The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results.

In this paper, fixed-time stability problem of nonlinear system is investigated. Firstly, a new fixed-time stability theorem is established, and a higher precise estimate of settling time is provided. Secondly, by theoretical deduction, the provided estimate is compared with the ones in existing fixed-time stabiity theorems. It is shown that our estimate is less conservative and more accurate than existing results. Moreover, as a practical application, fixed-time stabilization problem of general neural networks is studied. By developing a framework of protocol and applying the new fixed-time stability theorem, some new criteria are derived to solve fixed-time stabilization problem of general neural networks systems. Finally, two simulation examples are provided to verify the validity of our theoretical results.

In this paper, the finite-time bipartite consensus (FTBC) problem is investigated for the multi-agent system (MAS) with detail balanced structure. To realize FTBC of MAS, a unified protocol framework is developed. Some criteria are established for realizing FTBC. It is worth noticing that estimations of settling time can be given in form of mathematical expression. The unified framework can bring in various protocols by choosing different parameters, which extends previous results. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of corresponding theoretical results.

This study investigates the problem of asymptotic stabilization of underactuated surface vehicles (USVs) in the presence of simultaneous matched and mismatched disturbances. Within the framework of back-stepping control and by introducing a periodic term in the control laws of virtual yaw angle and surge velocity, a control design method is developed to stabilize the USVs into the bounded region. By the induction method, a novel fixed-time disturbance observer based on higher-order sliding mode differentiators are introduced. Then a control law based on the proposed observers is proposed, by which the errors between the virtual and actual yaw angle and surge velocity can converge to zero, and the state of the USVs converge to a bounded region. Numerical simulations are carried out to verify the proposed control schemes.

This article focuses on the fixed-time trajectory tracking problem for surface vehicles (SVs) with prescribed performance. First, to realize prescribed performance, the error transformation and fixed-time prescribed performance function are proposed. In this way, the constrained tracking error problem can be solved by the stabilization of the transformed system. Second, by introducing a reduced-order disturbance observer, a fixed-time sliding mode controller is developed to realize trajectory tracking control while satisfying both predefined performance and perturbance rejection. It notices that the associated settling time can be preselected by parameters and independent of system initial conditions. Finally, some simulation examples are provided to illustrate the effectiveness of our theoretical results.

In this note, we investigate the fixed time consensus in probability for stochastic multi-agent systems under undirected graph. First, a nonlinear consensus protocol with Gaussian white noise is given, and the concept of fixed-time consensus in probability is given. Second, we prove that multi-agent systems can achieve fixed-time consensus in probability under undirected topology by using graph theory, stochastic Lyapunov theory and probability theory. Finally, a simulation example is given to verify the effectiveness of the theory results.