Controllability of Directed Networked MIMO Systems With Heterogeneous Dynamics

Abstract

This paper studies the controllability of networked multi-input-multi-output (MIMO) systems, in which the network topology is weighted and directed, and the nodes are heterogeneous higher-dimensional linear time-invariant (LTI) dynamical systems. The primary objective is to search for controllability criteria beyond those already known for homogeneous networks. The focus is on the effects of the network topology, node dynamics, external control inputs, as well as the inner interactions on the network controllability. It is found that a network of heterogeneous systems can be controllable even if the corresponding homogeneous network topology is uncontrollable. The finding thus unravels another fundamental property that affects the network controllability-the heterogeneity of the node dynamics. A necessary and sufficient condition is derived for the controllability of heterogeneous networked MIMO LTI systems. For some typical cases, necessary and/or sufficient controllability conditions are specified and presented on the node dynamics, inner interactions, as well as the network topology.

Controllability of LTI Networked Systems with Heterogeneous Dynamics

“…Compared to the result in the work Xiang et. al [33], the condition in this paper does not require solving matrix equations and can be easily verified than the result by Wang et. al [29].…”

“…A necessary and sufficient condition for the controllability of a heterogeneous networked system was derived from Popov -Belevitch-Hautus (PBH) [28] rank condition by Wang et al [31] The connection between the controllability of the networked topology and controllability of the whole networked system is discussed in detail by Xiang et. al [33] and a necessary and sufficient condition for the controllability of a heterogeneous system is obtained in terms of some rank conditions. The notion of structural controllability of large scale networked systems is also studied extensively.…”

Controllability of Networked Sampled-data Systems

“…As a result, verifying a networked multi-rate sampled-data system by Corollary 13 or Corollary 14 greatly reduces the computational complexity than using the PBH criterion directly. However, it has not been proved that the controllability of system (6,7) can ensure that system (21,22) or system (26,27) is controllable, and vice versa. The above analysis also shed light onto increasing the controllability of networked sampleddata systems by adjusting the multiple relationship between the sampling periods on control channels and trasmission channels.…”

“…A controllability decomposition approach for networked systems was proposed in [26] to investigate each node system when the network is not completely controllable. The controllability of heterogeneous networked systems was investigated in [27]. The controllability conditions for networked systems with more complicated structure, such as deep-coupling networks [28] and Kronecker product networks [29] were also derived.…”

Controllability of multilayer networks

“…System controllability always is an essential issue in many engineering fields, while research interests on the controllability of complex network are recently stimulated by the pioneering article [1] published in 2011 which develops analytical tools to study the controllability of complex directed network via the graph theory and the structural controllability theory of systems proposed in the literature [2] and indicates that a network is structurally controllable if and only if there is an external control input on each unmatched node and there are directed paths from controlled nodes to all matched nodes, and the minimum number of driver nodes is determined by the maximum matching set. Over the last decade, some relevant control issues on networks have been extensively studied [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”