Formation–containment control for networked Euler–Lagrange systems with input saturation

This paper studies the formation–containment control problem for networked nonlinear Euler–Lagrange systems with input saturation. To realize the concurrency of leaders’ formation and followers’ containment, coordinated formation and containment control algorithms are designed, respectively, such that the formation–containment of multi-agent systems can be reached. Firstly, to handle the constraint of input saturation, a dynamic auxiliary system is introduced for each agent to obtain some auxiliary variables. Then, based on these auxiliary variables, coordinated saturated formation and containment control algorithms are designed for each leader and follower to achieve formation and containment, respectively. Note that the saturation bound of each agent in many proposed coordinated saturated control algorithms depends on the number of each agent’s neighbors, while the formation–containment system is usually large scale and each agent has many neighbors because there are multiple leaders and followers. Our proposed saturated formation–containment control algorithm has the advantage that the saturation bound of each agent is not related with the number of each agent’s neighbors. Finally, numerical simulation is given to illustrate the effectiveness of the theoretical results.