This article focuses on the finite-time and prescribed-time cluster synchronization problems of switched complex networks with proportional delays. Considering that the matched controller often switches behind the switched systems, asynchronous switching law and switching parameters have been introduced to the complex dynamical networks. By applying the stability theory of dynamical systems and the average dwell time approach, some sufficient criteria in form of linear matrix inequalities have been developed to guarantee such networks finite/prescribed-time cluster synchronization under the pinning control scheme. Finally, one numerical example is presented to show the effectiveness of the theoretical results.

This article is concerned with the global $$O(t^{-\alpha })$$ O ( t - α ) stabilization for a class of fractional-order memristive neural networks with time delays (FMDNNs). Two kinds of control scheme (i.e., state feedback control law and output feedback control law) are employed to stabilize a class of FMDNNs. Several stabilization conditions in form of algebraic criteria are presented based on a new fractional-order Lyapunov function method and Leibniz rule. Some examples are given to substantiate the effectiveness of the presented theoretical results.

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise. (C) 2019 Mathematical Institute Slovak Academy of Sciences

In this article, the encoding-decoding-based resilient state estimation problem is investigated for the mobile robot localization with state saturation under the buffer-aided mechanism. To reduce the impact of the intermittent measurements on estimation performance, the buffer-aided mechanism is introduced to store the untransmitted measurements when the transmission is impermissible. The unbiased probabilistic encoding–decoding approach is employed to improve the efficiency and security of the transmission. In addition, the state saturation modeled by a signum function is considered for a more accurate depiction of real-world engineering. The main objective of this article is to establish a buffer-aided-based resilient state estimator for the state-saturated mobile robot localization subject to the probabilistic encoding–decoding, such that the minimal upper bound on the estimation error covariance is guaranteed by appropriately designing the desired estimator gain. Finally, the effectiveness of the proposed estimation scheme is evaluated on a mobile robot platform with buffer capacities of $M=2, 4, 6$. The influence of different encoding interval/gain variation coefficients on the state estimation accuracy is also discussed by conducting comparison-based analyses. Furthermore, when compared to the extended Kalman filtering, the proposed estimation scheme achieves significant improvement in estimation performance while only increasing the computational time by 62.4%.

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.

This paper is concerned with the secure and resource-efficient cluster synchronization problem of a class of complex dynamical networks (CDNs) under random deception attacks. Each node in the CDNs is modeled by a nonlinear dynamical system with multiple time-varying delays and nonlinear couplings. The central aim is to make each cluster of nodes converge to the same reference trajectory that is distinct for each cluster regardless of the adverse effects of random deception attacks while ensuring communication efficiency for each node. Toward this aim, a distributed dynamic event-triggered mechanism is first proposed such that each node can make its own decisions to transmit or not its data of interest over the communication channel. Second, by suitably modeling the random deception attacks, secure and event-based cluster synchronization controllers are constructed, which incorporate both the effects of random deception attacks and intermittent data arrivals. Then, sufficient conditions ensuring the secure cluster synchronization of the delayed CDNs under randomly occurring deception attacks are established by constructing some appropriate Lyapunov functionals. Furthermore, tractable design criteria on the existence of desired cluster synchronization controllers are derived. Finally, an illustrative example is presented to validate the effectiveness of the main theoretical results.