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Model-Free Practical Cooperative Control for Diffusively Coupled Systems

Miel Sharf, Anne Koch, Daniel Zelazo, Frank Allgöwer

TL;DR

A data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $\epsilon$-neighborhood of the desired formation with the introduced scheme based on the assumption of passive systems.

Abstract

In this paper, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $ε$-neighborhood of the desired formation. The controller is comprised of a fixed controller with an adjustable gain on each edge. Via passivity theory and network optimization we not only prove that there exists a gain attaining the desired formation control goal, but we present a data-based method to find an upper bound on this gain. Furthermore, by allowing for additional experiments, the conservatism of the upper bound can be reduced via iterative sampling schemes. The introduced scheme is based on the assumption of passive systems, which we relax by discussing different methods for estimating the systems' passivity shortage, as well as applying transformations passivizing them. Finally, we illustrate the developed model-free cooperative control scheme with a case study.

Model-Free Practical Cooperative Control for Diffusively Coupled Systems

TL;DR

A data-based controller design framework for diffusively coupled systems with guaranteed convergence to an -neighborhood of the desired formation with the introduced scheme based on the assumption of passive systems.

Abstract

In this paper, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an -neighborhood of the desired formation. The controller is comprised of a fixed controller with an adjustable gain on each edge. Via passivity theory and network optimization we not only prove that there exists a gain attaining the desired formation control goal, but we present a data-based method to find an upper bound on this gain. Furthermore, by allowing for additional experiments, the conservatism of the upper bound can be reduced via iterative sampling schemes. The introduced scheme is based on the assumption of passive systems, which we relax by discussing different methods for estimating the systems' passivity shortage, as well as applying transformations passivizing them. Finally, we illustrate the developed model-free cooperative control scheme with a case study.

Paper Structure

This paper contains 13 sections, 14 theorems, 20 equations, 6 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background: Network Optimization and Passivity in Cooperative Control
  3. Diffusively Coupled Systems and Steady-State Relations
  4. Maximum Equilibrium-Independent Passivity and the Network Optimization Framework
  5. Problem Formulation
  6. Practical Formation Control with Uniform Gains
  7. Theory
  8. Data-Driven Determination of Gains
  9. Iterative Practical Formation Control: Applying Different Gains on Different Edges
  10. Case Study: Velocity Coordination in Vehicles with Drag and Exogenous Forces
  11. Conclusions and Future Work
  12. Proving Proposition \ref{['prop.MEIPFromObscureModel']}
  13. Proving Theorem \ref{['thm.DerivativeFreeConvergence']}.

Key Result

Theorem 1

Consider the diffusively coupled network $(\mathcal{G},\Sigma,\Pi)$. Assume all agents $\Sigma_i$ are MEIP, and all controllers $\Pi_e$ are output-strictly MEIP (or vice versa). Let $k_i,\gamma_e,k$ and $\gamma$ be the steady-state relations of $\Sigma_i,\Pi_e,\Sigma$ and $\Pi$ accordingly, and let

Figures (6)

  • Figure 1: Block-diagram of the diffusively-coupled network $(\Sigma, \Pi, \mathcal{G})$.
  • Figure 2: Block-diagram of the diffusively-coupled network $(\Sigma, \Pi, \mathcal{G},A)$.
  • Figure 3: Passivation of a passivity-short agent using feedback.
  • Figure 4: Experimental setup of the closed-loop experiment for estimating $m_i$ as used in Algorithm \ref{['alg.MEIPExperimentAndEstimate']}.
  • Figure 5: Experiment results for vehicle case study.
  • ...and 1 more figures

Theorems & Definitions (41)

  • Definition 1
  • Remark 1
  • Definition 2
  • Definition 3: Burger2014
  • Theorem 1: Burger2014
  • Example 1
  • Proposition 1
  • Lemma 1
  • proof
  • Theorem 2
  • ...and 31 more