Consensus control with a constant gain for discrete-time binary-valued multi-agent systems based on a projected empirical measure method

This paper studies the consensus control of multiagent systems with binary-valued observations. An algorithm alternating estimation and control is proposed. Each agent estimates 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 designed control, and the estimation and control design will be repeated. For the estimation, the projected empirical measure method is proposed for the binary-valued observations. The algorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the order of the reciprocal of the holding time ( the same order as that in the case of accurate outputs ). For the consensus control, a constant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observations. And, there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agentsʼ states. Finally, the systems updated by the designed control are proved to achieve consensus and the consensus speed is faster than that in the existing literature. Simulations are given to demonstrate the theoretical results.