This letter focuses on the optimal sum secure degree of freedom (SDoF) in a two-way wiretap channel (TW-WC), wherein two legitimate full-duplex multiple-antenna nodes cooperate with each other and are wiretapped by a multiple antenna eavesdropper simultaneously. It aims to find the optimal sum SDoF pertaining to secret-key capacity for the TW-WC. First, we analyze the upper bound and lower bounds of the optimal sum SDoF by establishing their equivalence to the expression of the optimal SDoF corresponding to the secrecy rate for the TW-WC. Subsequently, in scenarios where the legitimate nodes are configured with an equal number of transmit and receive antennas, it is elucidated that the upper and lower bounds of the optimal SDoF converge. Furthermore, the findings suggest that a higher SDoF can be achieved than the existing works, thereby heralding an enhancement in secure spectral efficiency.

This paper addresses the problem of prescribed-time output feedback stabilization for a class of nonlinear uncertain systems with both external disturbances and mismatched uncertainties. By utilizing a non-separation principle design approach, a novel active disturbance rejection control (ADRC) scheme is proposed. Firstly, a prescribed-time extended state observer (PTESO) is designed to simultaneously estimate unmeasured system states and external disturbances. Secondly, a feedforward-feedback composite controller is developed by integrating the PTESO with a constructive backstepping procedure. Furthermore, the prescribed-time stability of the entire closed-loop system is rigorously analyzed by using a Lyapunov function method. Finally, numerical simulations validate the effectiveness of the proposed control method.

This article investigates the fixed-time distributed average tracking (DAT) problem for nonlinear multiagent systems with unity relative degree under external disturbances. A distributed control framework is developed to guarantee fixed-time convergence of all agents' outputs to the target trajectory, which is defined as the average of multiple nonlinear reference signals. The approach consists of three main components. First, a steady-state generator is introduced to reconstruct the desired trajectory. Using this generator, a distributed observer is designed to estimate the target trajectory while ensuring robustness against initialization errors. Subsequently, an observer-based output-feedback controller is developed to guarantee the convergence of each agent's output to its corresponding reference signal within a fixed time. Through rigorous theoretical analysis, it is proved that the proposed control architecture ensures fixed-time convergence to the target trajectory, effectively solving the fixed-time DAT problem. The effectiveness of the proposed method is validated through numerical simulations.

In this paper, a fixed-time tracking control problem is investigated for an uncertain high-order nonlinear pure-feedback systems with practical state constraints. To this end, a new nonlinear transformation function with lower change rate at the state constraint boundary is first proposed, which can not only handle both constrained and unconstrained states in a unified way, but also reduce the control magnitude at the constraint boundary. With the help of the proposed transformation function, the original system is transformed to a new system without state constraints. Then, a non-singular fixed-time adaptive tracking controller is designed by applying an adding a power integrator technique and an adaptive neural network method. It is shown that the practical fixed-time stability can be guaranteed for the closed-loop system under the proposed tracking controller. Finally, two numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy.

In this article, a finite-time distributed average tracking (DAT) problem is considered for unity relative degree nonlinear multi-agent systems (MASs) subject to external disturbances. The objective of this article is to design a distributed controller such that the output of each agent converges to the desired trajectory (the average of multiple nonlinear signals) within a finite time. First, we introduce a steady-state generator, which can reproduce the desired trajectory. Based on the steady-state generator, we design a distributed observer to estimate the desired trajectory, which is robustness to initialization errors. Then, an observer-based output-feedback controller is proposed for each agent such that the output of each agent can converge to its own generated signal within a finite time. Finally, it is shown that the output of each agent can converge to the desired trajectory within a finite time using the proposed control strategy, and hence the finite-time DAT problem is solved. A numerical example is provided to demonstrate the effectiveness of the proposed algorithm.

In this article, an output regulation problem is considered for nonlinear multiagent systems with unity relative degree, in which nodes are coupled by dynamic edges. The inputs of the edge dynamic systems are determined by the error outputs of the node dynamic systems. Similarly, the neighboring inputs of the node dynamic systems are formed by the outputs of the edge dynamic systems and can influence node outputs. By introducing some coordinate transformations, we can transform the output regulation problem into a robust stabilization problem for an augmented system. Then, using the relative outputs of neighboring agents, we design a distributed output-feedback control law and suitable dynamic couplings between the nodes. Finally, it is shown that the global stabilization of the augmented system can be achieved using the proposed controller. An example is presented to demonstrate the effectiveness of our control strategy.

In this article, we consider an adaptive optimal output regulation problem for general linear systems. The purpose of the optimal output regulation problem is to guarantee the stability of the closed-loop system and disturbance rejection, as well by minimizing some predefined performance indices. It can be realized by using an optimal controller, in which both optimal feedback control gain and optimal feedforward control gain are included. First, an adaptive dynamic programming (ADP) technique is used to solve the optimal feedback control gain. Next, the unknown system matrices of the plant are explicitly computed. In addition, based on the property of the minimal polynomial, the coefficient of the exogenous disturbance in the expression of the regulated output can also be calculated. Finally, according to the regulator equation, an extra cost function is given, which aims to obtain the optimal feedforward control gain. The linear vector space optimization methods are used to solve the optimal problem. As a result, the linear optimal output regulation problem can be solved by the approximately optimal feedback and feedforward control gains.

In this paper, a bipartite consensus problem is considered for a high-order multiagent system with unknown disturbances and cooperative-competitive interactions. Two control strategies are proposed to guarantee bipartite consensus for two cases with and without an exogenous system (called leader for simplicity), respectively. Linearly parameterized approaches are applied to describe the time-varying unknown disturbances. Distributed adaptive laws are then designed for the unknown parameters in the disturbances. Adaptive consensus controllers are designed in a fully distributed fashion, which does not rely on any global information. Simulation results are presented to demonstrate the formation of bipartite consensus under the proposed adaptive control strategies.

In this paper, an antisynchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with cooperative-competitive interactions and time-varying coupling delays. The interaction topology among the neural nodes is modeled by a multilayer signed graph. The state evolution of a neuron in each layer of the coupled neural network is described by a reaction-diffusion equation (RDE) with Dirichlet boundary conditions. Then, the collective dynamics of the multilayer neural network are modeled by coupled RDEs with both spatial diffusion coupling and state coupling. An edge-based adaptive antisynchronization strategy is proposed for each neural node to achieve antisynchronization by using only local information of neighboring nodes. Furthermore, when the activation functions of the neural nodes are unknown, a linearly parameterized adaptive antisynchronization strategy is also proposed. The convergence of the antisynchronization errors of the nodes is analyzed by using a Lyapunov-Krasovskii functional method and a structural balance condition. Finally, some numerical simulations are presented to demonstrate the effectiveness of the proposed antisynchronization strategies.