Samuel Martin — Page 2

arXiv2012

Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights

In this paper, we present new results on consensus for continuous-time multi- agent systems. We introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights. Persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete- time consensus protocols. Slow divergence of reciprocal interaction weights generalizes the assumption of cut-balanced interactions. We show that under these two assumptions, the continuous-time consensus protocol succeeds: the states of all the agents converge asymptotically to a common value. Moreover, our proof allows us to give an estimate of the rate of convergence towards the consensus. We also provide two examples that make us think that both of our assumptions are tight.

math.OC↗

arXiv2011

Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices

In this paper, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart.

eess.SY↗