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This paper studies practical consensus problems for continuous-time multiagent systems with heterophilous dynamics. Agents in the network tend to cease communication when they are close enough to each other inspired by the heterophily principle in social and opinion dynamics. We propose two types of state constraints on dynamical agents, in which the hard constraint refers to exogenous restrictions that rule the entire evolution of the agent behavior and the soft constraint turns out to be endogenous and only the ultimate equilibria of the agents are restricted. Sufficient conditions have been established to achieve practical consensus for both types of constrained systems. Numerical simulations show that the practical consensus time grows logarithmically, revealing a rapid convergence with respect to disagreement of initial conditions. [ABSTRACT FROM AUTHOR]

Abstract This paper presents novel fixed-time controllers for the distributed tracking of multi-agent systems with double-integrator dynamics based on the input shaping technique under directed graphs. It is assumed that there is no cycle in the directed graph with a globally reachable leader. Distributed fixed-time controllers are designed for cases with various initial conditions by placing input shapers in all communication edges in the graph. Numerical simulations and experimental studies are conducted to verify the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders' outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders' states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results. [ABSTRACT FROM AUTHOR]