Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

Abstract

SUMMARYThis paper studies synchronization to a desired trajectory for multi-agent systems with second-order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov-based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second-order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller.

Robust synchronization of arrays of uncertain nonlinear second-order dynamical systems

“…In [22] the synchronization problem of uncertain second-order systems in normal form is studied. In this work the arrays have a reference system, and the connections are unidirectional.…”

“…The array may have or not a reference system; hence, the arrays considered in [21] and [22] are special cases. The nodes can be different, can be affected with external disturbances, and some parametric uncertainty is tolerated.…”

“…Two recent papers about synchronization of secondorder systems are [21] and [22]. In [21], a consensus analysis for special topologies in networks of secondorder systems is presented.…”

Robust Adaptive Cooperative Control for Formation-Tracking Problem in a Network of Non-Affine Nonlinear Agents

“…A class of nonlinear first-order multi-agent systems with external disturbances consensus problem was discussed in Ref. [7], whereas other works that involve second-order and higher order nonlinear multi-agent systems are reported in Refs. [8] and [9], respectively.…”

Distributed Task-space Tracking for Multiple Manipulators with Uncertain Dynamics and Kinematics

“…Distributed tracking problem is studied in [17] for networked Euler-Lagrange systems with a dynamic leader, and then a model-independent sliding mode controller is proposed. In [18], a continuous distributed robust tracking protocol is introduced for multiple Euler-Lagrange systems with uncertain dynamics. A distributed leaderless consensus algorithm is proposed for the networked Euler-Lagrange system without considering the gravity effect.…”