Optimal formation control for multi-agents systems with external disturbances

The optimal formation control for multi-agents systems with external disturbances is considered. Based on the internal model principle, a disturbance compensator is designed to reject the influence of external disturbances. An augmented system is constructed with the system and the compensator. By introducing some concatenation vectors, the single augmented system is transformed into a global multi-agents system and the quadratic performance index and output error are also transformed into the relevant format. According to the maximum principle, the formation control problem is transformed into solve a two-point boundary value problem. The obtained formation control law consists of compensation term and output feedback terms which are constructed by the solution of a Riccati matrix equation and a Sylvester matrix equation. Several numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.