others. The above problem involves complexity simultaneously in the time and space aspects. Yet existing works about distributed optimization mainly consider privacy protection in the space aspect where the decision variable is a vector with finite dimensions. In contrast, when the time aspect is considered in this paper, the decision variable is a continuous function concerning time. Hence, the minimization of the overall functional belongs to the calculus of variations. Traditional works usually aim to seek the optimal decision function. Due to privacy protection and non-convexity, the Euler-Lagrange equation of the proposed problem is a complicated partial differential equation. Hence, we seek the optimal decision derivative function rather than the decision function. This manner can be regarded as seeking the control input for an optimal control problem, for which we propose a centralized reinforcement learning (RL) framework. In the space aspect, we further present a distributed reinforcement learning framework to deal with the impact of privacy protection. Finally, rigorous theoretical analysis and simulation validate the effectiveness of our framework.

With the popularity of online learning in educational settings, knowledge tracing (KT) plays an increasingly significant role. The task of KT is to help students learn more effectively by predicting their next mastery of knowledge based on their historical exercise sequences. Nowadays, many related works have emerged in this field, such as Bayesian knowledge tracing and deep knowledge tracing methods. Despite the progress that has been made in KT, existing techniques still have the following limitations: 1) Previous studies address KT by only exploring the observational sparsity data distribution, and the counterfactual data distribution has been largely ignored. 2) Current works designed for KT only consider either the entity relationships between questions and concepts, or the relations between two concepts, and none of them investigates the relations among students, questions, and concepts, simultaneously, leading to inaccurate student modeling. To address the above limitations, we propose a graph counterfactual augmentation method for knowledge tracing. Concretely, to consider the multiple relationships among different entities, we first uniform students, questions, and concepts in graphs, and then leverage a heterogeneous graph convolutional network to conduct representation learning. To model the counterfactual world, we conduct counterfactual transformations on students’ learning graphs by changing the corresponding treatments and then exploit the counterfactual outcomes in a contrastive learning framework. We conduct extensive experiments on three real-world datasets, and the experimental results demonstrate the superiority of our proposed GraphCA method compared with several state-of-the-art baselines.

The grinding and classification process is one of the key sub-processes in mineral processing, which influences the final process indexes significantly and determines energy and ball consumption of the whole plant. Therefore, optimal control of the process has been very important in practice. In order to stabilize the grinding index and improve grinding capacity in the process, a process model based on population balance model (PBM) is calibrated in this study. The correlation between the mill power and the operating variables in the grinding process is modelled by using the response surface method (RSM), which solves the problem where the traditional power modeling method relies on some unobservable mechanism-related parameters. On this basis, a multi-objective optimization model is established to maximize the useful power of the grinding circuit to improve the throughput of the grinding operation and improve the fraction of –0.074 mm particles in the hydrocyclone overflow to smooth the subsequent flotation operation. The elite non-dominated sorting genetic algorithm-II (NSGA-II) is then employed to solve the multi-objective optimization problem. Finally, subjective and objective weighting methods and integrated multi-attribute decision-making methods are used to select the optimal solution on the Pareto optimal solution set. The results demonstrate that the throughput of the mill and the fraction of –0.074 mm particles in the overflow of the cyclone are increased by 3.83 t/h and 2.53%, respectively.

Plug-and-play priors are popular for solving ill-posed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-and-play priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual, which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering (BM3D) denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging (CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.