Guaranteed cost synchronization for second-order discrete-time multi-node networks with switching transmission topologies and cost limitations

Xinli Yin,Luogeng Tian,Zhong Wang,Kunyu Yang,Bailong Yang

doi:10.1177/0020294021989741

Abstract

The guaranteed cost synchronization control for discrete-time second-order leader-following multi-node networks with varying transmission topologies and cost limitations is investigated. First, the control law and its cost function are proposed to balance the tradeoff between the synchronization regulation and the control cost. Then, we derive the sufficient conditions without cost limitations to achieve guaranteed cost synchronization with varying transmission topologies, where the dimensions of matrix variables do not rely on the number of nodes. In addition, we calculate an upper bound on the cost consumption index, which is a function of the initial conditions. Moreover, guaranteed cost synchronization criteria are formulated for control with cost limitations, which are involved by establishing the relation between the cost limitation and the upper bound on the cost consumption index. Numerical simulation experiments were conducted to validate the theoretical results.

Highlights

As a basic problem in multi-node networks (MNNs), synchronization has received increasing attention mostly by its potential to handle problems such as multi-vehicle formation control,1–3 design of sensor networks,4–7 and rendezvous problems.8–10 Various node synchronization problems in MNNs have been addressed considering first- and second-order dynamics, where the transmission topology can be either leaderless or leader-following
For discrete-time MNN synchronization with cost limitations, guaranteed cost synchronization sufficient criteria are derived, in which we determine the control parameters that relate the cost limitations and the upper bound on the cost function
In Zhou et al.34 and Wang et al.,35 a different upper bound on the cost consumption index was reported, and the discrete-time MNNs did not consider cost limitations in those studies

Summary

Introduction

As a basic problem in multi-node networks (MNNs), synchronization has received increasing attention mostly by its potential to handle problems such as multi-vehicle formation control,1–3 design of sensor networks,4–7 and rendezvous problems.8–10 Various node synchronization problems in MNNs have been addressed considering first- and second-order dynamics, where the transmission topology can be either leaderless or leader-following. A guaranteed cost synchronization control law and a cost consumption index function are presented for discrete-time MNN with varying transmission topologies, where the tradeoff between synchronization regulation performance and control consumption cost is considered. Let a second-order discrete-time MNN consist of a group of N linear identical nodes, which are modeled as vertices in transmission topology graph G: Root node 1 is represented as a leader, and the others correspond to

Results

Conclusion