Robust optimal distance‐based formation control of uncertain nonlinear agents over directed topologies

Abstract This paper studies a formation control problem with distance constraints for nonlinear agents with uncertainties. Controlling an edge is assigned to only one of its incident agents. Directed graph theory is used to model the desired formation topology. The method is distributed, applicable to uncertain nonlinear agents, and is based on robust‐optimal control. The proposed control scheme is based on integral sliding mode control (ISMC) combined with the state‐dependent Riccati equation (SDRE) method. The method minimizes a weighted cost function that includes the formation and control input costs for a given mission while compensating for the effect of uncertainties. A rigorous Lyapunov stability analysis proved the local asymptotic convergence of the agents to the desired distances. We use the concept of mathematical induction to show that the formation of all agents is stable. Detailed simulation results are included to verify the proposed control scheme.