Ameer Mulla | Searcharxiv

arXiv2025

Minimum time consensus for damped second order agents using Gr\"{o}bner basis

A problem of achieving minimum time consensus for a set of $N$ second-order LTI system agents with bounded inputs and fuel constraints is considered. Unlike our other works, here the damping effect in agent dynamics is included. First, the attainable set for each agent with fuel budget constraints is characterized, and its boundary equations are derived. Then, using the convexity property, the minimum time at which attainable sets of all agents have a non-empty intersection is computed. By applying Helly's theorem, the computation reduces to finding the minimum time to consensus and the corresponding consensus point for each of the triplets separately.

math.OC↗

arXiv2024

Minimum Time Consensus of Multi-agent System under Fuel Constraints

This work addresses the problem of finding minimum time consensus point in the state space for a set of $N$ identical double integrator agents with bounded inputs and fixed fuel budget constraint. To address the problem, characterization of the attainable set for each agent subject to bounded inputs and fixed fuel budget constraints is done. Such attainable set is shown to be a convex set. The minimum time to consensus is the least time when the attainable sets of all agents intersect and the corresponding consensus state is the point of intersection. Using Helly's theorem, it is shown that the intersection is not empty at the time when all triplets of agents exhibit a non-empty intersection. Thus, a closed-form expression for the minimum time to consensus for a triplet of agents is obtained. The calculation of minimum time consensus for each of the triplets is performed independently and is distributed evenly among $N$ agents. The overall minimum time to consensus of $N$ agents is then given by the triplet that has the greatest minimum time to consensus. In the process, the set of initial conditions for agents from which consensus is possible under these input and fuel budget constraints is also characterized.

eess.SY↗