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Observer-based Control of Multi-agent Systems under STL Specifications

Tommaso Zaccherini, Siyuan Liu, Dimos V. Dimarogonas

Abstract

This paper proposes a decentralized controller for large-scale heterogeneous multi-agent systems subject to bounded external disturbances, where agents must satisfy Signal Temporal Logic (STL) specifications requiring cooperation among non-communicating agents. To address the lack of direct communication, we employ a decentralized k-hop Prescribed Performance State Observer (k-hop PPSO) to provide each agent with state estimates of those agents it cannot communicate with. By leveraging the performance bounds on the state estimation errors guaranteed by the k-hop PPSO, we first modify the space robustness of the STL tasks to account for these errors, and then exploit the modified robustness to design a decentralized continuous-time feedback controller that ensures satisfaction of the STL tasks even under worst-case estimation errors. A simulation result is provided to validate the proposed framework.

Observer-based Control of Multi-agent Systems under STL Specifications

Abstract

This paper proposes a decentralized controller for large-scale heterogeneous multi-agent systems subject to bounded external disturbances, where agents must satisfy Signal Temporal Logic (STL) specifications requiring cooperation among non-communicating agents. To address the lack of direct communication, we employ a decentralized k-hop Prescribed Performance State Observer (k-hop PPSO) to provide each agent with state estimates of those agents it cannot communicate with. By leveraging the performance bounds on the state estimation errors guaranteed by the k-hop PPSO, we first modify the space robustness of the STL tasks to account for these errors, and then exploit the modified robustness to design a decentralized continuous-time feedback controller that ensures satisfaction of the STL tasks even under worst-case estimation errors. A simulation result is provided to validate the proposed framework.
Paper Structure (11 sections, 1 theorem, 21 equations, 2 figures)

This paper contains 11 sections, 1 theorem, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Setting
  3. Signal Temporal Logic (STL)
  4. Multi-agent systems
  5. Cluster-induced graph
  6. Individual/collaborative tasks
  7. State observer
  8. Observer-based Task Satisfaction
  9. Decentralized Observer-based Controller
  10. Simulation
  11. Conclusion and Future Work

Key Result

lemma 1

$\Gamma_{\psi_i}(t)$ is a prescribed performance function as per Definition definition of prescribed performance function.

Figures (2)

  • Figure 1: Graphs $\mathcal{G}_C$ and $\mathcal{G}_T$, respectively in solid and dashed lines. The shadow areas represent the induced clusters, i.e., $\mathcal{C}_1$ and $\mathcal{C}_2$.
  • Figure 2: (a) State and estimation trajectories; initial states are represented by crosses, terminal state by dots. The pink and green areas represent the evolution of the state uncertainties with time; the gray circles are the target areas of the individual tasks. (b) Evolution of the norm of the state estimation errors performed by agent $2$; the dashed lines are the prescribed performance functions of the $k$-hop PPSO. (c) Minimum estimated robustness of $\phi_2$. (d) Robustness of tasks in $\phi_2$ with true state information.

Theorems & Definitions (11)

  • definition 1
  • definition 2
  • remark 1
  • remark 2
  • definition 3: zaccherini2025robustestimationcontrolheterogeneous
  • remark 3
  • remark 4
  • lemma 1
  • remark 5
  • remark 6
  • ...and 1 more