Adaptive formation control of networked Lagrangian systems with a moving leader

This paper investigates the formation control problem of networked Lagrangian systems with a moving leader under the directed network topology. A special form of geometric pattern is introduced to design the desired formation for such systems. Three adaptive control strategies are proposed for the networked Lagrangian systems to achieve the formation for the cases of the absence and presence of time delays. Some simple yet general algebraic criteria are developed to ensure that the networked Lagrangian systems can always achieve desired geometric formation. Furthermore, the effect of communication time delays on the performance of formation control is numerically investigated. Finally, numerical examples are given to illustrate and visualize the effectiveness of the theoretical results.