In this paper, the observer-based quasi-consensus control problem is investigated for a class of discrete-time multi-agent systems subject to time-varying delay. To improve communication quality and extend transmission distance, a stochastic communication protocol and an amplify-and-forward relay mechanism are incorporated. During the process of signal amplification and transmission in the AaF relay, stochastic packet loss is considered, which introduces additional complexity into the system analysis. The main objective is to design a distributed observer-based control strategy capable of handling time-varying delays, stochastic scheduling governed by a Markov chain, and random packet dropouts. Sufficient conditions are derived to guarantee the achievement of quasi-consensus in probability among the agents. These conditions are formulated in terms of matrix inequalities through which the required gain matrices are computed. A simulation example is provided to validate the effectiveness and robustness of the proposed control approach under realistic communication constraints.

Recommendation systems alleviate the issue of information overload via modeling user preferences from interaction sequences. Although self-attention based sequential models effectively capture long-range dependencies, they are susceptible to noise amplification in sparse sequences and over-smoothing of item representations, which obscures true user intent and reduces sensitivity to fine-grained behavioral changes. To overcome these challenges, we propose SAFA, a sparse sequential recommendation framework comprising: (1) an adaptive sparse attention mechanism that suppresses noisy interactions while preserving embedding diversity; (2) a frequency-aware encoder that decomposes interaction sequences into low-frequency components for long-term preference modeling and high-frequency components for short-term intent dynamics; and (3) a simplified focal loss that removes the class-balancing term while preserving the focusing factor, emphasizing hard-to-predict samples rather than class priors. Experiments on seven benchmark datasets demonstrate that SAFA consistently achieve state-of-the-art performance with average improvements of up to 3.77%, 4.10% and 4.25% in terms of HR@5, HR@10 and HR@20, respectively, and 4.30%, 4.78% and 4.58% in terms of NDCG@5, NDCG@10 and NDCG@20, respectively, over the best competing model. Ablation studies verify the importance of each component, with notable performance degradation upon removing the sparse attention or frequency-aware encoder. Overall, SAFA enhances sequential recommendation by improving robustness and discriminative learning under noisy and sparse conditions.

In many practical applications, it is difficult or impossible to obtain the exact solution of the mathematical model due to the limitations of solving methods and the complexity of the neural network itself. A natural problem is given as follows: does the exact solution of quaternion-valued neural networks (QVNNs) exist when successively improved approximate solutions can be obtained? Fortunately, the Hyers-Ulam stability happens to be one of the important means to deal with this problem. In this article, the issue of Hyers-Ulam stability of QVNNs with time-varying delays is addressed. First, inspired by the Hyers-Ulam stability of general functional equations, the concept of the Hyers-Ulam stability of QVNNs is proposed along with the QVNNs model. Then, by utilizing the successive approximation method, both delay-dependent and delay-independent Hyers-Ulam stability criteria are obtained to ensure the Hyers-Ulam stability of the QVNNs considered. Finally, a simulation example is given to verify the effectiveness of the derived results.

In this article, the problem of consensus control is investigated for a class of multiagent systems (MASs) with both stochastic noises and nonidentical exogenous disturbances. The signal transmission among agents is implemented through a digital communication network subject to both uniform quantization and round-robin protocol as a reflection of network constraints. The consensus strategy is designed by adopting the estimates of the relative states of the agent to its neighbors, which renders the distributed nature of the controller. A new consensus concept, namely, quasiconsensus in probability, is employed to evaluate the state response of the agents to the stochastic noises, the exogenous disturbances, and the quantization error. An augmented system is first formed that relies on the deviations of the individual state from the average state, the observer error of the relative state, as well as the relative measurement output. Based on the augmented model, an analysis approach on dynamical behaviors is developed to facilitate the consensus analysis of MASs by means of the switching Lyapunov function technique and the stochastic analysis methods. Then, the existence condition and the explicit expression of the time-varying gain matrices are proposed for the expected controller by resorting to the feasibility of several matrix inequalities. Numerical simulation results are presented to demonstrate the applicability of the theoretical results.

In this paper, the observer-based stabilization problem is investigated for a class of discrete-time nonlinear stochastic networked control systems (NCSs) with exogenous disturbances. The signal transmission from the sensors to the observer is implemented via a shared digital network, in which both uniform quantization effect and stochastic communication protocol (SCP) are taken into account to reflect several network-induced constraints. The notion of input-to-state stability in probability is introduced to describe the dynamical behaviors of the closed-loop stochastic NCS that is effectively characterized by a general nonlinear stochastic difference equation with Markovian jumping parameters. A theoretical framework is first established to felicitate the dynamics analysis of the closed-loop system in virtue of the switched Lyapunov function method and the stochastic analysis techniques. By making full use of the quantized measurement output under the scheduling of the SCP, the existence conditions for an observer-based controller are established under which the closed-loop system is input-to-state stable in probability. Then, the explicit expression of the gain matrices of the desired controller is given by resorting to a set of feasible solutions of certain matrix inequalities. The effectiveness of the theoretical results is demonstrated by a numerical simulation example.

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

This paper is concerned with the input-to-state stabilization problem for a class of delayed differential systems. Both time-delay in state and bounded exogenous disturbances are taken into account in the model. An event-triggered strategy, which depends simultaneously on the latest sampled state and a non-negative threshold, is proposed to reduce the transmission frequency of the feedback control signals with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to evaluate the dynamical performance of the controlled systems with considering the effects from both exogenous disturbances and event-triggered scheme. The estimations of the upper bounds for the system state and the measurement error are employed to analyze and further exclude the Zeno behavior for the proposed event-triggered scheme. The controller gain and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

This paper is concerned with the synchronization analysis and control problems for a class of nonlinear discrete-time stochastic complex dynamical networks (CDNs) consisting of identical nodes. The discrete-time stochastic dynamical networks under consideration are quite general that account for asymmetric coupling configuration, nonlinear inner coupling structures as well as nonidentical exogenous disturbances. By resorting to both the error bound and the synchronization probability, a notion of quasi-synchronization in probability is first introduced to assess the synchronization performance of the addressed CDNs. An event-triggered pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in the control process while preserving the desired dynamical behaviors of the controlled networks. By using the Lyapunov function method and the stochastic analysis techniques, a general framework is established within which the problems of dynamics analysis and controller synthesis are solved for the closed-loop stochastic dynamical networks. Two numerical examples and their simulations are presented to illustrate the effectiveness and the usefulness of our theoretical results.