Consensus Control With a Constant Gain for Dis-crete-time Binary-valued Multi-agent Systems Based on a Projected Empirical Measure Method

摘要

This paper studies the consensus control of multi-agent systems with binary-valued observations. An algorithm al-ternating estimation and control is proposed. Each agent estim-ates the states of its neighbors based on a projected empirical measure method for a holding time. Based on the estimates, each agent designs the consensus control with a constant gain at some skipping time. The states of the system are updated by the de-signed control, and the estimation and control design will be re-peated. For the estimation, the projected empirical measure method is proposed for the binary-valued observations. The al-gorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the or-der of the reciprocal of the holding time (the same order as that in the case of accurate outputs). For the consensus control, a con-stant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observa-tions. And, there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agents' states. Finally, the systems updated by the designed control are proved to achieve consensus and the con-sensus speed is faster than that in the existing literature. Simula-tions are given to demonstrate the theoretical results.