Iterative learning control for impulsive multi-agent systems with varying trial lengths

Xiaokai Cao,Dong Shen,Jinrong Wang,Michal Fečkan

doi:10.15388/namc.2022.27.25475

Abstract

In this paper, we introduce iterative learning control (ILC) schemes with varying trial lengths (VTL) to control impulsive multi-agent systems (I-MAS). We use domain alignment operator to characterize each tracking error to ensure that the error can completely update the control function during each iteration. Then we analyze the system’s uniform convergence to the target leader. Further, we use two local average operators to optimize the control function such that it can make full use of the iteration error. Finally, numerical examples are provided to verify the theoretical results.

Highlights

With the development of swarm intelligence algorithms, multi-agent systems are widely used in communication networks, wireless sensor networks, and unmanned vehicles
The consensus problem is a basic problem of MAS because it has a wide range of applications in formation control, distributed estimation, and congestion control
The problem of consensus tracking of researching impulsive MAS is to study whether an agent can return to a predetermined trajectory through information exchange after being subject to external interference

Summary

Introduction

With the development of swarm intelligence algorithms, multi-agent systems are widely used in communication networks, wireless sensor networks, and unmanned vehicles. Impulsive control approach has advantage in simplicity and flexibility for such kind of systems because the standard continuous state information is not required As a consequence, this approach has been offered to study adaptive consensus and synchronization problems [22, 23] and consensus problem [5, 26] for MASs. Iterative learning control (ILC) is suitable for robots to perform trajectory tracking tasks within a limited time interval. For impulsive multi-agent systems with VTL, we first use zeros to replace nonexistent errors and consider the system’s consensus tracking of the target trajectory under the DαD-type learning law. Compared with the previous work, this paper uses the memory effect of fractional-order calculus to adjust the input of the system and combines the domain alignment operator to design an appropriate learning law to control the multi-agent system in the VTL case.

Preliminaries and problem formulation

Main results

IβD-type learning law with local average operator 2

Numerical simulation

Conclusion