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Stabilizing scheduling logic for networked control systems under limited capacity and lossy communication networks

Anubhab Dasgupta

TL;DR

This work tackles stabilizing networked control systems with capacity-constrained and lossy communications by modeling each plant-controller pair as a switching subsystem and encoding network access as a graph with vertices representing which $M$ plants are in closed-loop. A contractive cycle on this graph, parameterized by positive integers $T_{v_k}$ (the $T$-factors), yields a tractable condition—expressed as a negative cycle metric $ar{Z}_i(c)<0$ across all plants—for guaranteeing global asymptotic stability under all admissible data-loss patterns. The authors derive an algorithm to design the stabilizing scheduling logic from such a cycle, and provide a constructive sufficient condition for the existence of contractive cycles via partitioning the plant set, along with LMIs-based methods to compute Lyapunov/ inter-mode scalars and $T$-factors. A numerical example demonstrates the approach's viability, computing $N=5$, $M=2$, and providing a concrete contractive cycle with associated $T$-factors that achieves GAS under burst losses. The results offer a static, offline scheduling solution applicable to safety-critical CPS domains, with potential extensions to co-design of gains, continuous-time systems, and probabilistic packet drops.

Abstract

In this paper we address the problem of designing scheduling logic for stabilizing Networked Control Systems (NCSs) with plants and controllers remotely-located over a limited capacity communication network subject to data losses. Our specific contributions include characterization of stability under worst case data loss using an inequality associated with a cycle on a graph. This is eventually formulated as a feasibility problem to solve for certain parameters (\(T\)-factors) used to design a periodic scheduling logic. We show that given a solution to the feasibility problem, the designed scheduling logic guarantees \emph{global asymptotic stability} for all plants of the network under all admissible data losses. We also derive sufficient conditions on the number of plants and the capacity of the network for the existence of a solution to the feasibility problem. Given that a sufficient condition is satisfied, we discuss the procedure to obtain the feasible \(T\)-factors. We use tools from switched systems theory and graph theory in this work. A numerical experiment is provided to verify our results.

Stabilizing scheduling logic for networked control systems under limited capacity and lossy communication networks

TL;DR

This work tackles stabilizing networked control systems with capacity-constrained and lossy communications by modeling each plant-controller pair as a switching subsystem and encoding network access as a graph with vertices representing which plants are in closed-loop. A contractive cycle on this graph, parameterized by positive integers (the -factors), yields a tractable condition—expressed as a negative cycle metric across all plants—for guaranteeing global asymptotic stability under all admissible data-loss patterns. The authors derive an algorithm to design the stabilizing scheduling logic from such a cycle, and provide a constructive sufficient condition for the existence of contractive cycles via partitioning the plant set, along with LMIs-based methods to compute Lyapunov/ inter-mode scalars and -factors. A numerical example demonstrates the approach's viability, computing , , and providing a concrete contractive cycle with associated -factors that achieves GAS under burst losses. The results offer a static, offline scheduling solution applicable to safety-critical CPS domains, with potential extensions to co-design of gains, continuous-time systems, and probabilistic packet drops.

Abstract

In this paper we address the problem of designing scheduling logic for stabilizing Networked Control Systems (NCSs) with plants and controllers remotely-located over a limited capacity communication network subject to data losses. Our specific contributions include characterization of stability under worst case data loss using an inequality associated with a cycle on a graph. This is eventually formulated as a feasibility problem to solve for certain parameters (-factors) used to design a periodic scheduling logic. We show that given a solution to the feasibility problem, the designed scheduling logic guarantees \emph{global asymptotic stability} for all plants of the network under all admissible data losses. We also derive sufficient conditions on the number of plants and the capacity of the network for the existence of a solution to the feasibility problem. Given that a sufficient condition is satisfied, we discuss the procedure to obtain the feasible -factors. We use tools from switched systems theory and graph theory in this work. A numerical experiment is provided to verify our results.

Paper Structure

This paper contains 20 sections, 8 theorems, 42 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Preliminaries
  4. Switched system modelling
  5. Graph theoretic representation of the NCS
  6. Main results
  7. Proof:
  8. Proof:
  9. On designing a contractive cycle
  10. Sufficient condition for the existence of a contractive cycle
  11. Proof:
  12. Proof:
  13. Numerical example
  14. Acknowledgement
  15. Concluding remarks
  16. ...and 5 more sections

Key Result

Theorem 1

Consider the NCS with limited capacity under data losses as described in section s:prob_stat. Let the matrices $A_i$, $B_i$, $K_{i}$ be given for $i=1,2,\ldots,N$ along with the constants $M$ and $\ell$. If there exists a cycle satisfying the condition in e:contractive-sol-2, then there exists a sch

Figures (2)

  • Figure 1: Plot for $\left\lVert x_i(t)\right\rVert^2$ versus $t$ for all the plants $i=1,2,3,4,5$, $t \in [0,60]$
  • Figure 2: Scheduling logic $\gamma$ obtained from Algorithm \ref{['algo:scheduling_policies-sol-2']}

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Remark 1
  • Proposition 1
  • Proposition 2
  • Corollary 1
  • ...and 1 more