Sampled-Data Consensus for Networked Euler-Lagrange Systems With Differentiable Scaling Functions

This paper is concerned with the sampled-data consensus of networked Euler-Lagrange systems. The Euler-Lagrange system has enormous advantages in analyzing and designing dynamical systems. Yet, some problems arise in the Euler-Lagrange equation-based control laws when they contain sampled-data feedback. The control law differentiates the discontinuous sampled-data signals to generate its control input. In this process, infinities in the control input are inevitable. The main goal of this work is to eliminate these infinities. To reach this goal, a class of differentiable scaling functions is designed to replace the conventional zero-order-hold and ensure a smooth transition between sampled states. The scaling functions work as multipliers on the sampled-data signals to make them differentiable, hence avoid the infinities. A consensus criterion compatible with the differentiable scaling functions is also obtained. It is shown in numerical examples that the proposed differentiable scaling functions approach both eliminates the infinities and ensures consensus under the criterion.