Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

Double Model Following Adaptive Control for a Complex Dynamical Network

This paper formulates and solves a new problem of the double model following adaptive control (MFAC) of nodes and links in a complex dynamical network (CDN). This is different from most existing studies on CDN and MFAC. Inspired by the concept of composite systems, the CDN with dynamic links is regarded as an interconnected system composed of an interconnected node group (NG) and link group (LG). Guided by the above-mentioned new idea of viewing a CDN from the perspective of composite systems, by means of Lyapunov theory and proposed related mathematical preliminaries, a new adaptive control scheme is proposed for NG. In addition, to remove the restriction that the states of links in a CDN are unavailable due to physical constraints, technical restraints, and expensive measurement costs, we synthesize the coupling term in LG with the proposed adaptive control scheme for NG, such that the problem of double MFAC of nodes and links in CDN is solved. Finally, a simulation example is presented to verify the theoretical results.

Finite-Time Synchronization of Reaction-Diffusion Inertial Memristive Neural Networks via Gain-Scheduled Pinning Control

For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and 2ⁿ controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov-Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.

Target Controllability in Multilayer Networks via Minimum-Cost Maximum-Flow Method

In this article, to maximize the dimension of controllable subspace, we consider target controllability problem with maximum covered nodes set in multiplex networks. We call such an issue as maximum-cost target controllability problem. Likewise, minimum-cost target controllability problem is also introduced which is to find minimum covered node set and driver node set. To address these two issues, we first transform them into a minimum-cost maximum-flow problem based on graph theory. Then an algorithm named target minimum-cost maximum-flow (TMM) is proposed. It is shown that the proposed TMM ensures the target nodes in multiplex networks to be controlled with the minimum number of inputs as well as the maximum (minimum) number of covered nodes. Simulation results on Erdős-Rényi (ER-ER) networks, scale-free (SF-SF) networks, and real-life networks illustrate satisfactory performance of the TMM.