Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control

In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol

Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays

This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional approach, the stability issues of almost periodic solution are investigated, and a sufficient condition for the existence, uniqueness, and global exponential stability of the almost periodic solution is established. Moreover, as a special case, the condition which ensures the global exponential stability of a unique periodic solution is also presented for the considered memristive neural networks. Two examples are given to illustrate the validity of the theoretical results

Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes

Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes

A One-Layer Recurrent Neural Network for Solving Pseudoconvex Optimization with Box Set Constraints

A one-layer recurrent neural network is developed to solve pseudoconvex optimization with box constraints. Compared with the existing neural networks for solving pseudoconvex optimization, the proposed neural network has a wider domain for implementation. Based on Lyapunov stable theory, the proposed neural network is proved to be stable in the sense of Lyapunov. By applying Clarke’s nonsmooth analysis technique, the finite-time state convergence to the feasible region defined by the constraint conditions is also addressed. Illustrative examples further show the correctness of the theoretical results

Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results

Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by using M-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results