Cooperative Adaptive Control for Systems with Second-Order Nonlinear Dynamics

In Chap. 8, we designed cooperative adaptive controllers for multi-agent systems having first-order nonlinear dynamics. In this chapter, we study adaptive control for cooperative multi-agent systems having second-order nonidentical nonlinear dynamics. The study of second-order and higher-order consensus is required to implement synchronization in most real-world applications such as formation control and coordination among unmanned aerial vehicles (UAVs), where both position and velocity must be controlled. Note that Lagrangian motion dynamics and robotic systems can be written in the form of second-order systems. Moreover, second-order integrator consensus design (as opposed to first-order integrator node dynamics) involves more details about the interaction between the system dynamics and control design problem and the graph structure as reflected in the Laplacian matrix. As such, second-order consensus is interesting because there one must confront more directly the interface between control systems and communication graph structure.