The discrete-time double-integrator consensus problem is addressed for multi-agent systems with directed switching proximity topologies and input constraints. Some model predictive control protocols are developed to achieve stable consensus under the condition that the proximity graph has a directed spanning tree and the sampling period is sufficiently small. Moreover, the control horizon is extended to larger than one, which endows sufficient degrees of freedom to accelerate the convergence to consensus. Numerical simulations are conducted to show the effectiveness of the control algorithm.
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Cheng et al. (2014) studied this question.
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