PD-like Consensus Tracking Algorithm for Discrete Multi-Agent Systems with Time-Varying Reference State Under Binary-Valued Communication

In this paper, a new consensus tracking control algorithm is proposed for discrete multi-agent systems under binary communication with noise and a time-varying reference state. Unlike previous studies, the leader’s reference state is time-varying and convergent. Each agent estimates its neighbors’ states using a recursive projection algorithm based on noisy binary-valued information. The controller design incorporates both the error between the current and estimated states and the rate of change of the estimated state, resulting in a proportional–derivative-like algorithm (PD-like algorithm). The algorithm achieves consensus tracking with a convergence rate of O(1/tε) under certain conditions. Finally, numerical simulations demonstrate the algorithm’s effectiveness and validate the theoretical results.