# Global optimal consensus for discrete-time multi-agent systems with bounded controls

## Abstract

In this paper, we consider the global optimal consensus problem for discrete-time multi-agent systems with bounded control protocols over xed undirected communication networks. Each agent is described by a discrete-time single integrator and endowed with a quadratic objective function which is private to itself. For each agent, we develop two bounded distributed protocols: bounded proportional-integral (PI) protocol and bounded integral (I) protocol, based on information receiving from its neighboring agents through the communication network and the gradient of its own objective function. We show that the proposed bounded distributed protocols with properly chosen parameters solve the global optimal consensus problem if the communication network is connected, i.e., the multi-agent system achieves consensus at a state that minimizes the sum of the objective functions of all agents. The theoretical results are illustrated by numerical simulations.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1489195

- Report Number(s):
- PNNL-SA-123639

Journal ID: ISSN 0005-1098

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Automatica

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: C; Journal ID: ISSN 0005-1098

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Consensus, multi-agent system, optimal control

### Citation Formats

```
Yang, Tao, Wan, Yan, Wang, Hong, and Lin, Zongli.
```*Global optimal consensus for discrete-time multi-agent systems with bounded controls*. United States: N. p., 2018.
Web. doi:10.1016/j.automatica.2018.08.017.

```
Yang, Tao, Wan, Yan, Wang, Hong, & Lin, Zongli.
```*Global optimal consensus for discrete-time multi-agent systems with bounded controls*. United States. doi:10.1016/j.automatica.2018.08.017.

```
Yang, Tao, Wan, Yan, Wang, Hong, and Lin, Zongli. Thu .
"Global optimal consensus for discrete-time multi-agent systems with bounded controls". United States. doi:10.1016/j.automatica.2018.08.017.
```

```
@article{osti_1489195,
```

title = {Global optimal consensus for discrete-time multi-agent systems with bounded controls},

author = {Yang, Tao and Wan, Yan and Wang, Hong and Lin, Zongli},

abstractNote = {In this paper, we consider the global optimal consensus problem for discrete-time multi-agent systems with bounded control protocols over xed undirected communication networks. Each agent is described by a discrete-time single integrator and endowed with a quadratic objective function which is private to itself. For each agent, we develop two bounded distributed protocols: bounded proportional-integral (PI) protocol and bounded integral (I) protocol, based on information receiving from its neighboring agents through the communication network and the gradient of its own objective function. We show that the proposed bounded distributed protocols with properly chosen parameters solve the global optimal consensus problem if the communication network is connected, i.e., the multi-agent system achieves consensus at a state that minimizes the sum of the objective functions of all agents. The theoretical results are illustrated by numerical simulations.},

doi = {10.1016/j.automatica.2018.08.017},

journal = {Automatica},

issn = {0005-1098},

number = C,

volume = 97,

place = {United States},

year = {2018},

month = {11}

}