The consensus problem for multi-agent systems with input saturation is addressed in this paper. For agents with double-integrator dynamics, we first propose two consensus algorithms, respectively, for the cases with and without velocity measurements. Based on graph theory, homogeneous method and the Lyapunov stability theory, it is proved that the proposed algorithms can guarantee not only the state agreement in finite time for all the agents but also the input saturation requirement. Then, the obtained results and techniques are extended to the finite-time consensus problem for multiple mechanical systems. Numerical simulations are finally provided to verify the effectiveness of the theoretical results. neighbors of each agent are known a priori. This could be a dilemma especially when the communication scale is large, and the control input limitation is small for each agent. To solve this problem, the authors in [12] propose a consensus algorithm based on a high-order dynamic auxiliary system, which guarantees that the control input of each agent can be a priori bounded regardless of the number of its neighbors. The aforementioned works are concerned with the asymptotic convergence issue and thus cannot guarantee finite-time consensus, which, in some cases, are more desirable because of many practical and theoretical reasons [13]. Many efforts have been made towards solving finite-time consensus problems for multi-agent systems [14,15]. Although a bounded finitetime consensus algorithm is proposed in [16] to achieve the leader-following consensus behavior, the method proposed therein, however, does not work for the leaderless framework as considered in our work.On the other hand, consensus for nonlinear multi-agent systems, especially the multiple mechanical systems whose dynamics can be modeled by Euler-Lagrange equations, has also received great interest in the control community. As compared with linear multi-agent systems, consensus problem for multiple Lagrangian systems appears to be technically more challenging due mainly to the nonlinearity in the system dynamics. The authors in [17] investigate the adaptive consensus algorithms for networked Euler-Lagrange systems with coupling time delay and switching topology, while [18] considers the distributed coordination problem for multiple Lagrangian systems in the presence of parametric uncertainties. In [19], the adaptive consensus problem of networked mechanical systems with time varying delay and jointly connected topologies is investigated. In [20], the continuous coordinated tracking control algorithms of multiple heterogeneous Lagrange systems are proposed. The synchronization problem of networked Euler-Lagrange systems with unknown parameters and communication delays is addressed in [21]. In [22], the finite-time tracking algorithms are proposed for the networked Lagrange systems in the presence of bounded model uncertainties and external disturbances. None of the above-mentioned works consider the consensus with input saturation constraints, which in f...
