Observer-Based Distributed Prescribed-Time Containment Control for Multiple Underactuated Unmanned Surface Vehicles with Input Saturation and Full-State Constraints

Abstract

This study solves the problem of distributed prescribed-time containment control of underactuated unmanned surface vehicles (USVs) in the presence of parametric uncertainties, unmodeled dynamics, and external environmental disturbances. Under the leader-follower approach, considering that only a subset of followers has access to the trajectory information of the virtual leaders, a novel distributed adaptive prescribed-time observer is presented. Given the general uncertainties in the USV model, an improved prescribed-time extended state observer (PTESO) is established for estimation and compensation. Then, a prescribed-time command filter and a filter compensation system are introduced to estimate the virtual control signal and address the differential explosion problem. Furthermore, a prescribed-time anti-saturation auxiliary system is proposed to address the actuator input saturation. Moreover, a prescribed-time distributed guidance protocol and a distributed control protocol are developed for each USV by employing the backstepping method and the variable transformation strategy. The use of graph theory, prescribed-time theory, and Lyapunov analysis ensures that the follower converges to the convex hull spanned by the multiple virtual leaders within a prescribed time. This approach involves dynamically adjusting the distance among USVs according to the channel width. The errors associated with the distributed adaptive observer and PTESO exhibit bounded convergence within a prescribed time. In addition, the full-state constraints have been confirmed, which implies that the containment errors, including position, velocity, and acceleration errors of the followers, can converge and remain bounded within a prescribed time. The originality of this study lies in overcoming key challenges, including general model uncertainties, actuator saturation, limited information available to follower USVs, and ensuring prescribed-time convergence. Future research can explore an event-based communication protocol to realize intermittent communication among USVs.

Keywords

Unmanned surface vehicles / Prescribed time / Distributed adaptive observer / Extended state observer / Input saturation / Full-state constraints

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