Adaptive Discontinuous Control for Fixed-Time Consensus of Nonlinear Multi-Agent Systems

Abstract

This paper mainly focuses on the fixed-time consensus (FXC) control problem for nonlinear multi-agent systems (MASs). For the cases of leader-following and leaderless, two adaptive discontinuous protocols are designed, respectively, to realize our control goals. Common adaptive control protocols always significantly increase the dimension of the considered system model, while the protocols presented here only require two adaptive update laws and are therefore simpler to apply in the engineering control. Moreover, no additional conditions are required to ensure that the system can achieve FXC successfully, except for some necessary assumptions. Simulation examples also illustrate that these two protocols are effective.

Distributed Adaptive Fault-Tolerant Control for Leaderless/Leader–Follower Multi-Agent Systems against Actuator and Sensor Faults

“…From Figure 2a,b, the dashed and solid lines almost overlap with each other, indicating that the observer accurately estimated the states and faults of the MAS quickly. Moreover, as shown in Figure 2c, even if multiple faults occur in the MAS, the overall convergence performance is satisfactory, and the consensus error is bouned by e 1∼4 ≤ 0.5, verifying the effectiveness and demonstrating the performance of the proposed observer (3) and distributed FTC protocol (19) for leaderless MAS against concurrent actuator and sensor faults.…”

“…It can be obtained from (19) and c ij (0) = c ji (0) that c ij = c ji holds for t ≥ 0, and ∑ N j=1 ∑ N j=1 a ij c ij ( xi − xj ) = 0. Furthermore, Assumption 4 gives BB + F a = F a .…”

“…According to whether the communications are unidirectional or bidirectional, MASs can also be divided into two categories: directed graphs and undirected graphs, which makes the leader-follower become a special case in directed graphs [18]. In [19], adaptive discontinuous control protocols are studied to achieve fixed-time consensus of nonlinear MASs in leader-following and leaderless cases. A consensus-based formation control strategy of discrete MASs is investigated in [20], where bounded uncertain time-delays and directed switching topologies are considered.…”

Stochastic Fixed-Time Tracking Control for the Chaotic Multi-Agent-Based Supply Chain Networks with Nonlinear Communication

“…This means that these two forms of consensus will encounter great obstacles in practical application. However, the fixed-time consensus [20][21][22][23] not only has a fast convergence rate but also has a uniform upper bound that is independent of the initial value on its settling time. Therefore, it is worth studying the fixed-time consensus of the multi-agent-based supply chain networks.…”