Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Abstract

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.

A Unified Framework Design for Finite-Time Bipartite Consensus of Multi-Agent Systems

“…Remark 3.9: From Theorem 3.8, it can be seen that for the structurally unbalanced signed graphs, the finite time bipartite consensus problem is equal to the finite-time stability problem. That is to say, Theorem 3.8 solved finite time stability problem of continuous system (11) in virtue of positive definite matrix L(B p ). If power parameter p = 0, the finite time stability of discontinuous system needs to be analyzed by Filippov solutions and set-valued Lie derivative.…”

“…It aims to guarantee agent states converge to the same ideal values by some suitable protocols. Most existing works [1]- [4], [11], [12] on consensus of MAS are based on the fundamental assumption that the interactions among the agents are cooperative. However, there are cooperatives and antagonism simultaneously in practical applications, such as two-party political systems, trust networks, and so on.…”

A novel bipartite consensus tracking scheme for unknown nonlinear multi-agent systems: Theoretical analysis and applications

“…It is noted that most approaches 1–15 are dependent on the structure, dynamics, and assumptions imposed on the system model. Hence, these methods are called model-based control (MBC) approaches.…”

“…The proposed DDDBCT scheme for MASs only uses the I/O data without requiring any information of the controlled plant’ dynamics, which are required by most existing methods. 1–10…”

“…The consensus aims to guarantee that all agents reach a certain target, such as the same position, velocity, and angle. To address this problem, many effective methods have been proposed recently, such as finitetime consensus methods, 4,5 fixed-time consensus methods, 6,7 event-trigger-based consensus methods, 8 and also some novel methods. 9,10 However, the above methods presume that the interaction among agents is collaborative.…”