Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Estimation and Control for Heterogeneous Multi-agent Systems Based on Decentralized k-hop Prescribed Performance Observers

Tommaso Zaccherini, Siyuan Liu, Dimos V. Dimarogonas

TL;DR

This work addresses robust estimation and control for heterogeneous multi-agent systems subject to bounded disturbances by introducing decentralized $k$-hop Prescribed Performance State and Input Observers that estimate states and inputs up to $k$ hops away using only $1$-hop communication. The core methods deploy a Prescribed Performance Observer (PPO) framework with nonlinear transformations to enforce predefined transient and steady-state error bounds, and a set-ISS-based controller that preserves convergence to the team objective when using estimated states. Theoretical guarantees are established for observer convergence, with a specialized input observer design that can be omitted under certain conditions, and a PPSO-based controller that bounds the ultimate tracking error in terms of the prescribed estimation accuracy. Simulations validate scalability and effectiveness in achieving consensus while maintaining strict estimation-performance bounds in a heterogeneous, disturbance-prone network.

Abstract

We propose decentralized k-hop Prescribed Performance State and Input Observers for heterogeneous multi-agent systems subject to bounded external disturbances. In the proposed input/state observer, each agent estimates the state and input of agents located two or more hops away using only local information exchanged with 1-hop neighbors, while guaranteeing that transient estimation errors satisfy predefined performance bounds. Conditions are established under which the input observer can be omitted, allowing the state observer convergence to be independent of the input estimates. Theoretical analysis demonstrates that if a closed-loop controller with full state knowledge achieves the control objective and the estimation-based closed-loop system is set-Input to State Stable (set-ISS) with respect to the goal set, then the estimated states can be used to achieve the system objective with an arbitrarily small worst-case error governed by the accuracy of the states estimates. Simulation results are provided to validate the proposed approach.

Robust Estimation and Control for Heterogeneous Multi-agent Systems Based on Decentralized k-hop Prescribed Performance Observers

TL;DR

This work addresses robust estimation and control for heterogeneous multi-agent systems subject to bounded disturbances by introducing decentralized -hop Prescribed Performance State and Input Observers that estimate states and inputs up to hops away using only -hop communication. The core methods deploy a Prescribed Performance Observer (PPO) framework with nonlinear transformations to enforce predefined transient and steady-state error bounds, and a set-ISS-based controller that preserves convergence to the team objective when using estimated states. Theoretical guarantees are established for observer convergence, with a specialized input observer design that can be omitted under certain conditions, and a PPSO-based controller that bounds the ultimate tracking error in terms of the prescribed estimation accuracy. Simulations validate scalability and effectiveness in achieving consensus while maintaining strict estimation-performance bounds in a heterogeneous, disturbance-prone network.

Abstract

We propose decentralized k-hop Prescribed Performance State and Input Observers for heterogeneous multi-agent systems subject to bounded external disturbances. In the proposed input/state observer, each agent estimates the state and input of agents located two or more hops away using only local information exchanged with 1-hop neighbors, while guaranteeing that transient estimation errors satisfy predefined performance bounds. Conditions are established under which the input observer can be omitted, allowing the state observer convergence to be independent of the input estimates. Theoretical analysis demonstrates that if a closed-loop controller with full state knowledge achieves the control objective and the estimation-based closed-loop system is set-Input to State Stable (set-ISS) with respect to the goal set, then the estimated states can be used to achieve the system objective with an arbitrarily small worst-case error governed by the accuracy of the states estimates. Simulation results are provided to validate the proposed approach.

Paper Structure

This paper contains 12 sections, 6 theorems, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Setting
  3. Disagreement dynamics
  4. Disagreement vector and problem reformulation
  5. Prescribed Performance Observer
  6. $k$-hop Prescribed Performance State Observer
  7. $k$-hop Prescribed Performance Input Observer
  8. Input disagreement dynamics
  9. $k$-hop Prescribe Performance Input Observer design
  10. $k$-hop PPSO-Based Controller
  11. Simulations
  12. Conclusion and Future Work

Key Result

Lemma 1

If $\mathcal{G}$ is connected, then ${M}_{i}^{\text{kc}} \succ 0$ for all $i \in \mathcal{V}$ with $\mathcal{N}_{i}^{{k}\text{-hop}} \neq \emptyset$.

Figures (2)

  • Figure 1: Graphs $\mathcal{G}_C$ and $\mathcal{G}_T$, respectively in solid and dashed lines.
  • Figure 2: (a) Agents' state evolution; initial states are represented by crosses. (b) and (c) Maximum absolute estimation error and estimation disagreement on Agent 4's state and input. The performance bounds are represented by dashed lines.

Theorems & Definitions (19)

  • Lemma 1: 11187218
  • Remark 1
  • Lemma 2
  • proof
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • Remark 5
  • ...and 9 more