On the controllability and observability of networked dynamic systems

Abstract

a b s t r a c tSome necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant (LTI) dynamics. The topology of this system is fixed but arbitrary, and every subsystem is permitted to have different dynamics. These conditions essentially depend only on transmission zeros of every subsystem and the subsystem connection matrix, which makes them attractive in the analysis and synthesis of a large-scale networked system. As an application, these conditions are utilized to characterize systems whose steady estimation accuracy with the distributed predictor of Zhou (2013) is equal to that of the lumped Kalman filter. It has been made clear that to guarantee this equivalence, the steady update gain matrix of the Kalman filter must be block diagonal.

Control principles of complex systems

“…Early attempts have focused on the issues of controllability or observability with linear dynamics (Chapman et al, 2014;Menichetti et al, 2015;Wang et al, 2015;Yuan et al, 2014;Zhang et al, 2016;Zhou, 2015). For example, some controllability conditions on the overall network topology, the node dynamics, the external control inputs and the inner interactions have been derived for a networked MIMO system .…”

Controllability of Kronecker product networks

“…For most large-scale networked systems, these criteria cannot be applied practically because of their complex structures and heavy computational burdens. Therefore, in recent years, the notion of network controllability has received compelling attention with some efficient criteria established [15,17,18,19,12,1,23,27,25,9,28,30,31,32,33,34]. In [31], an exact controllability framework was introduced to identify the minimum set of input nodes for a general network with an arbitrary link-weight distribution.…”

“…Recently, the controllability of networks with higherdimensional nodes has attracted a great deal of interest [9,25,27,28,30,32,33,34]. Some controllability conditions for networked LTI systems were presented in [34,33], which depend on the transmission zeros of every subsystem and the connection matrix. The controllability of diffusively coupled LTI systems was studied in [32] and [27].…”

Structural Properties of Networked Control Systems With Bandwidth Limitations and Delays

“…An NCS is characterized by a graph representing components' access to each other, characteristics of individual components, and the shared network [1]. NCS covers several situations, including a fixed topology and constrained communications [4][5][6][7][8][9], a networked multi-agent system in which control [10][11][12][13] or other data processing tasks [14] are distributed between several agents and the topology of network may be subject to changes [10][11][12][13][14], and many other situations [2]. This paper studies the situation in which the network topology is fixed and communication constraints exist in the shared network.…”