A Continuation Method for Large-Scale Modeling and Control: From ODEs to PDE, a Round Trip

Continuification Control of Large-Scale Multiagent Systems in a Ring

“…By making the kinematic assumption widely used in the literature [30] (that is, neglecting Fig. 1: Continuification-based control approach used in this paper, inspired by [21].…”

“…We assume the multiagent system of interest to be described by a large set of N coupled ordinary differential equations (ODEs), and adopt an approach based on continuification 1 (or continuation) [21]. We describe next how each of the four steps depicted in Fig.…”

“…Inspired from the paradigm proposed in [21] (see Fig. 1), we adopt a continuification approach in which a macroscopic model, derived from the agents' dynamics, is used to design a control strategy at the macroscopic level.…”

“…We propose a mathematical proof of convergence at the macroscopic level, and then we discretize the control action to obtain the required control inputs acting on the individual agents. In contrast with [21], the microscopic control inputs are obtained by spatially sampling the macroscopic control action at the agents' positions. Theoretical derivations are complemented by numerical simulations validating the effectiveness and robustness of the proposed strategy.…”

“…Here, we use the term continuification instead of continuation, used in[21], to distinguish this procedure from the parametric continuation of dynamical systems.This article has been accepted for publication in IEEE Control Systems Letters. This is the author's version which has not been fully edited and content may change prior to final publication.…”