Partial differential equation‐based multiagent systems formation‐containment control with α‐leader input delay

This paper investigates the formation‐containment problem for a multiagent system, where the agents are classified into containment followers, formation leaders, anchor leader, and α$$ \alpha $$‐leader. The α$$ \alpha $$‐leader stabilizes formation leaders to desired formation deployment, while formation leaders adopt local state feedback distributed control law without desired formation position and the anchor leader fixes to its desired position. The containment followers adopted consensus distributed control law and converge to the convex hull spanned by the leader agents. Formation leaders' distributed control law parameters are proposed based on the discrete form of the desired partial differential equation (PDE) formation deployment, which is stabilized by the α$$ \alpha $$‐leader agent and transited by communication topology. Based on its neighbor leader agent's delay state, α$$ \alpha $$‐leader control law designed an integral‐type delay‐compensated control law by the backstepping method and the equivalence principle. In order to prove the rightness and existence of delay‐compensated control law, the well‐posedness of kernel functions are given by C0$$ {C}_0 $$ semigroup perturbation theory and solutions in the sense of distribution. Finally, a simulation example is given to verify the theoretical results.