Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Optimal Output Consensus Control of Heterogeneous Multi-Agent Systems with Safety Constraints

Ji Ma, Shu Liang, Yiguang Hong

TL;DR

A novel dynamic distributed optimal safe consensus protocol to simultaneously achieve safety requirements and output optimal consensus is developed, which adopts a mild assumption on the dynamics of multiagent systems (MASs) by using the transmission zeros condition.

Abstract

In this paper, we develop a novel dynamic distributed optimal safe consensus protocol to simultaneously achieve safety requirements and output optimal consensus. Specifically, we construct a distributed projection optimization algorithm with an expanding constraint set in the decision-making layer, while we propose a reference tracking safety controller to ensure that each agent's output remains within a shrinking safety set in the control layer.We also establish the convergence and safety analysis of the closed-loop system using the small-gain theorem and time-varying control barrier function (CBF) theory, respectively. Besides, unlike previous works on distributed optimal consensus, our approach does not require prior knowledge of the local objective or gradient function and adopts a mild assumption on the dynamics of multiagent systems (MASs) by using the transmission zeros condition.

Distributed Optimal Output Consensus Control of Heterogeneous Multi-Agent Systems with Safety Constraints

TL;DR

A novel dynamic distributed optimal safe consensus protocol to simultaneously achieve safety requirements and output optimal consensus is developed, which adopts a mild assumption on the dynamics of multiagent systems (MASs) by using the transmission zeros condition.

Abstract

In this paper, we develop a novel dynamic distributed optimal safe consensus protocol to simultaneously achieve safety requirements and output optimal consensus. Specifically, we construct a distributed projection optimization algorithm with an expanding constraint set in the decision-making layer, while we propose a reference tracking safety controller to ensure that each agent's output remains within a shrinking safety set in the control layer.We also establish the convergence and safety analysis of the closed-loop system using the small-gain theorem and time-varying control barrier function (CBF) theory, respectively. Besides, unlike previous works on distributed optimal consensus, our approach does not require prior knowledge of the local objective or gradient function and adopts a mild assumption on the dynamics of multiagent systems (MASs) by using the transmission zeros condition.
Paper Structure (6 sections, 2 theorems, 7 equations)

This paper contains 6 sections, 2 theorems, 7 equations.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries and Problem Formulation
  3. Graph theory
  4. Control Barrier Function
  5. Problem formulation
  6. Detailed explanations of the challenge

Key Result

Lemma II.1

Let $h(x,t)$ be a time-varying CBF for the system linear sys with $h(x(0),0)\geq0$. Define where $\alpha(s)$ is a class $\mathcal{K}$ function satisfying $\alpha(s)=as,~s\geq0$ for some positive constant $a$. Then $K(x,t)$ is Lipschitz in $x\in \mathbb{R}^n$. Moreover, the CBF $h(x,t)\geq 0$, for any controller $u\in K(x,t)$ in the system linear sys and all $t\geq0$.

Theorems & Definitions (10)

  • Definition II.1
  • Lemma II.1
  • Remark II.1
  • Remark II.2
  • Remark II.3
  • Remark II.4
  • Lemma II.2
  • proof
  • Remark II.5
  • Example II.1