Stability analysis of large-scale distributed networked control systems with random communication delays: A switched system approach

Abstract

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump linear system framework. There have been considerable researches on stability analysis of Markov jump systems, however, these methods are not applicable to large-scale systems because large numbers of subsystems result in an extremely large number of the switching modes. To avoid this scalability issue, we propose a new reduced mode model for stability analysis, which is computationally efficient. We also consider the case in which the transition probabilities for the Markov jump process contain uncertainties. We provide a new method that estimates bounds for uncertain Markov transition probability matrix to guarantee the system stability. The efficiency and the usefulness of the proposed methods are verified through examples.

A switched dynamical system framework for analysis of massively parallel asynchronous numerical algorithms

“…, π m }. If the initial state e(0) is given and has no uncertainty, the expected value of e(k) is updated bȳ e(k) E[e(k)] = Λ k e(0) orē(k + 1) = Λē(k), (14) where…”

“…Thus, a rigorous analysis of the tradeoff between speed and accuracy is critical. This paper present a framework for quantifying this tradeoff by analyzing the asynchronous numerical algorithm as a switched dynamical system [5]- [14]. While there is a large literature for analysis of such systems, these techniques are not applicable to our application.…”

A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programming via Dual Decomposition

“…Above assumption is not restrictive because the master node will receive more concurrent data for x k i from its slave nodes while waiting for the condition (15) to be satisfied. Thus (15) will be eventually satisfied as the iteration count increases.…”

“…To circumvent this concern, we synthesize the following control algorithm. In Algorithm 1, ζ is k ← k + 1 11: while y k+1 − y k p ≥ ε or ζ = 0 defined as a masking index to prevent immediate termination of the code when (15) is not satisfied. In this way, the code keeps running until both conditions y k+1 − y k p < ε for some positive constant ε and ζ = 0 are met.…”

Minimal Sufficient Conditions for Structural Observability/Controllability of Composite Networks via Kronecker Product

“…We are particularly interested in the observability and controllability of Kronecker composite networks, whereas in contrast most of the related literature studies composite networks via Cartesian products [10]- [14]. The Kronecker composite networks find direct applications in networked control system [17]- [19], distributed Fault Detection and Isolation (FDI) [20], distributed detection [21], and distributed estimation over sensor networks [22]- [28]. For example, in distributed estimation, the overall distributed system can be considered as Kronecker product of the system digraph and the sensor/estimator network.…”