Network Control
Network Control
See the talk Advances on the Control of Nonlinear Network Dynamics by Adilson E. Motter at the 2015 SIAM Conference on Applications of Dynamical Systems.
State observation and sensor selection for nonlinear networks
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the tradeoff between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that, owing to the crucial role played by the dynamics, purely graph-theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.
A. Haber, F. Molnar, and A.E. Motter,
State observation and sensor selection for nonlinear networks,
IEEE Trans. Control Netw. Syst. 5(2), 694 (2018).
doi:10.1109/TCNS.2017.2728201
arXiv:1706.05462
Control of stochastic and induced switching in biophysical networks
Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. This framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.
D.K. Wells, W.L. Kath, and A.E. Motter,
Control of stochastic and induced switching in biophysical networks,
Phys. Rev. X 5, 031036 (2015).
doi:10.1103/PhysRevX.5.031036 -
Supplemental Material
arXiv:1509.03349
Optimal Least Action Control (OLAC) Algorithm
Daniel K. Wells, William L. Kath, and Adilson E. Motter
This work offers a ready-to-use code that can be applied to identify interventions to control transitions between attractors of large complex networks, both in the presence and in the absence of noise. The algorithm is highly scalable and applicable to systems with general nonlinear dynamics under rather general constraints on the feasible control interventions. To download the code and its description, please visit here.
Controllability transition and nonlocality in network control
A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely underexplored. Here we show that (i) numerical control fails in practice even for linear systems if the controllability Gramian is ill conditioned, which occurs frequently even when existing controllability criteria are satisfied unambiguously, (ii) the control trajectories are generally nonlocal in the phase space, and their lengths are strongly anti-correlated with the numerical success rate and number of control inputs, and (iii) numerical success rate increases abruptly from zero to nearly one as the number of control inputs is increased, a transformation we term numerical controllability transition. This reveals a trade-off between nonlocality of the control trajectory in the phase space and nonlocality of the control inputs in the network itself. The failure of numerical control cannot be overcome in general by merely increasing numerical precision — successful control requires instead increasing the number of control inputs beyond the numerical controllability transition.
J. Sun and A.E. Motter,
Controllability transition and nonlocality in network control,
Phys. Rev. Lett. 110, 208701 (2013).
doi:10.1103/PhysRevLett.110.208701
arXiv:1305.5848
Realistic control of network dynamics
The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behaviour or fail. Here we show that it is possible to exploit the same principle to control network behaviour. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task, as well as rescuing networks from the brink of failure — which we illustrate through the mitigation of cascading failures in a power-grid network and the identification of potential drug targets in a signalling network of human cancer.
S.P. Cornelius, W.L. Kath, and A.E. Motter,
Realistic control of network dynamics,
Nature Communications 4, 1942 (2013).
doi:10.1038/ncomms2939 -
PDF -
Supplementary Information -
Movie
arXiv:1307.0015v1
NECO - A scalable algorithm for NEtwork COntrol
We present an algorithm for the control of complex networks and other nonlinear, high-dimensional dynamical systems. The computational approach is based on the recently-introduced concept of compensatory perturbations — intentional alterations to the state of a complex system that can drive it to a desired target state even when there are constraints on the perturbations that forbid reaching the target state directly. Included here is ready-to-use software that can be applied to identify eligible control interventions in a general system described by coupled ordinary differential equations, whose specific form can be specified by the user. The algorithm is highly scalable, with the computational cost scaling as the number of dynamical variables to the power 2.5.
S.P. Cornelius and A.E. Motter,
NECO - A scalable algorithm for NEtwork COntrol,
Protocol Exchange (2013), doi:10.1038/protex.2013.063.
doi:10.1038/protex.2013.063 -
Source Codes
arXiv:1307.2582
Other publications
A.E. Motter,
Cascade control and defense in complex networks,
Phys. Rev. Lett. 93, 098701 (2004).
doi:10.1103/PhysRevLett.93.098701
arXiv:cond-mat/0401074
A.E. Motter, N. Gulbahce, E. Almaas, and A.-L. Barabási,
Predicting synthetic rescues in metabolic networks,
Molecular Systems Biology 4, 168 (2008).
doi:10.1038/msb.2008.1 -
Supplementary Information - EMBO and Nature Publishing Group
arXiv:0803.0962
D.-H. Kim and A.E. Motter,
Slave nodes and the controllability of metabolic networks,
New J. Phys. 11, 113047 (2009).
doi:10.1088/1367-2630/11/11/113047 -
Supplementary Information
arXiv:0911.5518
A.E. Motter,
Improved network performance via antagonism: From synthetic rescues to multi-drug combinations,
BioEssays 32, 236 (2010) - Problems and Paradigms.
doi:10.1002/bies.200900128 -
Online Open
arXiv:1003.3391
S. Sahasrabudhe and A.E. Motter,
Rescuing ecosystems from extinction cascades through compensatory perturbations,
Nature Communications 2, 170 (2011).
doi:10.1038/ncomms1163 - PDF - Supplementary Information
arXiv:1103.1653
Y. Yang, J. Wang, and A.E. Motter,
Network observability transitions,
Phys. Rev. Lett. 109, 258701 (2012).
doi:10.1103/PhysRevLett.109.258701 -
Supplementary Information
arXiv:1301.5916
A.E. Motter, S.A. Myers, M. Anghel, and T. Nishikawa,
Spontaneous synchrony in power-grid networks,
Nature Physics 9, 191 (2013).
doi:10.1038/nphys2535 -
Supplementary Information
arXiv:1302.1914
A.E. Motter,
Networkcontrology,
Chaos 25, 097621 (2015).
doi:10.1063/1.4931570
arXiv:1510.08320
