Selection of driver nodes based on region of attraction for single-input complex networks
01 Jan 2016-pp 188-193
TL;DR: This paper presents a theory and algorithms to select an appropriate driver node based on region of attraction (ROA) of single-input complex networks considering limited capacity of driver node considering single- input unstable network with saturated actuator.
Abstract: This paper presents a theory and algorithms to select an appropriate driver node based on region of attraction (ROA) of single-input complex networks considering limited capacity of driver node. A single-input complex network is called controllable network if it can be driven from any initial state to desired state within finite time in n dimensional state space using a driver node. A driver node through which a network can be controlled is not unique. Non-uniqueness of driver node poses a challenge to select a right driver node when multiple possibilities exist. It is important to characterize these driver nodes and select the right driver node. In this paper, we consider a single-input unstable network with saturated actuator.
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01 Jan 2017
TL;DR: This paper develops an algorithm to select the optimal set of driver nodes corresponding to minimum networked sensitivity w.r.t. maximum DC-Gain and a range of frequency.
Abstract: In this paper, we investigate the correlation between optimal set of driver nodes and networked sensitivity of Complex Networked Systems (CNS). Here, we study the networked sensitivity between a pair of control and output nodes for interconnected directed and undirected networks. We investigate the importance of the optimal driver nodes based on new index of the networked control system, which is networked sensitivity in the networked system. In this paper, we discuss to select the optimal set of driver nodes corresponding to minimum networked sensitivity w.r.t. (i) maximum DC-Gain and (ii) a range of frequency. In particular, we develop an algorithm to select the optimal set of driver nodes which has minimum networked sensitivity. Finally, we validate theoretical results with the help of network examples.
Cites methods from "Selection of driver nodes based on ..."
...The techniques involving the selection of right set of driver nodes based on Region Of Attraction (ROA) [16]– [18], minimal actuator placement based on an average control energy bound [19], and optimal actuator placement based on Control Energy Centrality [20] in the complex networked systems....
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TL;DR: In this article, the authors developed analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics.
Abstract: The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.
2,889 citations
Book•
26 Jun 2001
TL;DR: In this article, a control system with actuator saturation analysis and design is presented, in which a control law is designed a priori to meet either the performance or stability requirement.
Abstract: From the Publisher:
"Control Systems with Actuator Saturation Analysis and Design examines the problem of actuator saturation depth. The overall approach takes into account the saturation nonlinearities at the outset of the control design. In the case that a control law is designed a priori to meet either the performance or stability requirement, it analyzes the closed loop system under actuator saturation systematically and redesigns the controller in such a way that the performance is retained while stability is improved. It also presents some related results on systems with state saturation or sensor saturation." "This book is a resource for professionals, researchers, practitioners, graduate students in control, electrical, and mechanical engineering, and all scientists and engineers interested in control systems with actuator saturation. Some first-year graduate courses in linear systems and multivariable control or some background in nonlinear control systems would greatly facilitate the reading of this book."--BOOK JACKET.
1,102 citations
TL;DR: This work shows how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system.
Abstract: In this work, we consider the controlled agreement problem for multi-agent networks, where a collection of agents take on leader roles while the remaining agents execute local, consensus-like protocols. Our aim is to identify reflections of graph-theoretic notions on system-theoretic properties of such systems. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system. Moreover, we introduce network equitable partitions as a means by which such controllability characterizations can be extended to the multileader setting.
784 citations
TL;DR: A metric is proposed to quantify the difficulty of the control problem as a function of the required control energy, bounds are derived based on the system dynamics to characterize the tradeoff between the control energy and the number of control nodes, and an open-loop control strategy with performance guarantees is proposed.
Abstract: This paper studies the problem of controlling complex networks, i.e., the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem, 1) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, 2) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and 3) we propose an open-loop control strategy with performance guarantees. In our strategy, we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show several control limitations and properties. For instance, for Schur stable and symmetric networks: 1) if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes; 2) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension; and 3) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks and epidemics spreading.
544 citations