Bipartite Consensus for Second-Order Multiagent Systems With Matrix-Weighted Signed Network

Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network's consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.

Hierarchical prescribed-time bipartite consensus for multiple Euler-Lagrange systems with input-to-output redundancy and directed matrix-weighted signed graph

This paper studies the prescribed-time bipartite consensus problem for multiple Euler-Lagrange systems (MELSs) under directed matrix-weighted signed graph, in which input-to-output redundancy, external disturbances and uncertain dynamic terms have been taken into consideration. Firstly, this paper proposes the prescribed-time hierarchical control (PTHC) algorithm to tackle the aforesaid issue. It is worth pointing out that the convergence time can be arbitrarily prescribed based on actual engineering needs. Then, the corresponding sufficient conditions for achieving the prescribed-time bipartite consensus are obtained by invoking Lyapunov stability analysis. Eventually, the numerical simulation results are performed, which vividly reflect the effectiveness and feasibility of the developed control algorithm.

Modeling multi-opinion propagation in complex systems with heterogeneous relationships via Potts model on signed networks

This paper investigates how the heterogenous relationships around us affect the spread of diverse opinions in the population. We apply the Potts model, derived from condensed matter physics on signed networks, to multi-opinion propagation in complex systems with logically contradictory interactions. Signed networks have received increasing attention due to their ability to portray both positive and negative associations simultaneously, while the Potts model depicts the coevolution of multiple states affected by interactions. Analyses and experiments on both synthetic and real signed networks reveal the impact of the topology structure on the emergence of consensus and the evolution of balance in a system. We find that, regardless of the initial opinion distribution, the proportion and location of negative edges in the signed network determine whether a consensus can be formed. The effect of topology on the critical ratio of negative edges reflects two distinct phenomena: consensus and the multiparty situation. Surprisingly, adding a small number of negative edges leads to a sharp breakdown in consensus under certain circumstances. The community structure contributes to the common view within camps and the confrontation (or alliance) between camps. The importance of inter- or intra-community negative relationships varies depending on the diversity of opinions. The results also show that the dynamic process causes an increase in network structural balance and the emergence of dominant high-order structures. Our findings demonstrate the strong effects of logically contradictory interactions on collective behaviors, and could help control multi-opinion propagation and enhance the system balance.