Adaptive backstepping synchronization for networked Lagrangian systems

Abstract

A decentralized control law using a backstepping scheme is proposed to deal with a leader follower multiple robots structure. Based on graph theory and Laplacian, the coordination strategy combines the leader follower control with the decentralized control. In fact, in the proposed approach, each follower robot only needs the information exchange with its connected neighbors and does not assume the existence of direct communication channel with the leader, which mitigate the implementation cost, mainly when the cooperative robots number increases. The objective of the designed control law is to synchronize positions and velocities of multiple followers interconnected via the neighbor-based rule with respect to the leader's state. The proposed strategy is further extended to adaptive neural network coordination.The performance of synchronization control system and the nonlinear stability are derived by Lyapunov method. Simulations were performed to demonstrate the effectiveness of the proposed synchronization control approach. General TermsSynchronization and cooperative robot control.

Distributed adaptive tracking backstepping control in networked nonidentical Lagrange systems

“…By backstepping approach, the appropriate Lyapunov function can be redesigned and selected carefully; consequently, the track control algorithm can be designed. Though the leader's velocityq 0 and accelerationq 0 are accessible to every follower; in contrast to the existing algorithms in [17,18,26,27], the proposed control algorithm for the general networked Lagrange systems with uncertain parameters shows that only a subgroup of the followers have access to q 0 .…”

“…It is a common requirement in the existing literatures [17,18,26,27,30]. In contrast to the control algorithms requiring q 0 in [17,18,26,27,30], the designed control algorithm (3) illustrate that only a subgroup of the followers have access to leader's position q 0 , and each follower can only get its neighbors' position information.…”

“…In addition, the benefits of the proposed algorithms can be summarized as the following three points: To begin with, compared with the tracking or synchronization Lagrange systems with undirected graph [8,9,12,16,27], the proposed techniques can deal with tracking control under general directed graph with a spanning tree. Moreover, in contrast to the tracking control algorithms with measuring the neighbors' both positions and velocities [9,17,19], the proposed control algorithm for uncertain external disturbance systems is only positions measurement of the neighbors.…”

“…Finally, it can guarantee asymptotic stability, and it also has robustness to some unmatched uncertainties [21][22][23]. The importance of the backstepping control method lies in that it can well prescribe the practical structures of the designed controller, and so it can be usually used as an effective control strategy to stabilize and synchronize underlying dynamical systems in some practical applications [23][24][25][26][27]. Recently, the backstepping methodology has been developed for the design and analysis of adaptive synchronization algorithms for networked Lagrange systems [26,27] and references therein.…”

Practical tracking synchronization of networked Lagrangian systems via pinning control

“…Refs. [4][5] further investigated adaptive backstepping-based synchronization of networked Lagrangian systems. Synchronizing networked Lagrangian systems also was studied by binary control protocols [6].…”