This note proposes a notion of scaled cluster consensus, wherein the final consensus states within different clusters converge to prescribed ratios. Unlike most results in existing literature on cluster consensus, no constraints are imposed on the system topologies under the designed protocol, i.e. the agents are not required to possess any cluster affiliation information of others. For the delay-free case, an explicit scaled cluster consensus function is provided by exploring the characteristics of stochastic matrices. Diverse input delays and asymmetric communication delays are both considered, and sufficient condition for scaled cluster consensus is derived based on frequency domain analysis. Finally, numerical examples are given to illustrate the effectiveness of the presented results.

In the realm of online learning, where resources are abundant, it is essential to customize recommendations and plans to meet individual learning needs. This involves not only identifying and addressing areas of weakness but also aligning the learning journey with each learner’s cognitive preferences. However, existing methods for suggesting and structuring learning paths have notable limitations. To address these challenges, this paper introduces a knowledge graph-based personalized learning path planning method (KG-PLPPM). By leveraging a knowledge graph and refining cognitive diagnosis models, the proposed method tailors learning paths to individual needs. It evaluates knowledge concept similarity and learner mastery, and employs an algorithm for path planning. In the experiments, two metrics—the concept sequence degree and learning efficiency—are used to assess our work. Experimental results demonstrate that the method presented enhances the coherence and relevance of recommended learning paths, and achieves a higher concept sequence degree, indicating that knowledge concepts are arranged in a manner consistent with the learning sequence, which aligns more closely with learners’ cognitive preferences. Moreover, across various learning progresses and path lengths, it effectively addresses weak knowledge areas, significantly enhancing learning efficiency.

This study investigates the consensus problem of second‐order multi‐agent systems which are subject to Markov jumping input delays. A unified framework is established to address both the stationary and dynamic consensus issues in sampled‐data settings. The authors first derive the sufficient conditions for consensus in terms of matrix inequalities. Thereafter, a cone complementarity linearisation‐based algorithm and its simplified implementation alternative are proposed for the delay‐dependent switching controller design. Compared with the existing works, the proposed algorithms possess less conservativeness and larger solution domains. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Navigation spoofing has been widely utilized in unmanned aircraft vehicle (UAV) countermeasures, due to its advantages of covertness, effectiveness, and dynamic trajectory control ability. However, existing research faces two primary challenges. Firstly, sudden changes in the target UAV’s trajectory can result in a significant degradation in the spoofing performance, which may enable the onboard inertial components to detect and identify the ongoing spoofing attempts. Secondly, gradual accumulation of control errors over time degenerates the spoofing effect. To address these problems, we propose a dynamic trajectory spoofing approach for UAVs based on model predictive control (MPC), which progressively steers the UAVs towards the predetermined trajectory of the spoofer. Simulation results demonstrate a substantial enhancement in dynamic trajectory control performance and decrease in accumulation error compared to the existing methods.

The hybrid phased multiple‐input‐multiple‐output (MIMO) radar with subarray partition can provide the transmit coherent gain of phased array and the waveform diversity of MIMO radar. The current researches mainly focus on the different subarray partition schemes of the transmit array. In this letter, a full phased‐MIMO (FPMIMO) radar with equally overlapped subarrays is introduced, and a robust adaptive transmit/receive beamforming algorithm is proposed based on the virtual interference‐plus‐noise covariance matrix (INCM) reconstruction and the virtual steering vector estimation. In the FPMIMO radar, the conventional beamforming is used for the signal transmission and reception on each subarray, and all subarrays can be assumed as a uniform linear array. Based on the presumed uniform linear array, the virtual INCM can be reconstructed by Eigen‐decomposition of the reconstructed INCM, and the virtual steering vector can be obtained by the estimated steering vector. With fewer antenna elements and sampling channels in the FPMIMO radar, simulation results demonstrate better performance of the proposed algorithm in a wide range of input signal‐to‐noise ratio.