Cascade Super-Twisting Observer for Linear Multi-Agent Systems Without Communication

The paper addresses the consensus problem (i.e., the agreement of phase vectors) for a multi-agent system consisting of identical linear agents. The study focuses on the case where there is no communication between agents, meaning there is no exchange of information, and agent control is achieved through the agents’ own sensors, providing incomplete information about the phase vector of the agent and its neighbors, with the information possibly being noisy. To solve this problem, a linear protocol based on observer data for systems under uncertainty is proposed. Cascade observers based on the “super-twisting” method are suggested as such observers. Sufficient conditions for the existence of a controller are obtained, where the observation error converges to zero under limited disturbances. An example illustrating the proposed approach is provided.