This paper investigates the bipartite synchronization problem of cooperative-antagonistic neural networks (CANNs) that suffer from hybrid attacks, i.e., denial-of-service (DoS) attacks and replay attacks. A resilient sampled-data control scheme is proposed to deal with the hybrid attacks. In addition, the Laplacian matrix with zero-row-sum is obtained based on the coordinate transformation method. On this basis, an easy-to-handle error system is constructed by integrating the sampling scheme, cooperative-antagonistic interactions and hybrid attacks. Subsequently, an interval-dependent function is designed by considering the characteristics of both replay and DoS attacks. Based on this, using Lyapunov function methods, inequality techniques, and other mathematical skills, some sufficient criteria are obtained for the bipartite synchronization of CANNs. Finally, three algorithms are proposed to minimize the coupling strength, or maximize the replay attack rate or the DoS attack rate, respectively. The effectiveness of the proposed control schemes and the advantages of the interval-dependent function are verified through numerical examples. Note to Practitioners —This work addresses the bipartite synchronization control problem of CANNs, which can be applied to some practical systems such as drone bidirectional formation and team competition. For example, the dynamics of drones within the same formation, including their velocity and position, are consistent with each other but opposite to those of other teams. Additionally, network systems across various industries often encounter DoS attacks or replay attacks during network transmission. A resilient sampled-data control scheme is proposed, and a Lyapunov function dependent on intervals is designed,taking into account the characteristics of the attack. Then, some algorithms are presented to minimize the allowable coupling strength or maximizing the allowable replay attack rate and DoS attack rate. Preliminary simulation experiments indicate that this sampling scheme is feasible. The types of network attacks are diverse. Therefore, obtaining system synchronization control schemes for more complex network attacks is a challenge.

This paper addresses the bipartite leader-follower synchronization (BLFS) of cooperation-competition neural networks (CCNNs) via sampled-data (SD) control. First, the directed signed graph (SG) theory is applied to describe the cooperation and competition interactions, and thus, an appropriate mathematical model is constructed for such kind of multiple CCNNs. Based on the coordinate transformation technique, the main challenges encountered from the Laplacian matrix of the directed SG are circumvented. Then, a tractable error system can be established in the presence of SD control. Two interval-scheduled looped-functions are well-structured by relaxing the requirements of positive definiteness and continuity, respectively. In combination with discrete Lyapunov theory and some inequality techniques, some less conservative criteria are derived to guarantee the BLFS of CCNNs. Compared with the previous analysis methods, a smaller coupling strength or a larger sampling interval can be permitted on the basis of the developed results. Finally, two examples are presented to verify the effectiveness and advantages of the obtained results.

Studies have shown that fractional calculus can describe and characterize a practical system satisfactorily. Therefore, the stabilization of fractional-order systems is of great significance. The asymptotic stabilization problem of delayed linear fractional-order systems (DLFS) subject to state and control constraints is studied in this article. Firstly, the existence conditions for feedback controllers of DLFS subject to both state and control constraints are given. Furthermore, a sufficient condition for invariance of polyhedron set is established by using invariant set theory. A new Lyapunov function is constructed on the basis of the constraints, and some sufficient conditions for the asymptotic stability of DLFS are obtained. Then, the feedback controller and the corresponding solution algorithms are given to ensure the asymptotic stability under state and control input constraints. The proposed solution algorithm transforms the asymptotic stabilization problem into a linear/nonlinear programming (LP/NP) problem which is easy to solve from the perspective of computation. Finally, three numerical examples are offered to illustrate the effectiveness of the proposed method.

This paper deals with the bipartite synchronization problem of cooperation-competition neural networks (CCNNs) subject to denial-of-service (DoS) attacks. A resilient sampled-data control strategy is proposed to mitigate the adverse impact of DoS attacks, which takes both the attack signal and the periodic sampling communication protocol into account. The directed signed graph is introduced to characterize the cooperation and competition interactions among nodes. By leveraging coordinate transformation and graph theory techniques, a zero-row-sum Laplacian matrix is constructed to facilitate subsequent analysis. In combination with DoS attacks and control strategies, a tractable error system model is formulated. An interval-dependent function is further introduced, taking into account both attack intervals and data transmission intervals. Based on Lyapunov stability theory, the convex combination approach, and inequality techniques, the bipartite synchronization criteria for CCNNs are obtained. Moreover, the constructed interval-dependent function can improve the maximum allowable attack rate or reduce the minimum allowable coupling strength. The proposed control scheme is demonstrated to be effective and superior through the two numerical examples.

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.