Consensus in Networks of Nonidentical Euler–Lagrange Systems Using P+d Controllers

Synchronization of nonlinear systems with communication delays and intermittent information exchange

“…The control scheme in Corollary 2 extends the relevant literature dealing with Euler-Lagrange systems with communication constraints (Abdessameud et al, 2014a;Chopra & Spong, 2006;Nuño et al, 2011Nuño et al, , 2013Wang, 2014, for instance) to the case where a non-zero final velocity is assigned to the team, the communication between agents is intermittent and subject to varying delays and possible packet loss, and under a directed interconnection graph that contains a spanning tree. In addition, this control scheme extends the work in Wang (2013) to the case of intermittent and delayed communication without using a centralized information on the interconnection topology.…”

“…In addition to constant delays, a virtual systems approach has been suggested in Tayebi (2011b, 2013) to account for input saturations and remove the requirements of velocity measurements. Control schemes that consider time-varying communication delays have also been proposed for some second-order nonlinear multi-agent systems in Tayebi (2011a, 2013); Abdessameud, Tayebi, and Polushin (2012) ;Erdong, Xiaolei, and Zhaowei (2008); Nuño, Sarras, and Basañez (2013), in the case of undirected interconnection graphs, and in Abdessameud, Polushin, and Tayebi (2014a) in the case of more general directed interconnection topologies.…”

A Passivity-based Controller without Velocity Measurements for the Leaderless Consensus of Euler-Lagrange Systems

“…The PBC reported here generalizes different control schemes that rely on velocity measurements, as the P+d controller, or those which do not require velocity measurements. Interestingly, the conditions on the gains (14) of the new PBCs-that do not require velocity measurements-are the same as those for the P+d controller reported in (Nuño et al, 2013b). Remark 3.…”

“…⋄ Proof. Using the properties of the Laplacian matrix, as in (Nuño et al, 2013b), it is easy to show that the time derivative of the desired energy function (8)-evaluated along (2), (12) and (13)-is given by…”

“…invoking Lemma 1 on the double integral term and following the same steps as in (Nuño et al, 2013b), it can be shown, that setting the controller's gains such that (14) is satisfied, then there exists…”