Observer-based prescribed-time time-varying output formation-containment control of heterogeneous multi-agent systems

Abstract This paper investigates the observer-based prescribed-time time-varying output formation-containment (PT-TV-OFC) control problem for heterogeneous multi-agent systems in which the different agents have different state dimensions. The system comprises one tracking leader, multiple formation leaders, and followers, where two types of leaders are used to generate a reference trajectory for movement and achieve specific formation, respectively. Firstly, a prescribed-time dynamics observer is constructed for the formation leaders to estimate the tracking leader’s dynamic model and state. On this basis, a prescribed-time control protocol is designed for the formation leaders to achieve time-varying output formation. Then, a prescribed-time convex hull observer is designed for the followers to estimate information regarding the convex hull formed by the formation leaders. Using the estimated convex hull information, a prescribed-time containment control protocol is designed to ensure the followers converge into the convex hull. Furthermore, using Lyapunov stability theory, the stability of systems is proved in detail, which implies that the heterogeneous multi-agent systems can achieve PT-TV-OFC control. Finally, numerical simulations validate the feasibility of the theoretical results.