268 research outputs found
On Submodularity and Controllability in Complex Dynamical Networks
Controllability and observability have long been recognized as fundamental
structural properties of dynamical systems, but have recently seen renewed
interest in the context of large, complex networks of dynamical systems. A
basic problem is sensor and actuator placement: choose a subset from a finite
set of possible placements to optimize some real-valued controllability and
observability metrics of the network. Surprisingly little is known about the
structure of such combinatorial optimization problems. In this paper, we show
that several important classes of metrics based on the controllability and
observability Gramians have a strong structural property that allows for either
efficient global optimization or an approximation guarantee by using a simple
greedy heuristic for their maximization. In particular, the mapping from
possible placements to several scalar functions of the associated Gramian is
either a modular or submodular set function. The results are illustrated on
randomly generated systems and on a problem of power electronic actuator
placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network
Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary
documents) that explains an error in a proof of the original paper and
provides a counterexample to the corresponding resul
Performance guarantees for greedy maximization of non-submodular controllability metrics
A key problem in emerging complex cyber-physical networks is the design of
information and control topologies, including sensor and actuator selection and
communication network design. These problems can be posed as combinatorial set
function optimization problems to maximize a dynamic performance metric for the
network. Some systems and control metrics feature a property called
submodularity, which allows simple greedy algorithms to obtain provably
near-optimal topology designs. However, many important metrics lack
submodularity and therefore lack provable guarantees for using a greedy
optimization approach. Here we show that performance guarantees can be obtained
for greedy maximization of certain non-submodular functions of the
controllability and observability Gramians. Our results are based on two key
quantities: the submodularity ratio, which quantifies how far a set function is
from being submodular, and the curvature, which quantifies how far a set
function is from being supermodular
Resilient Submodular Maximization For Control And Sensing
Fundamental applications in control, sensing, and robotics, motivate the design of systems by selecting system elements, such as actuators or sensors, subject to constraints that require the elements not only to be a few in number, but also, to satisfy heterogeneity or interdependency constraints (called matroid constraints). For example, consider the scenarios:
- (Control) Actuator placement: In a power grid, how should we place a few generators both to guarantee its stabilization with minimal control effort, and to satisfy interdependency constraints where the power grid must be controllable from the generators?
- (Sensing) Sensor placement: In medical brain-wearable devices, how should we place a few sensors to ensure smoothing estimation capabilities?
- (Robotics) Sensor scheduling: At a team of mobile robots, which few on-board sensors should we activate at each robot ---subject to heterogeneity constraints on the number of sensors that each robot can activate at each time--- so both to maximize the robots\u27 battery life, and to ensure the robots\u27 capability to complete a formation control task?
In the first part of this thesis we motivate the above design problems, and propose the first algorithms to address them. In particular, although traditional approaches to matroid-constrained maximization have met great success in machine learning and facility location, they are unable to meet the aforementioned problem of actuator placement. In addition, although traditional approaches to sensor selection enable Kalman filtering capabilities, they do not enable smoothing or formation control capabilities, as required in the above problems of sensor placement and scheduling. Therefore, in the first part of the thesis we provide the first algorithms, and prove they achieve the following characteristics: provable approximation performance: the algorithms guarantee a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections. We achieve the above ends by taking advantage of a submodular structure of in all aforementioned problems ---submodularity is a diminishing property for set functions, parallel to convexity for continuous functions.
But in failure-prone and adversarial environments, sensors and actuators can fail; sensors and actuators can get attacked. Thence, the traditional design paradigms over matroid-constraints become insufficient, and in contrast, resilient designs against attacks or failures become important. However, no approximation algorithms are known for their solution; relevantly, the problem of resilient maximization over matroid constraints is NP-hard.
In the second part of this thesis we motivate the general problem of resilient maximization over matroid constraints, and propose the first algorithms to address it, to protect that way any design over matroid constraints, not only within the boundaries of control, sensing, and robotics, but also within machine learning, facility location, and matroid-constrained optimization in general.
In particular, in the second part of this thesis we provide the first algorithms, and prove they achieve the following characteristics: resiliency: the algorithms are valid for any number of attacks or failures; adaptiveness: where applicable, at each time step the algorithms select system elements based on both the history of selections, and on the history of attacks or failures; provable approximation guarantees: the algorithms guarantee for any submodular or merely monotone function a solution close to the optimal; minimal running time: the algorithms terminate with the same running time as state-of-the-art algorithms for matroid-constrained maximization. We bound the performance of our algorithms by using notions of curvature for monotone (not necessarily submodular) set functions, which are established in the literature of submodular maximization.
In the third and final part of this thesis we apply our tools for resilient maximization in robotics, and in particular, to the problem of active information gathering with mobile robots. This problem calls for the motion-design of a team of mobile robots so to enable the effective information gathering about a process of interest, to support, e.g., critical missions such as hazardous environmental monitoring, and search and rescue. Therefore, in the third part of this thesis we aim to protect such multi-robot information gathering tasks against attacks or failures that can result to the withdrawal of robots from the task. We conduct both numerical and hardware experiments in multi-robot multi-target tracking scenarios, and exemplify the benefits, as well as, the performance of our approach
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound
Sensor and actuator selection problems (SASP) are some of the core problems
in dynamic systems design and control. These problems correspond to determining
the optimal selection of sensors (measurements) or actuators (control nodes)
such that certain estimation/control objectives can be achieved. While the
literature on SASP is indeed inveterate, the vast majority of the work focuses
on linear(ized) representation of the network dynamics, resulting in the
placements of sensors or actuators (SA) that are valid for confined operating
regions. As an alternative, herein we propose a new general framework for
addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs
and outputs are linearly coupled with the nonlinear dynamics. This is
investigated through (i) classifying and parameterizing the NDS into various
nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations,
and (iii) designing a new customized branch-and-bound (BnB) algorithm that
exploits problem structure of the SASP. The newly designed BnB routines are
computationally more attractive than the standard one and also directly
applicable to solve SASP for linear systems. In contrast with contemporary
approaches from the literature, our approach is suitable for finding the
optimal SA combination for stable/unstable NDS that ensures stabilization of
estimation error and closed-loop dynamics through a simple linear feedback
control policy
Constrained expectation-maximization (EM), dynamic analysis, linear quadratic tracking, and nonlinear constrained expectation-maximation (EM) for the analysis of genetic regulatory networks and signal transduction networks
Despite the immense progress made by molecular biology in cataloging andcharacterizing molecular elements of life and the success in genome sequencing, therehave not been comparable advances in the functional study of complex phenotypes.This is because isolated study of one molecule, or one gene, at a time is not enough byitself to characterize the complex interactions in organism and to explain the functionsthat arise out of these interactions. Mathematical modeling of biological systems isone way to meet the challenge.My research formulates the modeling of gene regulation as a control problem andapplies systems and control theory to the identification, analysis, and optimal controlof genetic regulatory networks. The major contribution of my work includes biologicallyconstrained estimation, dynamical analysis, and optimal control of genetic networks.In addition, parameter estimation of nonlinear models of biological networksis also studied, as a parameter estimation problem of a general nonlinear dynamicalsystem. Results demonstrate the superior predictive power of biologically constrainedstate-space models, and that genetic networks can have differential dynamic propertieswhen subjected to different environmental perturbations. Application of optimalcontrol demonstrates feasibility of regulating gene expression levels. In the difficultproblem of parameter estimation, generalized EM algorithm is deployed, and a set of explicit formula based on extended Kalman filter is derived. Application of themethod to synthetic and real world data shows promising results
Robotic Wireless Sensor Networks
In this chapter, we present a literature survey of an emerging, cutting-edge,
and multi-disciplinary field of research at the intersection of Robotics and
Wireless Sensor Networks (WSN) which we refer to as Robotic Wireless Sensor
Networks (RWSN). We define a RWSN as an autonomous networked multi-robot system
that aims to achieve certain sensing goals while meeting and maintaining
certain communication performance requirements, through cooperative control,
learning and adaptation. While both of the component areas, i.e., Robotics and
WSN, are very well-known and well-explored, there exist a whole set of new
opportunities and research directions at the intersection of these two fields
which are relatively or even completely unexplored. One such example would be
the use of a set of robotic routers to set up a temporary communication path
between a sender and a receiver that uses the controlled mobility to the
advantage of packet routing. We find that there exist only a limited number of
articles to be directly categorized as RWSN related works whereas there exist a
range of articles in the robotics and the WSN literature that are also relevant
to this new field of research. To connect the dots, we first identify the core
problems and research trends related to RWSN such as connectivity,
localization, routing, and robust flow of information. Next, we classify the
existing research on RWSN as well as the relevant state-of-the-arts from
robotics and WSN community according to the problems and trends identified in
the first step. Lastly, we analyze what is missing in the existing literature,
and identify topics that require more research attention in the future
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