Due to the widespread development of microgrid (MG) systems, this paper mainly focuses on the edge-based prescribed-time adaptive secondary control problem for direct current (DC) MG systems. Firstly, a new voltage regulator is designed by the time-varying scaling function and the dynamic average consensus protocol of multi-agent systems. Meanwhile, in order to avoid the dependence of the algorithm on the global network information, an edge-based adaptive control update rate is proposed. Secondly, by applying the prescribed-time stability theory, it is rigorously proven that the bus voltage can be restored to its desired value under the presented voltage regulator within a prescribed time, and the current is allocated according to the droop coefficient ratio. Finally, the effectiveness and feasibility of the proposed algorithm are verified through Matlab/Simulink simulation under different working conditions, and it is compared with the existing asymptotic consensus algorithm to demonstrate the superiority of the algorithm presented in this paper.

In this article, the prescribed-time optimization problem is considered for multiagent systems (MASs) with inconsistent constraint sets. First, the constrained optimization problem is transformed into an unconstrained one using the sliding mode control approach, in which the sliding surface is constructed based on the projection errors. Subsequently, three distinct prescribed-time optimization control protocols are developed by utilizing the sliding mode variables and optimization algorithms. In particular, compared with the existing works in which the gain of each controller approaches infinity at the prescribed instant, this article effectively mitigates singularity by integrating fixed-time theory with the time-domain transformation method. Furthermore, it can be verified that all agents achieve optimization consensus under the three different algorithms by the Lyapunov stability theory and convex optimization analysis. Finally, we provide an application example to verify the validity of theoretical results.

This article studies the prescribed-time practical consensus problem for nonlinear multi-agent systems (MASs) subject to denial-of-service (DoS) attacks via an intermittent-based event-triggered mechanism. To this end, we first propose a time-varying scaling function based on the intermittent period, and then use this function to derive a new practical prescribed-time stability theory. Second, this paper further designs an intermittent-based event-triggered control protocol, along with a corresponding triggered function. The main innovation of this protocol is its ability to avoid singular phenomena as time approaches the prescribed instant and to reduce communication costs among all agents. Additionally, some sufficient conditions for achieving leader-following practical consensus are deduced by the proposed prescribed-time stability theory while also excluding Zeno behavior. Finally, two examples are given to verify the effectiveness and feasibility of the theoretical results.

This article presents two fixed-time (FXT) distributed adaptive algorithms to solve a class of convex optimization problems for multiagent systems. First, a distributed adaptive protocol based on edge weights is developed to achieve global FXT optimization, in which the initial states are the local optimal points. Subsequently, an adaptive power-law algorithm is designed to realize local FXT optimization for each agent with arbitrary initial state. In the convergence analysis, unlike previous analysis method based on Lyapunov FXT stability criteria, this study employs the definition of FXT stability with Laplace transformation and a method of contradiction, several sufficient conditions are obtained to ensure that the states of all agents converge to the global optimal value within a fixed time, and the upper bound of convergence time is estimated. Furthermore, these adaptive algorithms on undirected graphs are extended to weight-balanced digraphs. Finally, the validity of the proposed edge-based adaptive distributed algorithms is demonstrated through numerical simulations of two packet-level charge-state balance problems.

In this paper, a periodic intermittent sampled data control strategy, which both reduces the load of updating rate of the controller and cuts down the working time of the controller in each sampling interval, is proposed to investigate the second-order consensus of multiagent systems. In order to reach consensus, a necessary and sufficient condition depending on the coupling gains, the communication width, the sampling period, and the spectrum of the Laplacian matrix, is established. Furthermore, the feasible region of communication width is derived for given coupling gains and structure of network. Besides, the coupling gains are also carefully designed. On the other hand, when the time delay exists in the sampling process, a time delayed protocol is proposed. A necessary and sufficient condition based on the communication width, the sampling period, the coupling gains, the time delay, and the network structure is also derived for achieving consensus. It is amazing found that the sampling period should have both lower and upper bounds for given time delay and communication width for the sake of reaching consensus. Finally, several numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.