Centralized Control in Networks of Underactuated Nonidentical Euler–Lagrange Systems Using a Generalised Multicoordinates Transformation

Controlling the network of underactuated Euler–Lagrange (EL) systems is challenging because of their coupled inertia matrices and time-variant control input matrices. We present generalized multi-coordinates transformation that renders the network of underactuated Euler-Lagrange dynamics in particular forms, whose mechanical properties should be preserved. The network of
$\mathbf {N}$
nonidentical Euler–Lagrange EL-systems is modeled as a weighted interconnection graph where each EL-system is a node, and the control action at each node is a function of its state and the states of its neighbors. Second, we propose an online optimally centralized control mechanism with the prime objective of energy efficiency. The result is applied to the network of underactuated vertical takeoff and landing aircraft with strong input coupling, including the effect of the weight of the rotors into the dynamical system models. In this regard, we obtain very simple and powerful state-feedback solutions.