Patterned linear systems: Rings, chains, and trees

Abstract

Abstract-In a first paper we studied system theoretic properties of patterned systems and solved classical control synthesis problems with the added requirement to preserve the system pattern. In this second paper we study canonical patterns: rings, chains, and trees, and we give examples drawn from multiagent systems, cellular chemistry, and control of diffusion processes.

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

“…This is not the first attempt to introduce a hierarchy to network structures for multi-agent systems. For example, Smith et al [6] proposed a hierarchical cyclic pursuit scheme and Hamilton and Broucke [7,8] introduced a framework named patterned linear system which is capable of dealing with a class of hierarchy. This paper is related to [6], where agents, which are modeled as the integrator, are divided into some groups and the hierarchy means that cyclic pursuit is achieved both on a micro and a macro levels.…”

Hierarchical Decentralized Controller Synthesis for Heterogeneous Multi-Agent Dynamical Systems by LQR

“…where ξ i = y iẏi T is the vector of the position and velocity of the ith vehicle, u i is the control input. Let us define a new state vector x i = y i − (N − i)γẏ i T , then we obtain the state-space model for the new state variables of the form as (3).…”

Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

“…In another study Smith et al [2005], a hierarchical network is developed for increasing the rate of consensus among vehicles but the structure in each layer is limited to be cyclic. Recently, Hamilton and Broucke [2010] introduced a concept of patterned linear systems for a restrictive class of structures. Since the hierarchical networks in the real world usually have dense interactions inside the subnetworks and sparse communication between them Fortunato [2010], the proposed frameworks in those researches failed to describe this characteristic.…”