In microgrids, distributed load sharing plays an important role in maintaining the supply-demand balance of power. Because False Data Injection (FDI) is one of the crucial threats faced by future microgrids, the study of the impact of FDI on distributed load sharing is of both theoretical merit and practical value. In this paper, we consider the distributed load sharing problem of the microgrids operating in autonomous mode under FDI. Each bus is assumed to be equipped with an agent. Under a well developed distributed load sharing protocol based on multiagent systems, we first construct an FDI attack model, where the attacker is capable of injecting false data into the bus agents. Then, a utilization level is introduced for coordinating generators and its variation is evaluated in the presence of FDI attacks with given injection strategies. The stable region of the microgrid is defined and conditions are given to determine stability. Finally, the theoretical results are validated on the Canadian urban distribution system.

The tracking control of a wastewater treatment process (WWTP) is considered. The process is highly nonlinear, with strong coupling, difficult to model mathematically, and the operation is subject to unknown disturbances. We address this multivariable tracking control problem by applying the direct heuristic dynamic programming (dHDP)-based reinforcement learning control. The control goal is to track a desired reference of the dissolved oxygen (DO) concentration of the 5th aerobic zone ( $S_{O5}$ ) and nitrate concentration of the 2nd anoxic zone ( $S_{NO2}$ ) by manipulating the oxygen transfer coefficient of the 5th aerobic zone ( $K_{L}a_{5}$ ) and internal recycle flow rate ( $Q_{a}$ ). The dHDP aims at achieving a minimal accumulated WWTP tracking error while dealing with strong coupling between the $S_{O5}$ and $S_{NO2}$ and eliminating unknown disturbances in the process. The proposed dHDP approach devises an optimal control strategy entirely driven by WWTP process data as an online learning control method. We have conducted extensive and systematic simulations based on the well-known BSM1 platform of the WWTP controlled by dHDP to compare and contrast performances with other methods.

For pure-feedback nonlinear systems under asymmetric output constraint, we present a low-cost neuroadaptive tracking control solution with salient features benefited from two design steps. In the first step, a novel output-dependent universal barrier function (ODUBF) is constructed such that not only the restrictive condition on constraining boundaries/functions is removed but also both constrained and unconstrained cases can be handled uniformly without the need for changing the control structure. In the second step, to reduce the computational burden caused by the neural network (NN)-based approximators, a single parameter estimator is developed so that the number of adaptive law is independent of the system order and the dimension of system parameters, making the control design inexpensive in computation. Furthermore, it is shown that all signals in the closed-loop system are semiglobally uniformly ultimately bounded, the tracking error converges to an adjustable neighborhood of the origin, and the violation of output constraint is prevented. The effectiveness of the proposed method can be validated via numerical simulation.

An adaptive consensus algorithm is proposed for a class of nonlinear multiagent systems with completely unknown agent dynamics. Due to uncertainties in the agent's dynamics, previous consensus approaches usually yield uniformly ultimately bounded consensus error. Our main contribution includes a novel robust consensus algorithm which can guarantee that the consensus error converges to zero asymptotically. In order to address the unknown dynamics, a two-layer neural network (NN) is utilized to learn the unknown dynamics in an online manner, and a robust continuous term is introduced to alleviate effects of the NN residual reconstruction error and external disturbances. The continuousness of the control signal is guaranteed to remove the actuator bandwidth requirement and avoid the caused chattering phenomenon. The proposed consensus algorithm is distributed in the sense that each agent only exchanges information with its neighbor agents. The asymptotic consensus result is achieved via Lyapunov synthesis. Furthermore, the proposed algorithm can also be extended to the case where the agents are required to form a prescribed formation. Finally, simulation studies on a nonlinear multiagent system are provided to demonstrate the performance of the scheme.

Anomaly detection in multivariate time series has been widely studied in one-class classification (OCC) setting. The training samples in this setting are assumed to be normal. In more practical situations, it is difficult to guarantee that all samples are normal. Meanwhile, preparing a completely clean training dataset is costly and laborious. Such a case may degrade the performance of OCC-based anomaly detection methods which fit the training distribution as the normal distribution. To overcome this limitation, in this paper, we propose MTGFlow, an unsupervised anomaly detection approach for M ultivariate T ime series anomaly detection via dynamic G raph and entity-aware normalizing Flow . MTGFlow first estimates the density of the entire training samples and then identifies anomalous instances based on the density of the test samples within the fitted distribution. This relies on a widely accepted assumption that anomalous instances exhibit more sparse densities than normal ones, with no reliance on the clean training dataset. However, it is intractable to directly estimate the density due to the complex dependencies among entities and their diverse inherent characteristics, not to mention detecting anomalies based on the estimated distribution. In order to address these problems, we utilize the graph structure learning model to learn interdependent and evolving relations among entities, which effectively captures the complex and accurate distribution patterns of multivariate time series. In addition, our approach incorporates the unique characteristics of individual entities by employing an entity-aware normalizing flow. This enables us to represent each entity as a parameterized normal distribution. Furthermore, considering that some entities present similar characteristics, we propose a cluster strategy that capitalizes on the commonalities of entities with similar characteristics, resulting in more precise and detailed density estimation. We refer to this cluster-aware extension as MTGFlow_cluster. Extensive experiments are conducted on six widely used benchmark datasets, in which MTGFlow and MTGFlow_cluster demonstrate their superior detection performance.