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A probabilistic algorithm for scheduling networked control systems under data losses

Anubhab Dasgupta, Darsana Udayakumar, Atreyee Kundu

TL;DR

Addresses scheduling for networked control systems with limited-bandwidth shared networks and data losses by extending a probabilistic scheduling framework to MJLS-based stability analysis. The method selects disjoint plant subsets $s_j$ with $|s_j|\le M$ and probabilities $p_j$, modeling each plant as a Markovian jump linear system with transitions driven by $p_j$ and $q$, and uses LMIs to certify stochastic stability via $P_{i_s}$, $P_{i_u}$ and stabilizing gains $K_i$ (with $K_i = Y_i P_{i_s}$). The framework generalizes lossless results ($q=0$) and provides a co-design procedure for controllers under data losses, demonstrated through two numerical examples. While effective, the work assumes a known, uniform data-loss probability across channels and suggests future work on heterogeneous or unknown loss rates and adaptive scheduling for broader applicability.

Abstract

This paper deals with the design of scheduling logics for networked control systems (NCSs) whose communication networks have limited capacity and are prone to data losses. Our contributions are twofold. First, we present a probabilistic algorithm to generate a scheduling logic that under certain conditions on the plant and the controller dynamics, the capacity of the network and the probability of data losses, ensures stochastic stability of each plant in the NCS. Second, given the plant dynamics, the capacity of the shared communication network and the probability of data losses, we discuss the design of state-feedback controllers such that our stability conditions are obeyed. Numerical examples are presented to demonstrate the results reported in this paper.

A probabilistic algorithm for scheduling networked control systems under data losses

TL;DR

Addresses scheduling for networked control systems with limited-bandwidth shared networks and data losses by extending a probabilistic scheduling framework to MJLS-based stability analysis. The method selects disjoint plant subsets with and probabilities , modeling each plant as a Markovian jump linear system with transitions driven by and , and uses LMIs to certify stochastic stability via , and stabilizing gains (with ). The framework generalizes lossless results () and provides a co-design procedure for controllers under data losses, demonstrated through two numerical examples. While effective, the work assumes a known, uniform data-loss probability across channels and suggests future work on heterogeneous or unknown loss rates and adaptive scheduling for broader applicability.

Abstract

This paper deals with the design of scheduling logics for networked control systems (NCSs) whose communication networks have limited capacity and are prone to data losses. Our contributions are twofold. First, we present a probabilistic algorithm to generate a scheduling logic that under certain conditions on the plant and the controller dynamics, the capacity of the network and the probability of data losses, ensures stochastic stability of each plant in the NCS. Second, given the plant dynamics, the capacity of the shared communication network and the probability of data losses, we discuss the design of state-feedback controllers such that our stability conditions are obeyed. Numerical examples are presented to demonstrate the results reported in this paper.
Paper Structure (5 sections, 4 theorems, 24 equations, 5 figures)

This paper contains 5 sections, 4 theorems, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Main results
  4. Numerical example
  5. Concluding remarks

Key Result

Theorem 1

Consider an NCS described in Section s:prob_stat. Let the plant dynamics, $(A_i,B_i)$, $i=1,2,\ldots,N$, the controller dynamics, $K_i$, $i=1,2,\ldots,N$, the capacity of the communication network, $M$, and the probability of data loss, $p$, be given. Each plant $i=1,2,\ldots,N$ is stochastically st where $\mathcal{P}^i = p_j(1-q)P_{i_s}+\bigl((1-p_j)+p_jq\bigr)P_{i_u}$.

Figures (5)

  • Figure 1: $\bigl(\left\lVert{x_1(t)}\right\rVert^2\bigr)_{t\geqslant 0}$ for Plant $1$ in Example \ref{['ex:numex1']}
  • Figure 2: $\bigl(\left\lVert{x_2(t)}\right\rVert^2\bigr)_{t\geqslant 0}$ for Plant $2$ in Example \ref{['ex:numex1']}
  • Figure 3: One choice of $\bigl(\gamma(t)\bigr)_{t\geqslant 0}$ for Example \ref{['ex:numex2']}
  • Figure 4: One choice of $\bigl(\kappa_m(t)\bigr)_{t\geqslant 0}$, $m=1,2$ for Example \ref{['ex:numex2']}
  • Figure 5: $\bigl(\left\lVert{x_i(t)}\right\rVert^2\bigr)_{t\geqslant 0}$, $i=1,2,3,4,5$ for Example \ref{['ex:numex2']}

Theorems & Definitions (17)

  • Definition 1
  • Remark 1
  • Theorem 1
  • Remark 2
  • Remark 3
  • proof : Proof of Theorem \ref{['t:mainres1']} (Sketch)
  • Remark 4
  • Corollary 1
  • proof
  • Remark 5
  • ...and 7 more