This article takes up for discussion the distributed secure state estimation issue for a specific category of nonlinear systems with random measurement delays and being subject to random deception attacks. To prolong the signal transmission distance, the amplify-and-forward (AF) relays are incorporated. A distinctive recursive state estimation algorithm is formulated, adopting a pattern reminiscent of a Kalman-type filter. Firstly, an upper bound matrix (UBM) for the estimation error (EE) variance is calculated. Then the estimator gain matrices are obtained by minimizing the calculated UBM. Subsequently, the impact of the transmission energies from sensors and relays on estimation performance is analyzed. Finally, the proposed estimation algorithm is confirmed through a simulation example, demonstrating its effectiveness.

The leader-following problem for the heterogeneous nonlinear multiagent systems under output constraints is investigated in this paper. It is focused on the cases where the underlying communication graph is directed and switching, and each agent is a multi-input multi-output block-triangular system with totally unknown and inherently nonlinear dynamics. They render the existing distributed control solutions infeasible. To surmount this challenge, a novel distributed mixed control strategy, composed of a group of robust decoupling constrained controllers and a set of PI-type gain adaption-based controllers, is developed in this paper. It ensures that the outputs of each follower evolve inside the prescribed constraint bands and track the leader outputs with the tunable settling time and accuracy, despite the topology switching. Moreover, it exhibits a prominent simplicity, in spite of the severe model uncertainties, without parameter identification, function approximation, disturbance estimation, or derivative calculation or estimation. The theoretical findings are illustrated by a comparative simulation on a team of planar mobile robots.

This paper introduces novel approaches and applications for hyper-differential operator-based graph fractional Fourier transform (HGFrFT), which provides a more flexible and efficient framework for graph signal processing. Its mathematical foundation is derived through the relationship between the graph Fourier transform and the fractional graph Fourier transform, thereby enhancing its ability to represent the underlying structure of graph signals. Specifically, four solutions to the Sylvester equation are discussed, and two fixed hyperdifferential operator matrices are introduced to define the HGFrFT. Furthermore, the applications of the HGFrFT in vertex-frequency analysis and optimal filter design are explored. Finally, the effectiveness of the HGFrFT is validated in electrocardiogram signal classification, demonstrating its applicability to real-world signal processing tasks. The theoretical framework and experimental results collectively advance fractional operator theory in graph domains.

State estimation plays a crucial role in Boolean networks as it determines the capability of predicting and regulating network dynamic behaviors. Particularly, state-dependent packet dropouts (SDPDs) are of critical importance, as it enables more accurate modeling of communication constraints in practical systems, thereby significantly affecting the reliability of state estimation. This paper addresses the state estimation problem in stochastic Boolean networks (SBNs) with SDPDs through a novel interactive coupled estimation framework. Using the semi- tensor product technique, we first derive the algebraic form of SDPD-affected SBN, where SDPDs are characterized by a transition probability matrix linking region labels to states. Our framework decomposes the estimation process into two interactively coordinated components: region label estimation and state estimation. We develop a matrix-based recursive method to compute the forward state-label probability distribution, enabling optimal region label sequence estimation. Based on the estimated region labels and the observation sequence, we then derive a state estimator to reconstruct the internal states of SDPD-affected SBNs. The effectiveness of this dual estimation structure is validated through a biological case study.

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under consideration. In the first scenario, the matrix of interest is row wisely available in each local node in the network. In the second scenario, the matrix of interest implicitly forms an outer product from two different series of measurements. By combining the lightweight local rational function approximation approach with parallel averaging consensus algorithms, two d-SVD algorithms are proposed to cope with the two aforementioned scenarios. We evaluate the proposed algorithms using two application examples: decentralized sensor localization via low-rank matrix completion and decentralized passive radar detection. Moreover, a novel and non-trivial truncation technique, which employs a representative vector that is orthonormal to the principal signal subspace, is proposed to further reduce the communication cost associated with the d-SVD algorithms. Simulation results show that the proposed d-SVD algorithms converge to the centralized solution with reduced communication cost compared to those facilitated with the state-of-the-art decentralized power method.

This paper proposes an accelerated bipartite iterative learning control protocol with self-learning input sharing and errors quantitation to address the problem of bipartite consensus for singular nonlinear switched delayed multi-agent systems (MASs) under antagonistic networks. By constructing a quasi-adjacency matrix, each agent can automatically detect and communicate input information in the form of weights among antagonistic networks, and a novel accelerated learning method based on exponential gain is adopted. Additionally, a logarithmic quantizer is added to the aforementioned protocol to saving communication resources. Then, the above protocol is extended to the bipartite formation problem under antagonistic networks and the scenarios where the topology changes randomly with the number of iterations. Based on the operator theory, the sufficient conditions for its convergence are given, and the convergence of the self-learning input sharing iterative learning control protocol is strictly analyzed. Through three simulation experiments, the efficacy of the protocol is further validated, and it is proved that the proposed protocol has faster convergence speed than the traditional iterative learning control protocol.

This paper proposes a reinforcement learning approach to the output synchronization problem for heterogeneous leader-follower multi-agent systems, where the system dynamics of all agents are completely unknown. First, to solve the challenge caused by unknown dynamics of the leader, we develop an experience-replay learning method to estimate the leader's dynamics, which only uses the leader's past state and output information as training data. Second, based on the newly estimated leader's dynamics, we design an event-triggered observer for each follower to estimate the leader's state and output. Furthermore, the experience-replay learning method and the event-triggered leader observer are co-designed, which ensures the convergence and Zeno behavior exclusion. Subsequently, to free the followers from reliance on system dynamics, a data-driven adaptive dynamic programming (ADP) method is presented to iteratively derive the optimal control gains, based on which we design a policy iteration (PI) algorithm for output synchronization. Finally, the proposed algorithm's performance is validated through a simulation.

In this paper, we investigate the distributed optimization problem for heterogeneous linear multi-agent systems with unknown disturbances. To solve this problem, we propose a distributed controller design framework, which reduces the controller design for heterogeneous linear multi-agent systems to the stabilizer design for first-order multi-agent systems. By this framework, we propose two kinds of dynamic controllers under the strong convexity of the objective function and the restricted secant inequality condition, respectively. Based on the optimal condition and singular perturbation analysis technique, we prove that the system converges to the optimal state if the disturbances tend to be constant or vary slowly. To further optimize the performance criterion under system stability and input constraint, we provide an optimal gain tuning algorithm such that the system stability, optimality and feasibility are simultaneously achieved. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

Subspaceclustering (SC), which aims to cluster the high-dimensional data samples into their exclusive low-dimensional subspaces, has been widely used in data mining and computer vision. However, an in-depth study of existing models reveals that most of them ignore the prior rank information of the encountered problem, which prevents them from effectively extracting the inherent features embedded in the data. To this end, a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</u>runcated <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</u>robenius norm minimization-based <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lat</u>ent <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</u>ow-<underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</u>ank <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</u>epresentation (TFLatLRR) model is proposed for SC. Our proposed model can not only sufficiently preserve the crucial data components within the truncated rank, but also characterize a global subspace structure of data in the presence of deficiency and occlusions. Thus, a more accurate and effective representation matrix can be learned by TFLatLRR, and its corresponding affinity can be quantitatively measured by the newly defined <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</u>lock <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</u>ensity <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</u>ndex (BDI). More importantly, we theoretically demonstrate that the global optimum of the <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u>quare of <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</u>runcated <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u>ingular <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</u>alues (STSV) operator can be directly achieved in closed form, rather than transforming the corresponding problem into a convex optimization problem. Then, an efficacious algorithm is devised to solve the proposed model by employing the alternating direction method of multipliers (ADMM) framework, where each subproblem can be efficiently solved in closed form. Furthermore, a rigorous mathematical proof shows that the sequence produced by the proposed algorithm converges to a Karush-Kuhn-Tucker (KKT) point. Experimental results on several real-world datasets demonstrate the superiority of our model in comparison with state-of-the-art models.

The prevalence of Internet platforms, such as social media and web pages, enables users to share their opinions and observe each other's actions. Users may show strong advocacy and support for each other's opinions and decisions at one moment, while they may disagree with each other with polarized views later. These dynamic changes of supportive relationships pose challenges to influential entities such as government agencies, firms, politicians, experts and weblebrities, who aim to gain support from and have large influence on the public. To study this dynamics, we consider the Social Networks with Supportive Relationships (SN-SR), whose links represent actively supportive relationships and are disconnected when users disagree with each other. For these influential entities, their reputation and social influence impact each other's evolution over SN-SR, while few works study how to model this co-evolving pattern and how to analyze and predict the dynamics of their influence over networks. In this work, we use the network topology of the SN-SR as an intermediate variable to model and study the interplay between the reputation and influence, and propose an integrated framework called CoRNI to theoretically analyze its impact on social influence. We use simulations on synthetic networks and real Weibo data to validate our proposed model and theoretical analysis. This investigation provides important guidelines for influential entities to adjust their actions and improve their influence over the network.