Learning‐based containment control in the absence of leaders' information

Abstract

This article considers the containment control problem of continuous‐time dynamic agents without leaders' state information. The leaders have first‐ and second‐order dynamics, respectively, while first‐order dynamics always govern the followers. Each agent has inherent nonlinear dynamics and can only measure the output information of its neighbors. The output of each leader is expressed as the product of an unknown coefficient and a position‐like state, while the output of each follower is equal to its position‐like state. To stabilize the position‐like states of the followers to the convex hull spanned by leaders, the unknown coefficients are asymptotically tracked by leveraging reinforcement learning based on the inherent dynamics and the output information. Two distributed learning‐based containment protocols are proposed, respectively. It is proved that if the directed communication topology has a spanning forest and certain conditions in terms of the inherent nonlinear dynamics are satisfied, then the proposed controllers with proper control gains solve the containment control problem asymptotically under arbitrary initial states. An exciting conclusion is that the learning algorithms' convergence rate plays an important role in achieving containment control. Numerical simulations are performed to validate the effectiveness of the obtained theoretical results.