Fully Distributed Optimal Position Control of Networked Uncertain Euler–Lagrange Systems Under Unbalanced Digraphs

The distributed optimal position control problem, which aims to cooperatively drive the networked uncertain nonlinear Euler–Lagrange (EL) systems to an optimal position that minimizes a global cost function, is investigated in this article. In the case without constraints for the positions, a fully distributed optimal position control protocol is first presented by applying adaptive parameter estimation and gain tuning techniques. As the environmental constraints for the positions are considered, we further provide an enhanced optimal control scheme by applying the
$\epsilon $
-exact penalty function method. Different from the existing optimal control schemes of networked EL systems, the proposed adaptive control schemes have two merits. First, they are fully distributed in the sense without requiring any global information. Second, the control schemes are designed under the general unbalanced directed communication graphs. The simulations are performed to verify the obtained results.