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Communication-Aware Dissipative Control for Networks of Heterogeneous Nonlinear Agents

Ingyu Jang, Leila J. Bridgeman

TL;DR

Problem: designing controllers for networks of heterogeneous nonlinear agents with sparse communication while ensuring performance and robustness is NP-hard. Approach: a dissipativity-based, sparsity-promoting framework identifies an optimal sparse topology using weighted $\ell_1$ penalties or ADMM with a cardinality term, and iteratively solves a convexified version of the structured optimal control problem. Findings: numerical experiments on networks with uncertain and unstable dynamics demonstrate sparse, practically meaningful communication topologies that preserve closed-loop stability and deliver moderate performance. Significance: the approach enables scalable, communication-efficient control of large-scale networks and can be extended from full-state feedback to dynamic output-feedback in future work.

Abstract

Communication-aware control is essential to reduce costs and complexity in large-scale networks. However, it is challenging to simultaneously determine a sparse communication topology and achieve high performance and robustness. This work achieves all three objectives through dissipativity-based, sparsity-promoting controller synthesis. The approach identifies an optimal sparse structure using either weighted l1 penalties or alternating direction methods of multipliers (ADMM) with a cardinality term, and iteratively solves a convexified version of the NP hard structured optimal control problem. The proposed methods are demonstrated on heterogeneous networks with uncertain and unstable agents.

Communication-Aware Dissipative Control for Networks of Heterogeneous Nonlinear Agents

TL;DR

Problem: designing controllers for networks of heterogeneous nonlinear agents with sparse communication while ensuring performance and robustness is NP-hard. Approach: a dissipativity-based, sparsity-promoting framework identifies an optimal sparse topology using weighted penalties or ADMM with a cardinality term, and iteratively solves a convexified version of the structured optimal control problem. Findings: numerical experiments on networks with uncertain and unstable dynamics demonstrate sparse, practically meaningful communication topologies that preserve closed-loop stability and deliver moderate performance. Significance: the approach enables scalable, communication-efficient control of large-scale networks and can be extended from full-state feedback to dynamic output-feedback in future work.

Abstract

Communication-aware control is essential to reduce costs and complexity in large-scale networks. However, it is challenging to simultaneously determine a sparse communication topology and achieve high performance and robustness. This work achieves all three objectives through dissipativity-based, sparsity-promoting controller synthesis. The approach identifies an optimal sparse structure using either weighted l1 penalties or alternating direction methods of multipliers (ADMM) with a cardinality term, and iteratively solves a convexified version of the NP hard structured optimal control problem. The proposed methods are demonstrated on heterogeneous networks with uncertain and unstable agents.

Paper Structure

This paper contains 1 section, 3 figures, 1 table.

Table of Contents

  1. Conclusion

Figures (3)

  • Figure 2: performance index.
  • Figure 3: Pole locations for ${\sum}_{i{,}j}\text{card}(\left\| \mathbf{K}_{ij} \right\|_F){=}24$; "(unc.)" denotes poles from randomly generated uncertain dynamics of each agent, "(vert.)" denote poles from 256 vertices of polytopic uncertainty. The red dashed line indicates the boundary of the stable region.
  • Figure 4: Block structure of $\mathbf{K}$ when ${\sum}_{i{,}j}\text{card}(\left\| \mathbf{K}_{ij} \right\|_F){=}50$; Green blocks denote nonzero blocks of $\mathbf{K}$. From left to right, the subfigures correspond to the results of the proposed algorithm with the weighted-$\ell_1$ norm and cardinality, lin2013design, and lian2018sparsity.